Electrostatic or Electrodynamic Gravity

john.erich.ebner@gmail.com
http://blackholeformulas.com/
23 March 2012
Abstract and purpose
We demonstrate that electrostatic force can model gravitational force, centrifugal force and inertia in calculations. Electrostatic force may keep the Earth in orbit if the electrostatic force equals the gravitational force and if the charge of the Earth and Sun are of opposite polarity. We show that the source of gravity is atomic and dynamic which also explains the van der Waal's forces. Sometimes when you model nature, the model speaks with clarity to the questions that you ask of nature.
Key Words
gravity, gravitational force, electro static, electro dynamic, van der Waal's force, elliptical orbits of atoms, polarized atoms, gravitational refraction of light

We simplify and imagine nature to be composed of machines which we can understand. The Cosmos is a machine. We use these machines by analogy to explain the behavior of nature. Bohr's planetary atom and the ring electron are examples of tiny machines which illuminate matter. We extended the realm of the machines to the electromagnetic wave. Here we will look first at how gravity works and then how electrostatic gravity might replace its common functions. We followed a similar procedure in Pushing gravity. Pushing gravity has a rich and interesting history but is an unlikely mechanism to explain gravity because of pushing gravities huge continuous energy demand. Electrostatic gravity also has a long history. See the paper by Assis which describes his work and Faraday's experiments along these lines. Electrostatic gravity provides a clear plausible mechanism for how gravity works, with forces in equilibrium and no continuous energy demand. Electrodynamic gravity also explains much about why it works. Heisenberg said the position and orbits of the electron in the hydrogen atom can not be observed and therefore they should be set aside as fruitless ideas. He focused only on observable quantities of spectral frequency and intensity. We will see that these unobservable qualities of the hydrogen atom are exactly what are needed to explain gravity. The next section might be clearer after reading, Gravity, rosettes and inertia
Fc = ce2/(4*pi*e0*r2), This is the electrostatic force between two charges with a charge ce at a separation of r meters. ce is the charge of the electron or proton. e0 is the permittivity of vacuum.
Fg = G*me*mp/r2, This is the gravitational force between an electron and a proton at a separation of r meters. G is the gravitational constant. me and mp are the mass of the electron and proton.
Fc/Fg = ce2/(4*pi*e0*G*me*mp) = 2.269E39, This is the huge ratio of electrostatic to gravitational forces. Small charges produce big forces. Any theory of gravity must explain the smallness of gravity.
Balancing electrostatic and gravitational forces
ce2/(4*pi*e0*r2) = G*kg2/r2, the electrostatic force between two opposite charges equals the gravitational force between two masses.
(a*s)2/(4*pi*e0) = G*kg2, The forces are equal at any distance. They are both inverse square forces. The r2 cancel. Replace ce with the more general a*s, amps*seconds for the charge, so the equation can work with any charge and mass.
(4*pi*e0*G).5 = a*s/kg = 8.617E-11_a*s/kg, this is the gravitational charge per kilogram, coulombs/kg. There are 6.41E18_a*s/(a*s), charges per amp per second.
a*s = kg*(4*pi*e0*G).5, the gravitational charge equals the mass*(4*pi*e0*G).5

The force of gravity can not be like the simple charge on a capacitor. I have a weight of 200 pounds, 90.2 Newtons, a mass of 9.25 kilograms.
mass *(4*pi*e0*G).5 = 9.25_kg*8.617E-11_a*s/kg = 7.97E-10_a*s, my gravitational charge. This is around 800 pico_a*s. This is for a static charge. We can quickly rule out static charge as follows,
7.97E-10_Farad *1_volt = 7.97E-10_a*s, Our answer can not be static charge as someone would have noticed if this tiny 800 pico farad capacitor charged to 1_volt would have the weight of 200 pounds or changing or charging a variable capacitor hooked to a battery would vary the weight.

The dynamic charge we seek is somewhere in the constantly moving oscillating charges and reversing dipole forces of the electron and proton dipole pair in the atom. We will see the charge and the mass of the electron and proton become more separated as the atoms become more ellipsoid. As the electron and proton follow their elliptical paths, their orbital and radial velocity and location of their charges varies. The direction of their plus to minus dipole charges their polarization and forces reverses as in figure 1. It is this directional non-equal reversing dipole force which attracts us. The cause of gravity on the micro scale is atomic and dynamic. It is only at macro scales that gravity appears static. Thus, the two names in the title of the paper.

msun = 1.9884E30_kg, mass of the Sun.
mearth = 5.9722E24_kg, mass of the Earth.
a*s = kg*(4*pi*e0*G).5, the gravitational charge equals the mass*(4*pi*e0*G).5
gcsun = msun*(4*pi*e0*G).5 = 1.713E20_a*s, the gravitational charge of the Sun.
gcearth = mearth*(4*pi*e0*G).5 = 5.146E14_a*s, the gravitational charge of the Earth.
Sun and Earth gravitation
msun*mearth*G/au2, the gravitational force between the Sun and Earth. An au astronomical unit is the average distance from the Earth to the Sun.
msun*mearth*(4*pi*e0*G) /(4*pi*e0*au2), multiplied by 4*pi*e0/(4*pi*e0)
msun*(4*pi*e0*G).5 *mearth*(4*pi*e0*G).5 /(4*pi*e0*au2), factored (4*pi*e0*G) into two square roots.
gcsun*gcearth/(4*pi*e0*au2), electrostatic force using gravitational charge.
1.713E20_a*s *5.146E14_a*s/(4*pi*e0*(149.598E9_m)2) = 3.5401E22_kg*m/s2
1.98843E30_kg *5.9722E24_kg *G/(149.598E9_m)2 = 3.5414E22 _kg*m/s2,
The Coulomb forces calculated using gravitational charge and Newtonian gravity calculated with masses are the same. Gravitational charge and mass are equivalent. The force is the same only the units used to calculate the force change.

Sun and Earth centrifugal force
mearth*vearth2/dbcearth = msun*vsun2/dbcsun = 3.55E22_kg*m/s2, there are two equal centrifugal forces unchanged by using gravitational charge instead of mass. dbc is the distance to the barycenter, the center of mass of the Earth-sun system
mearth*vearth2/dbcearth =
mearth *(4*pi*e0*G).5 *vearth2/(dbcearth*(4*pi*e0*G).5),
multiplied by (4*pi*e0*G).5/(4*pi*e0*G).5
gcearth *vearth2/(dbcearth*(4*pi*e0*G).5), substituted for gcearth = mearth*(4*pi*e0*G).5

msun *vsun2/dbcsun =
msun *(4*pi*e0*G).5 *vsun2/(dbcsun*(4*pi*e0*G).5),
multiplied by (4*pi*e0*G).5/(4*pi*e0*G).5
gcsun *vsun2/(dbcsun*(4*pi*e0*G).5), substituted for gcsun = msun*(4*pi*e0*G).5

Gravitational acceleration
mearth*G/rearth2 = 9.79822007_m/s2, gravitational acceleration at the surface of the Earth.
rearth = 6378000_m.
mearth*(4*pi*e0*G) /(4*pi*e0*rearth2), multiplied by 4*pi*e0/(4*pi*e0)
mearth*(4*pi*e0*G).5*(4*pi*e0*G).5 /(4*pi*e0*rearth2), factored (4*pi*e0*G) into two square roots.
gcearth*(4*pi*e0*G).5/(4*pi*e0*rearth2) = 9.79822007_m/s2, substituted for gcearth = mearth*(4*pi*e0*G).5.
gcearth/(rearth2)*(G/(4*pi*e0)).5, collected terms.
gcearth/(rearth2)*.77448_m3/(a*s3) = 9.7979_m/s2, since (G/(4*pi*e0)).5 = .77448_m3/(a*s3),
The electrostatic acceleration of the Earth at the surface of the Earth, using gravitational charge is the same as the gravitational acceleration using mass. Calculations using charge or mass produce the same gravitational accelerations.
Sun and Earth gravitational energy
msun*mearth*G /au, gravitational energy using mass.
msun*mearth*(4*pi*e0*G) /(4*pi*e0*au), multiplied by 4*pi*e0/(4*pi*e0)
msun*(4*pi*e0*G).5 *mearth*(4*pi*e0*G).5 /(4*pi*e0*au), factored (4*pi*e0*G) into two square roots.
gcsun*gcearth/(4*pi*e0*au), gravitational energy using gravitational charge.
G*1.98843E30_kg*5.9722E24_kg/149.598E9_m = 5.2978E33_kg*m2/s2, gravitational energy using mass.
1.713E20_a*s *5.146E14_a*s /(4*pi*e0*149.598E9_m) = 5.2975E33_kg*m2/s2, gravitational energy using gravitational charge.
gcearth/charge per electron = charges
5.146E14_a*s/(1.602E-19_a*s/charge) = 3.212E33_charges, the number of electron charges required for the Earth. Since the Sun shines on half the Earth, area = 4*pi*r2/2, there are 1.256E19_charges/m2 required on the Sun lit side of the Earth. This is 2.013_amp/m2 but the solar output is 1366_volts*amps/m2 = watts. This is more than enough charge for electrostatic gravity. We must remember however, the gravitational charge is spread throughout the volume of the Earth not just on half its surface area.
charges * mass/charge = mass of electrons
3.212E33_charges * 9.109E-31_kg/charge = 2926_kg of electrons
There are 6.241E18_a*s/(a*s), charges per amp per second. The surprisingly small charge of 2926_kg of electrons when balanced by the same amount of opposite proton charge in the Sun will provide the tensile force to keep the Earth in orbit without any ongoing power requirements. Small charges produce big forces. Compare this charge disparity of 2926_kg of electrons that is required for electrostatic gravity with the solar output of millions of kilograms of protons and electrons in the solar wind.

The solar output on the surface of the Earth, the Earth's insolation is 1366 watts per square meter in space or a total of 1.75E17 watts. The dark night side of the Earth has no such power inputs. There would be no solar inputs to a region during an eclipse. This suggest powerful currents and polarizations. One might extract a current from a plate heated on one side or a solar cell or a plant in the Sun. Does a tiny current flow from a plant in the Sun to the ground. Does a plant need a ground? Not the ground. Does photosynthesis leave a residual charge on an algae or on the Sun lit side of the Earth? Life does have electricity. Electricity flows in circuits. Does it seem amazing or absurd that the electricity of life might affect gravity? Breathing works because oxygen is a good electron receptor. Before oxygen became common on the Earth, life used several mineral electron receptors, like iron and sulfur compounds, to fuel its reactions. These life forms are still common in low oxygen environments. Chemical reactions and bonding are based on charge and its flow which is electricity. All of these might leave different charges on the day and night side of the Earth. This very slight differential charge throughout a planet is what is required for electrostatic gravity.
The solar output or solar wind could provide the slight charge imbalance necessary for gravity, but we will look at it from another perspective. All the electrons in the Sun and Earth repel each other. All the protons in the Sun and Earth repel each other. All the electrons in the Sun and Earth attract all the protons in the Sun and Earth. All the atoms in the Sun and Earth are polarized in this way which causes a charge imbalance force. Charge imbalance is everywhere; in bonding of atoms, in chemistry and in dielectric and deformable dielectric materials. We will look for the charge imbalance in the atoms themselves. This is a search for the mechanics and mechanism of the polarized atom. We seek the geometry of Bohr's planetary atom that allows it to store charge and act like a capacitor when pulled and pushed by the charges in other masses or when accelerated.  Binary systems can generalize Bohr's planetary atom with an unmoving center proton to a system where both the electron and proton move producings red-electron and blue-proton currents and green magnetic fields which are
forces due to moving charge. The centrifugal force equals the Coulomb force in these binary atoms and is what holds them in orbit. The magnetic fields in series due to the force = q*v*b shown above do attract their neighbor atoms when they have the same sense of rotation but these forces are 59000 times smaller than the Coulomb forces. The gravitational force is 3.84E34 times smaller than the magnetic force. We see two atoms when their protons and electrons line-up in their in-phase orbits which they do only twice in each orbit. The binary systems contains the proper amount of energy to agree with the Balmer series hydrogen spectral lines while also agreeing with the energy of ionization. When the hydrogen atom is ionized the electron-proton pair separate and absorb energy. When the electron-proton pair merge to become a hydrogen atom they give off energy.

A binary system with orbiting charged particles has wavelike orbits. • The red dots are electrons and the blue dots are protons orbiting on their circular paths.
• The red and blue sine waves are an edge view of the orbital plane and currents traced out by the electron and proton pair as they move across the page on a helical path like a spring on a string.
• Both orbit each other on opposite sides of the center of mass of the system.
• There are both wave and particle descriptions of atoms. We will be looking at both.
• The orbital period of the proton and electron pair is the same. They are a dipole.
• Looking at a point, in the orbital plane as they orbit, would show alternating charges and dipole forces at the frequency that the electron and proton orbit and pass in front of each other. Blue-red-blue-red or plus-minus-plus-minus at 6.6E15_hertz as the dipoles reverse direction at a wavelength of 45.5E-9_m in the extreme ultraviolet.
• ve/(2*pi*re) = frequency = 6.58327E15_1/s
• , ve is the velocity of the electron and re is the radius of the electron orbit.
• c/frequency = wavelength = 45.54E-9_m. This is in the extreme ultraviolet, EUV. Here is a reference to the Solar Dynamics Observatory, (SDO) "EUV wavelengths range between 50 and 5 nanometers, which coincide with the characteristic absorption wavelengths of inner-shell electrons in the atoms that compose matter. As a result, EUV light directed onto a standard mirror or lens at normal incidence is absorbed rather than reflected, making it undetectable. For this reason, EUV light is also absorbed by Earth's atmosphere, which is why telescopes must travel to space to study the light emitted from the Sun."

• A distant static charge would only see the oscillating high frequency plus-minus-plus-minus merged to neutrality which excludes gravity from being caused by the interaction of dipoles and static charges.
• A distant in-phase rotating dipole would however experience Coulomb, magnetic and gravitational forces.
The stationary unmoving center proton and orbiting electron view of the planetary atom conceals their binary wavelike behavior which the red and blue sine waves emphasize.
Click figure to animate! Electron and proton binary atom with circular orbits • The dipole of the electron and proton pair in their orbits make rings of charge or currents.
• These orbiting charges are electron and proton torroidal currents which orbit the long way around the torus or ring.
• We have helical poloidal magnetic fields which orbit around the toroidal currents, looping the short way around the torus through the hole like the wires on torroidal transformers.
• The magnetic field points out of the page along the axis of rotation.
• mass proton/mass electron = velocity electron/velocity proton = orbital radius electron/orbital radius proton = 1836 if to scale.
• There is a uniform charge density. The velocity of the electron and proton charge along their orbital path around the center of mass is uniform.
• The charge per radian of the electron and proton on their binary orbital path are constant and equal since they have the same angular velocity.
• The radial distance between the charges is constant.
• This is a charge neutral binary atom confined to orbit in a plane. It is not the sphere of the atom which we see in scanning tunneling microscope pictures.
Tokamaks and spheromaks and ring electrons have torroidal currents and helical poloidal magnetic fields.
Rotating dipoles - Click figure to animate! The red rings are the spherical shells of atoms. Atoms in scanning tunneling microscopes look like neatly stacked spheres. This shows a group of atoms at equilibrium. They are held together by electrostatic bipolar van der Waal's forces which are weak in gases, stronger in liquids and stronger still in solids. The dipoles consist of blue dots which are protons and the red dots which are electrons. The dipoles rotate and are in phase like the hands of two clocks. Huygens reported in 1657 that the forces between pendulum clocks on a shelf caused their synchronization. Likewise, we expect the powerful forces between series dipoles to be synchronized like a series of compasses. The net force on a distant static charge would average to zero as the dipoles orbit. The net force on a distant rotating in-phase dipole would be electrical and gravitational. With unaccelerated motion of atoms there is a balance between the charges or charge neutrality which is absent when they follow a curved path or are accelerated. We seek a charge imbalance along the radial line which connects the Sun and Earth. The electron and proton both have the same orbital period. They are a dipole. The red and blue waves are an edge view of the elliptical orbital plane and currents traced out by the electron and proton dipole as they move across the page on a helical-elliptical path. With a circular orbit, the orbital velocity and momentum are constant and there is no radial velocity or momentum. Charge and gravity have radial interactions and forces so radial velocity and momentum may be important. With elliptical orbits we see a variable orbital and radial velocity, a variable orbital and radial momentum and the electron and proton spend more of their time far out on the apogee side of their orbits. I recommend the orbit simulator websites of Dunn, Burtle and Koppen.
Atoms are polarized on a curved path • The red and blue sine waves are an edge view of the orbital plane traced out by the electron and proton pair as they move around the red circles on a helical path like a spring on a string.
• The axis of rotation is along the ring path.
• The electrons in the atoms travel farther on the outside of the ring path than on the inside of the ring path where they are pinched together. They are like a bent helical spring which is pinched together on the inside of the red circles.
• They each trace the surface of a torus which is somewhat stretched in the radial direction because of its elliptical cross section.
• The helical path of the electron and proton is a toroidal current path with a superimposed helical poloidal magnetic field path. We have a helix on a helix.
• A cross section along the red circle ring path would show ellipses.
• There is a charge density imbalance between the inside and outside of the rings. The atoms are polarized by forces. • The dipole of the electron and proton pair in their orbits make elliptical rings of charge.
• mass proton/mass electron = velocity electron/velocity proton = orbital radius electron/orbital radius proton = 1836 if to scale.
• The barycenter, the center of mass, is at one focus of the two ellipses.
• Using Kepler's law, the charge points or dots are separated by equal periods of time and each sweep out equal area triangles in equal periods of time along their elliptical orbits.
• A text file which can be opened with Basic calculates the elliptical radii and angles.
• The velocity of elliptical orbits slow down as they move toward apogee.
• Since they spend more time near apogee at a slower speed the charge and mass density is non-uniform and is greater farther out. The charges and masses are separated.
• This ellipse is very polarized. The centers of the electron and proton rings are not concentric. They are separated.
• The electron is on the left most of the time so the left side is negative.
• The proton is on the right side most of the time so the right side is positive.
• The moment of inertia of the dipole and the angular acceleration vary, the product of which is a torque, the orbital energy.
• The long axis of the ellipse is the dipole moment of the ellipse.
• Its charged poles would attract the opposite charged poles of similarly polarized ellipses.
This is the origin of van der Waal's forces. Can you see how there is a concentration of charge and mass along the long axis of the ellipsoid? Can you see how a chain of these ellipsoids, with oppositely charged ends, would stick together like magnetic beads? Can you see how there is a concentration of charge and mass along the line of a long chain of these ellipsoids?
• force = -acceleration*mass, as the charges move away from the center of mass of their ellipse their tangent and radial velocity decrease so the acceleration is negative.
• force = +acceleration*mass, as the charge approaches the center of mass of their ellipse their tangent and radial velocity increase so the acceleration is positive.
• The forces on both sides of the axis of symmetry of the ellipses are equal and opposite so they cancel. The only points where the orbital forces do not cancel is at the points of inflection.
• The rate of change in orbital and radial velocity are zero at apogee and at perigee.
• The acceleration of the charges go through zero and change sign so there is a point of inflection.
• d/dt (length) = velocity = m/s
• d/dt (velocity) = acceleration = m/s2
• d/dt (acceleration) = jerk = m/s3
• The charges jerk at the points of inflection.
We have a pulse of force each time that the acceleration of charge is zero, at both ends of its orbit, at apogee and at perigee. These pulses of force are oppositely directed but they are not equal. There is a net pulse of force when the ellipses are in a line at the point of inflection.
Electron and proton binary atoms or dipoles force lines - Click figure to animate! • Two in-phase electron and proton dipole pairs in a series experience forces.
• The red electron and blue proton dots are the instantaneous location of the charges as the charge pairs orbit.
• The dots along their paths on each ellipse are separated here by 41 equal intervals of time. 36 intervals are on the apogee side of the center of mass and 5 intervals are on the perigee side of the center of mass.
• The charges spend more time on the apogee half of the ellipse so the apogee dots are closer together than the perigee side of the center of mass in both the electron and proton ellipses.
• The left end of this atom pair is negatively charged and the right end is positively charged.
• These atoms could not stick together without atomic eccentricity and the charge polarity it creates.
• This is the origin of the van der Waal's force.
• The green lines connect the forces between the right proton and the left electron.
• The pink lines connect the forces between the left proton and the right electron.
• The pair of repulsive electrons like the pair of repulsive protons stay the same distance apart, both dipoles are in phase, as they follow parallel elliptical paths so the repulsive forces are constant. The attractive forces are variable.
• The left proton is more strongly attracted to the right electron along the red lines than the right proton is attracted to the left electron along the green lines.
• The green lines are longer so the charges are further apart and the forces are weaker than the pink lines where the charges are closer together and the forces are stronger.
• The vertical and oscillating components of the forces cancel so we are left with only horizontal forces along the center line.
Series dipoles - The left end of this series is negatively charged and the right end is positively charged The ends of the ellipses are highly oppositely charged. They stick together like magnetic beads and precess along the long axis of the ellipsoids like beads rotating on a string. The internal electron-proton forces hold the atom together. The external electron-proton forces hold the string of atoms together.
Ellipse definitions • The electron and proton in an atom are most separated when they are at apogee, in the middle drawing and are least separated when they are at perigee, in the drawing on the right.
• The radial movements of the charges also generate currents and magnetic fields.
When the dipoles line up in a series at apogee or perigee they generates a pulse of force. The sum of these forces are stronger when the dipoles are at apogee because the period of alignment of the electrons and protons are longer. The red electrons and blue protons are moving slower when they are at apogee. When the electrons are at apogee the protons are also at apogee on their own much smaller elliptical orbit.
Position at apogee - Click figure to animate! • The dipoles are in phase like the always moving hands of two clocks.
• In the figure, these dipoles would be attracted to a positive charge to the left and a negative charge to the right.
• This generates a very short pulse of force when the dipoles line up in series. The momentum imparted is proportional to the length the pulses.
• These forces at apogee are greater than the force at perigee.
• The charges are moving slower at apogee than at perigeee. The dipoles line up for a longer period of time at apogee. The duration of the pulse of force is longer at apogee.
• The electron in one atom is closer to the proton in the next atom when they are at apogee so the forces between neighbor atoms are stronger at apogee.
• These pulsed Coulomb force equations are of the form, ce2/(4*pi*e0*r2), where r is the distance between the electron and proton.
• eq1 = ce2/(4*pi*e0) /(cc-((a+p)*(1+e)))2, pulsed attractive force, plus to minus, left to right.
• eq2 = ce2/(4*pi*e0) /(cc+((a+p)*(1+e)))2, pulsed attractive force, minus to plus, left to right.
Position at perigee - Click figure to animate! • The dipoles are in phase like the always moving hands of two clocks.
• In the figure, these dipoles would be attracted to a positive charge to the right and a negative charge to the left.
• This generates a pulse of force when the dipoles line up in series.
• These forces at perigee are less than the forces at apogee.
• The charges are farther apart and are moving much faster when they are at perigee. Because the dipoles line up for a shorter peroid of time at perigee than at apogee, the duration of the pulse of force is less at perigee than it is at apogee. These simplified equations look only at the distances between the charges not at the duration of alignment or the duration of the pulses of force.
• eq3 = ce2/(4*pi*e0) /(cc-((a+p)*(1-e)))2, pulsed attractive force, minus to plus, left to right.
• eq4 = ce2/(4*pi*e0) /(cc+((a+p)*(1-e)))2, pulsed attractive force, plus to minus, left to right.
• eqR = ce2/(4*pi*e0) /(cc)2, electron-electron and proton-proton repulsive force. These repulsive forces are not pulsed. They are continous.
These forces are weak because the dipoles primarily interact only when they are in a line. They are only in a line for a moment twice in each revolution of the binary pair when they produce momentary pulses of force along the line of interaction. The distance apart for the electron and proton on their elliptical orbits vary. The force between series dipoles is strongest when the chain of dipoles is longest and when the dipoles are most elliptical.
Short interaction times of forces causes the weakness of gravity
eq1 through eq4 use pulses of force when the dipoles line up in series. Since the dipoles are rotating at 6E15_hertz and the related atoms electrons and protons are moving in opposite directions. They pass each other at 6E15_hertz squared. If we say the dipoles align for 1/20 of a degree in each revolution or 1/7200 of a revolution. Then we have
1/(7200)2 * 1/(6.576E15)2 = 1/(2.242E39),
This is the ratio of gravitational to Coulomb forces. Gravity is so much weaker than electrostatic force because of the short duration of the in-line interaction of the pulses of force between the in-phase series dipoles.

Source of the dipoles
This is a quote from a chapter on dipoles by Tatum; "But what if the molecules do not have a permanent dipole moment, or what if they do, but they cannot easily rotate (as may well be the case in a solid material)? The bulk material can still become polarized, because a dipole moment is induced in the individual molecules, the electrons inside the molecule tending to be pushed towards one end of the molecule. Thus, one way or another, the imposition of an electric field may induce a dipole moment in most material, whether they are conductors of electricity or not, or whether or not their molecules have permanent dipole moments. If two molecules approach each other in a gas, the electrons in one molecule repel the electrons in the other, so that each molecule induces a dipole moment in the other. The two molecules then attract each other, because each dipolar molecule finds itself in the inhomogeneous electric field of the other. This is the origin of the van der Waal's forces."

has attributed the van der Waal's forces and the Casimir forces to the Heisenberg uncertainty principle; the more certain we are of where something is, the less certain we are about where it is heading. Quantum field theory holds that empty space, the vacuum, is fizzing with short-lived particle-anti-particle pairs according to the uncertainty principle. The shorter the time the pair exists, the greater energy the pair may impart to the vacuum so very short lived pairs have near infinite energy. This means that one calculates the energy density of the vacuum as near infinite, which many do, which is silly, of course. The actual energy density in a vacuum is near zero. Particle-anti-particle pairs annihilate each other transforming their mass into energy. Electron-positron pairs annihilate each other producing gamma rays. Particle-anti-particle pairs are only created out of energy, not vacuum, if there is enough energy for mass pair creation, as there is in a particle accelerator. Energy is conserved. Nothing is created out of nothing.
The polarization and separation of charge considered as the origin of van der Waal's forces is also here considered as the origin of gravitational, centrifugal and inertial forces. The blue lines show a few of the many ways the in phase atomic dipoles may line up producing van der Waal's force. It is clear why so many materials shear off in a plane and why crystals cleave in certain planes. The atoms in this figure prefer to make hexagons.
This shows the profoundly exaggerated effect of
• the push and pull of the electrons and protons in a mass,
• or an acceleration,
• or an electric field,
• or a current,
• or a centrifugal force to the left,
• or a pressure from above and below like a gravitational force.
Group properties of ellipsoidal atoms
• The atoms are far from equilibrium.
• The atoms are polarized, bipolar and ellipsoid.
• All the dipoles are in phase like the the hands of two clocks.
• The proton and electron orbit around one focus of the ellipse, shown as a blue dot.
• The opposite charges of the negative ends and positive ends of the ellipsoid atoms produce attractive forces.
• The atoms stick together like magnetic beads. See magnets.
• The opposite charges of the atoms, which hold them together, are almost hidden within the mass. Only the charged outside ends are apparent.
• The net charge is zero if the mass is in a homogeneous electric field but the electric field is not homogeneous. It is greater near the source of the electric field.
• There is an electrical gradient.
• The electric field of the dipoles decreases quickly with the inverse cube of the distance between the dipoles but since the dipoles are close to each other all are polarized. They act like a mass of polarized dielectric inside a capacitor.
• Charges produce inverse square Coulomb forces.
• Large currents cause exploding wires as charge separation cause the atoms to elongate beyond the elastic limit of the material of which they are composed.
The atoms are bipolar ellipsoids. In the following, we have drawn them as dipoles. These dipoles are atoms or molecules where their opposite ends are slightly polarized or slightly oppositely charged. This overly bold compact notation, for a very subtle effect, emphasizes their end charge and relationship to their neighbors. In the figures below, the opposite charges of the ends of the dipoles attract each other with tensile forces along a row. The opposite charges in neighbor atoms along columns also attract each other so the rows also experience compressive or flattening forces. This is the origin of the van der Waal's forces, the electrostatic glue that holds atoms into solids, liquids and gases. The Casimir force and its repulsive opposite quantum buoyancy are also due to van der Waal's forces.
We extend the electrostatic force of polarization to gravity, centrifugal force and inertia.

The atoms are bipolar ellipsoids. They stick together in clumps, rows, columns, loops and rings. They experience tensile and compressive forces. There are linear polarizations perpendicular to an axis of rotation as in the centrifugal force of an orbiting planet or a rotating planet. There are circular polarization as in gravity. Polarizations of planets are always the vector sum of these two polarizations. Electrostatic dipoles can make any shape possible for magnets. Dipoles can make loops just as well as magnets. The loops apply an obvious compressive force. The ends of the individual atomic dipoles tend to line up, opposite charge to opposite charge, around the planet in long dipole loops. The two spheres above attract each other in the same way as oppositely directed columns of magnets. Loops can attract or repel. They attract each other when their north poles point in opposite directions and the loops repel each other when their north poles point in the same direction. Dipole atoms or molecules demonstrate the circular polarizations and flattening of gravity in the figure above. There are no open ends on the closed dipole loops. They are loops that wrap around a planet. Where there is gravity one would expect dipole loops. The dipole loops may extend into the atmosphere, ionosphere, magnetosphere and space. Atoms respond to orbital or planetary rotation with a centrifugal force which is perpendicular to the axis of rotation. It is always directed away from the axis and is proportional to the square of the tangent velocity at a distance from that axis. The force of rotation moves the proton slightly away from the center of the atom. The electron and proton orbits in the atom become elliptical. The atom becomes polarized. The polarized atom is attracted to its neighbors and the background charge of the Cosmos. The charges due to the centrifugal force are greatest at the equator where the dipole chains are longest, on each side of the axis of rotation.

Along the orbit of the planet, near the axis of rotation and the day-night line of the planet, the orbital centrifugal force equals the Sun-planet gravitational force. This is a neutral axis of equilibrium. The atoms on the night side of the planet, facing away from the Sun, have a bipolar positive polarity. This raises many questions about the solar wind and the plasmasphere of the Earth and any part they might play in electrostatic gravity. The orbital centrifugal force exceeds the orbital gravitational force on the dark, night side of the planet. This polarization extends across the planet in a very long series dipole so that the Sun side of the planet has a weak slightly negative polarity.

The gravity on the surface of the planet far exceeds the gravity imposed by the Sun. The centrifugal force of rotation usually exceeds the orbital centrifugal force. See planetary data. There is a superposition of solar gravitation and orbital centrifugal force on top of the larger local gravitational force and local rotational centrifugal force. The charges and dipoles of the larger local forces tend to cancel out when seen from a distance. This leaves us with the long series dipoles and their forces seen below. These long series dipoles also extend above the surface into space. • G>C, gravity is greater than centrifugal force.
• G=C, orbital gravitational force equals orbital centrifugal force along the orbit.
• C>G, centrifugal force is greater than gravity.
This is more complex than our original simple hypothesis of opposite charge in the Sun and planets causing gravity. The polarized atoms stick together in long rows, rather like magnetic beads making long dipoles. The Suns atoms are polarized in the same direction as the planets. The positive end of a row of atoms in the Sun is attracted to the negative end of a row of atoms in the first planet. The positive end of the row of atoms in the first planet is attracted to the negative end of a row of atoms in the second planet and so on to the other planets. These are series dipoles the width of the planets which can extend into space. These long series dipoles have large q*d products and proportionally large forces. The force on dipoles is proportional to the q*d product, the charge on the end of the dipole times the length of the dipole, and dE/dx the inhomogeneous electric field caused by similar dipoles in other planetary bodies. This is from an article on his Electrostatic Autopilot, "The operating principle of the system. are based on two key facets of atmospheric electricity that have been known for a very long time. One is Benjamin Franklin's demonstration in 1752 that lightning transfers large amounts of negative charge to the Earth. The other is Lord Kelvin's analogy, proposed in 1860, that the atmosphere is like a large capacitor where there is a highly conducting layer in the upper atmosphere that acts like a highly charged positive plate, while Earth acts as the negative plate of the capacitor. Through experiments we have shown that there are voltage levels within the atmosphere that are almost as smooth and horizontal as the equipotential planes seen in sketches in college text books describing the electric field between capacitor plates... The upper plate of the capacitor, typically charged to 350_Kv, we will assume resides sufficiently high to permit most air breathing vehicles to fly under it. The capacitor leaks. Based on 2.5E-12_A/m2� 15.6E6_electrons/m2*s an estimated 1800 amp� worldwide air-Earth conduction current, we can readily compute that a continuous 630_Mw flow of direct-current flow maintains this potential difference. � Chalmers clearly says only that thunderstorms transfer negative charge to Earth. But where does the charge come from? Where is the d.c. generator? These questions need an answer."
A charged capacitor showing its dielectric material Using this analogy, the surface of the Earth is at a negative potential on the left plate. The right plate is at a positive potential, as is the solar wind. Answering Maynard L. Hill's questions, the charges come from the Sun. The d.c. generator is the solar wind. This dipole paradigm of gravity is consistent with the index of refraction of gravitation suggested by Eddington in 1920 and currently with a series of papers by Ye and Lin, the authors of, "A Simple Optical Analysis of Gravitational Lensing." They assume that since only vacuum exists between the gravitational masses, vacuum is just a special optical medium which refracts light because of gravity. However, not usually being incumbered by quantum silliness, thinking the vacuum is a vacuum, I assume that the space between gravitational masses, the vacuum, is filled perhaps at a very low density - which is all that is required, with polarized molecules, atoms or dipoles. It should be noted that these dipoles could be part of the missing dark matter. Radio telescopes can detect the atomic hydrogen at 21_cm, if it is dense enough along their line of sight. Cold molecular hydrogen which is more stable and is probably much more common but is unfortunately invisible at radio wavelengths. Most dipoles of molecular hydrogen would also be invisible to radio telescopes. It may be detected in the future as the unseen dark matter. Atoms or molecules can be polarized and can be dipoles. I show these dipoles, not the vacuum, constitute the optical medium of gravitational lensing.

In another paper, "The Deviation of the Vacuum Refractive Index Induced by a Static Gravitational Field", Ye and Lin calculate the delta n, the change in the index of refraction caused by gravity as,
delta n = 2*G*mass/(radius*c^2), the right side is familiar.
4.24E-6, on the surface of the Sun and,
1.39E-9, on the surface of the Earth. The index of refraction caused by gravity is one plus these tiny increments.

These numbers need to be linked with the dipoles.
The atmospheric density at the surface of the Earth is 1.225_kg/m^3 at 0.02846_kg/mol or
1.225_kg/m^3 / 0.02846_kg/mol = 43.04_mol/m^3, *Avogadro's number =
43.04_mol/m^3 * 6.022E23_particles/mol = 2.592E25_particles/m^3 or 295.9E6 particles/meter. These dipoles are 3.379E-9_m apart. Gravity cause these 295.9E6 particles/meter to change the index of refraction by 1.39E-9. Each particle or dipole cause a change in the index of refraction of 4.696E-18 at the gravitational acceleration of the surface of the Earth of 9.8_m/s^2. The index of refraction change is caused by the product of the gravitational acceleration and the density of the dipoles per meter. By adjusting the phase of parallel beams of light, as seen in, helical electromagnetic waves, rotating the polarization, the beams may be made to attract or repel each other. This is demonstrated in this Nature article or this Discover article. Light bends in the electric and magnetic field of the dipoles. The dipoles cause gravity and bend the light.

Atomic scale ellipses with oppositely charged ends precess into ellipsoids. See Precession in atoms. The electrostatic torque, imposed on the elliptical dipoles of the atoms along their length by the other series dipoles, causes a perpendicular precession of the elliptical orbits of the electron and proton into ellipsoids which rotate like beads on a string. We see atoms as spherical not as orbiting in a plane like the planets.

The oppositely charged ends of atoms flattened by gravity attract their neighbors and they assemble into concentric rings of atoms. The rings are like lines of latitude which wrap around the planet. The rings are parallel to the surface of the planet. These rings have no exposed ends. Their charge is mostly hidden in the rings. When there is an equilibrium between the orbital centrifugal and gravitational forces, along the orbital path, like the astronauts in freefall in space, their polarizations cancel and they become unpolarized spherical atoms. They are free of both gravity and centrifugal force. They are still always subject to inertia, force = mass*acceleration, because any acceleration polarizes their atoms with respect to the background universe. Does this mean the background universe is charged? Indubitably! This is a charged example of Mach's principle. • Centrifugal force stretches the atom.
• Gravity flattens the atom.
• When the centrifugal force equals the gravitational force the atoms are spherical.
• When there are no accelerations the atoms are spherical.

Inertial centrifugal force pulls the proton away from the center of its atom which polarizes the atom proton out facing away from the Sun. This stretches the atom into a bipolar ellipsoid which may be called a bipolar prolate spheroid but this conceals its important elliptical roots. The inhomogeneous charge density of the elliptical orbit traced out by the electron and proton within the atom leaves the atom with pointed ends with opposite charges. These opposite charges attract each other into long rows with charged ends.

In a similar but perpendicular argument, gravity causes atoms to become flattened into bipolar ellipsoids. Their charged ends are perpendicular to the gravitational force and they are parallel to the surface of the planet. They are the result of being flattened not stretched. An oblate spheroid is the figure of the Earth due to its rotation since centrifugal force is greater at the equator. We have loop dipole forces and series dipole forces which work together to create planetary forces.

Memories
Do you have memories of centrifugal force as a child? Of being slung out from the center of a merry-go-round, while you held on for dear life? Centrifugal force polarized your atoms. It was the charge of the Cosmos that tried to throw you from the merry-go-round. Our polarized atoms holds us to the Earth. This is a profoundly small polarization of charge in each atom. Small charges produce big forces.

• Is mass due to gravitational charge?
• Is inertia due to gravitational charge?
• When atoms are accelerated, are they polarized proportional to the acceleration, with this acceleration polarization opposed by the gravitational charge of the universe?
• Is centrifugal force the pull of the background universe on the atoms polarized by the acceleration of rotation?

It does seem possible. Inertia and mass are related to gravity. Linking charge, gravitation and centrifugal force together is particularly important. These three bedrock's of physics were previously unrelated. Can this be proved?

• Atoms stick together like magnets. An atom has neighbors. The neighbor atoms impose an electrostatic force.
• Atoms become bipolar with oppositely charged ends when they are subjected to forces.
• The atoms along an axis of attraction or acceleration, increase in length and decrease in diameter, as they become ellipsoid. This is an increase in mass along that axis and a decrease in mass perpendicular to the axis.
• The atoms become ellipsoid as they are stretched, forced or flattened.
• As masses are moved there is gravitational energy stored in the space between the ellipsoid atoms or the gravitational energy may be stored within the atom by the separation of the charges.
• The charged ends on one atom attracts the oppositely charged ends of its neighbors. This is like capacitors. Two oppositely charged plates attract each other, store energy and make a capacitor.
• The atoms with charge neutrality are not capacitors. They are inert like parallel plate capacitors without a battery.
• The bipolar atoms act like capacitors with a tiny charge.
• The tiny charges have Coulomb forces.
• The forces adds up to gravity.
• Does this mean that gravity is a bulk property of atoms?
• Does anything smaller than an atom experience gravity?
• Particles have no gravity.
• There is no gravity.
• There is only charge.
• What we call gravity is a group property of charged orbiting particles.
Quarks are also charged orbiting particles. This view of nature has many consequences which need to be explored. The outer blobs are matter. The middle blob is antimatter. The rotation of the dipoles are in-phase and share a common phase angle. The matter dipoles attract each other in-series and repell the antimatter. The antimatter dipoles attract each other in-series and repell the matter. Antimatter would be repelled to the edge of the Cosmos. A natural segregation of matter and antimatter. CERN has isolated anti-hydrogen. I look forward to the identification of the gravitational repulsion of matter and antimatter in the next ten years. These are blobs of matter. The middle blob is out-of-phase with the other blobs. The outer matter dipoles attract each other in-series and repell the out-of-phase matter in the center. This repulsion is the same as that shown by the antimatter above. You can see that the right amplitude of out-of-phase matter would cancel the attractive force of the matter leading one to contemplate the shielding of gravitational and electrical forces. Since the forces of gravity and inertia are caused by the oscillating forces between charges, it is possible to shield for the forces. It is easy to shield for electromagnetic waves inside a conductive can. Shielding forces between dipoles is not so trivial because of the very high frequencies involved and because all the dipoles are in phase like the hands of two clocks. Only momentarily twice in each revolution do the dipoles line up. Gravity is the result of these momentary pulses of attraction when the dipoles line up at apogee. Any device to cancel gravity must be 180 degrees out of phase with the dipoles causing gravity. It has the polarity of its dipoles reversed relative to the gravitating bodies. Atoms absorb and emit energy in photons at a certain frequency. Our technology is in the terahertz or 1E12 hertz range. We will need 6 petahertz or 6E15 hertz. If Ray Kurzweil and Moore's Law are correct we can reach the 6 petahertz required for usable oscillators to operate at the atomic frequency in about thirteen years around 2024. A 6 petahertz frequency applied to a dielectric inside a plate capacitor with the right amount of oscillating charge, polarity and phase on the plates might cancel the oscillating charge caused by the Sun, Earth and background universe. When the oscillating charges in the capacitors are inverted and balanced by a phase locked loop, the effect of gravity and inertia might be shielded, reduced or eliminated. One might reduce the shielding in a certain direction and be attracted in that direction. We hope it can run a space ship. We are at the plate capacitor oscillator stage. An advanced technology could do the same thing with a tiny box. In a ship of this type, the ship and crew could not survive the failure of their shielding mechanism at high velocity. If it failed the ship could go from a residual mass of a few grams to a mass of thousands of kilograms in the time it takes for the circuit to fail. When a fuse blows, the ship disappears like a nuke. An unpleasant fact is that the space ships could be used as a bomb if the pilots went nuts and were willing to kill themselves and us. The ships could be accelerated to the speed of light and crashed into the Earth. Their ten thousand kilograms would become a mass times c squared extinction event. Hiroshima generated 5E10 joules. This would be 9E20 joules. This is eighteen billion Hiroshima's. So much for the progress of man, unlimited energy and for exploring space by shielding of mass and inertia.

• d/dt(---) is the rate of change of whatever is in the parenthesis. When you see,
force = d/dt(---) say,"force equals the rate of change of ---".
Newton said force is the rate of change of momentum.
• force = d/dt(momentum) or "force equals the rate of change of momentum." and momentum = mass * velocity. It is written in several ways with mass and velocity separated.
• force = d/dt(mass * velocity) or "force equals the rate of change of, mass times velocity."
• force = mass * d/dt(velocity). or "force equals the mass times the rate of change of velocity."
• force = mass * acceleration. Acceleration is the rate of change of velocity.
• force = d/dt(mass) * velocity or "force equals the rate of change of mass, times velocity." This is how conventional rockets work, by the rate of change of mass times velocity, dumping high speed mass out the back. If there is a huge change in mass in seconds then there is a gigantic acceleration which rips the ship apart. We can write,
• force = force,
mass * acceleration = d/dt(mass) * velocity. If all the mass becomes unshielded in a hundredth of a second, and the velocity is c/100 then
mass * acceleration = mass/0.01_second * c/100, the mass cancels,
acceleration = 300 million_meters/second2.
The acceleration of gravity on the Earth is 9.8_meters/second2. This acceleration is 30 million times the gravity of Earth. A severe flattening and nuclear event occurs.

Using shielding of mass and inertia
When you push something to get it going or to stop it, it is accelerated. Inertia is at work. It is the gravitational mass of the universe which pushes back against the acceleration. What else could there be to push back? A residual mass is the mass that is left when the mass is shielded. It is the mass available for inertia to act against. It is the mass that would be used to calculate the force if the mass is shielded. A shielded mass has the kinetic energy of the residual mass times half the velocity squared. We have a small mass and kinetic energy with a residual shielded mass, and a huge mass and kinetic energy with an unshielded mass at the same velocity. If the shielding fails at velocity, there is a huge increase in energy. Its not nice to fool mother nature. Nature responds poorly to the sudden appearance of a fast moving mass without the proper kinetic energy. It is a vaporization event. Particles can be easily accelerated inside the shielded ship since they have no mass and no inertia. Ionized gases are easily accelerated to the speed of light when they have no mass. When they acquire mass upon leaving the shielding of the ship the particles turn first into a plasma and then into gamma rays. This could work as an impulse drive and generator. It might be close to one hundred percent conversion of mass to energy. To get a ship up to the speed of light, without the shielding of mass, would require all of the ships mass being converted to energy. That is what mass times c squared means. However, here we are dealing with a residual mass which is the very small mass left after shielding. A ten thousand kilogram ship might have a residual mass of one gram. A small residual mass means a small fuel requirement. A force divided by a small mass means a big acceleration so the ships could accelerate fast. Shielded tanks of pressurized gas could become plasma or gas to gamma ray converters. These could be gamma ray guns as well as rocket motors. It would be necessary to harvest the currents from the plasma to generate the copious quantities of high frequency electricity required for the Drive. The gamma ray exhaust when the ships were close to the Earth might be seen by satellites which look for gamma rays or nuclear test explosions.

The Generator
A beam of accelerated shielded particles from pressurized gas or knocked loose from a solid by a laser, might create a plasma on its way to becoming gamma rays out of the stern as the particles loose their shielding. The small shielded mass and kinetic energy of the particles becomes a huge energy as the particles loose their shielding. Some of the plasma can be collected in a generator while it is still somewhat within the shielding of the ship. The generator is basically a magnet and two electrodes to collect some of the copious ion and electron flow in the plasma but the electrodes would not last long in the corrosive environment created by the plasma.

References
1. Assis @ www.ifi.unicamp.br/~assis/Can-J-Phys-V70-p330-340(1992).pdf
2. Cosmos @ blackholeformulas.com/files/Introduction.html
3. Bohr's planetary Atom @ blackholeformulas.com/files/BohrAtom.html
4. Ring Electrons @ blackholeformulas.com/files/RingElectron.html
5. Electromagnetic waves @ blackholeformulas.com/files/helicalelectromagneticwaves.html
6. Pushing gravity @ blackholeformulas.com/files/PushingGravity.html
7. Pushing Gravity @ metaresearch.org/publications/books/PushingG.asp
8. Gravity, Rosettes and Inertia @ blackholeformulas.com/files/gravity.html
9. Ellipse gif @ blackholeformulas.com/files/ellipse.gif
10. Electron and proton binary atom with circular orbits @ blackholeformulas.com/files/atomcircle10.gif
11. Tokamaks @ www-fusion-magnetique.cea.fr/gb/fusion/physique/configtokamak.htm
12. Spheromaks @ plasma.swarthmore.edu/SSX/faq.html
13. Ring electrons @ blackholeformulas.com/files/RingElectron.html
14. Atoms which have elliptical orbits are very polarized @ blackholeformulas.com/files/linearcharge.png
15. Dunn @ orbitsimulator.com/gravity/articles/simu.html
16. Burtle @ burtleburtle.net/bob/physics/orbit101.html
17. Koppen @ astro.u-strasbg.fr/~koppen/jeanlouis/BinaryStar.html
18. Electron and proton binary atom with elliptical orbits @ blackholeformulas.com/files/dips10.gif
19. Text file @ blackholeformulas.com/files/ellipse.txt
20. Click to animate! Ellipses @ blackholeformulas.com/files/dipocolor5.gif
21. Force and Eccentricity Table @ blackholeformulas.com/files/table.gif
22. Electron and proton binary atom with elliptical orbits @ blackholeformulas.com/files/dips10.gif
23. Tatum @ astro.uvic.ca/~tatum/elmag/em3.pdf
24. Planetary data @ blackholeformulas.com/files/planetary.html
25. Ye and Lin papers @ arxiv.org/PS_cache/arxiv/pdf/0704/0704.1173v1.pdf
26. Dark Matter @ blackholeformulas.com/files/DarkMatter.html
27. Molecular Hydrogen @ home.pacbell.net/skeptica/pc.html
28. Ye and Lin calculate @ arxiv.org/PS_cache/arxiv/pdf/0704/0704.3485v1.pdf
29. Helical electromagnetic waves @ blackholeformulas.com/files/helicalelectromagneticwaves.html
30. Nature @ nature.com/nphoton/journal/v3/n8/abs/nphoton.2009.116.html
31. Discover @ discovermagazine.com/2010/jan-feb/083
Appendix.html
32. Johnson tides @ mb-soft.com/public/tides.html
33. Hodograph @ faculty.ifmo.ru/butikov/Hodograph.pdf
34. Electric forces @ physics.upenn.edu/~uglabs/lab_manual/electric_forces.pdf
35. Coulomb Balance @ physics.nyu.edu/~physlab/GenPhysII_PhysIII/CoulBalance.pdf
36. Current Balance @ physics.nyu.edu/~physlab/GenPhysII_PhysIII/CurrentBalance.pdf
37. NIST Atoms @ nist.gov/public_affairs/releases/hiphopatoms.htm
38. Tajmar anti gravity @ en.wikipedia.org/wiki/Anti-gravity
39. emdrive @ emdrive.com/
40. HTML Calculator @ daniweb.com/code/snippet146.html
Precession.html
41. Larmor Precession @ blackholeformulas.com/files/LarmorAnimation.html
42. MRI site @ cis.rit.edu/htbooks/mri
44. Precession in electron and proton binary atoms or dipoles @ blackholeformulas.com/files/rosa10.gif
45. Two ways of shaping orbiting charges into spheres @ blackholeformulas.com/files/dual2.png
Magnets.html
46. K&J magnetic calculator @ kjmagnetics.com/calculator.asp
47. Hyperphysics magnetic @ hyperphysics.phy-astr.gsu.edu/hbase/magnetic/curloo.html#c1
50. Neocube magnets @ theneocube.com/

Shielding
Magnetic forces are not shielded or reduced by a copper plate between magnets. I didn't speculate about photons. I tried two magnets and a penny. Magnets are related to electricity. Electromagnetic waves could not go through a penny but forces do. Are the forces between two charges shielded by a conductive foil? Shielding of electromagnetic waves may be easily accomplished inside of a conductive can. Is the force between charges also easily shielded? Is the charge the same as the electric field of the charge? Forces between the orbiting bodies in our solar system have no calculated delay in their interactions. Do forces between charges have a delay in their interactions?

I haven't heard of any experimental evidence of gravitational shielding being evaluated from the July 22, 2009 solar eclipse in Asia. The Sun and Earth interaction are blocked by the moon, during the eclipse, over a tiny area of the Earth.
A copper or aluminum foil might be used to demonstrate shielding of electrostatic repulsion or attraction forces, if any shielding exists, if you can figure a way to avoid interaction of the charges with the plate. I tried a simple experiment. An electroscope works by the deflection of charges by electrostatic repulsion. Two styrofoam balls are suspended by threads making a crude electroscope. They are charged with a "Fun-fly-stick" battery powered portable toy van de Graff generator. Having the same charge, the styrofoam balls repel. Then I tried to insert an aluminum foil between the balls. The aluminum foil attracts the balls because it has less charge. The balls touch and loose their charge. With sufficient charge, I speculate, the foil would become a neutral surface in an electrical gradient. It would be charged to the local gradient. The forces would be unaffected. There are simple experiments here somewhere but I have yet to find an experimental answer. The force between charged plates can be measured with Kelvin's absolute electrometer. It can be nearly as easily measured with a digital scale as was the force between magnets in the appendix. We know the insertion of a dielectric between charged plates should decrease the force between the plates at low frequencies. What is the measurable effect? What measurable effect does the insertion of a conducting foil have on the force between the plates?

Dielectrics and capacitors
Dielectrics are insulators. When a dielectric is inserted in the charged plates of a capacitor, dipoles are induced in the dielectric. Insulators
Azaroff and Brophy in "Electronic processes in materials", "Another way of describing an insulator is to note that the electrons are so tightly bound to the atoms that at ordinary temperatures they cannot be dislodged either by thermal vibrations or with ordinary electric fields. The negative and positive charges in each part of the crystal can be considered to be centered at some point, and since no conductivity is possible, the localized charges remain that way essentially forever. When an electric field is applied to the crystal, the centers of positive charge in the crystal are slightly displaced in the direction of the applied field and the centers of negative charge are slightly displaced in the opposite direction. This produces local dipoles throughout the crystal, and the process of inducing such dipoles in the crystal is called polarization. The ratio of the induced dipole moment to the effective field is called the polarizability of the atom, and the dipole moment induced in a unit volume of a polarized insulator can be considered as the average of the dipole moments of all the atoms in that unit volume. It is possible that certain groups of atoms (complex ions or molecules) already possess permanent dipole moments. In crystals containing such atomic groups, an external field tends to orient the dipoles parallel to the field direction. In the absence of an external field, the dipoles are randomly oriented because of their thermal motion, so that the crystal has a zero net moment. The polarization of such polar crystals is strongly temperature-dependent since, even in the presence of an applied field, thermal motion tends to randomize the dipole orientation. On the other hand, the polarization of non polar crystals is independent of temperature since, in the absence of an external field, no dipoles exist in the crystal. The temperature dependence of polarization, therefore, can be used to distinguish polar insulators from non polar insulators." We will follow non polar insulators and the separation of charge mentioned above.
Origins of flux
Thomas L. Martin Jr. in the "Physical basis for Electrical Engineering"; "It now becomes convenient to assign a synthetic reality to the flux lines, although they are a creation of the mind only and do not exist physically, it is convenient to assume that flux lines do exist and to use them to describe the regions about charged bodies. Thus, we assume the following statements are true:
(1) Charged bodies are the sources of lines of electric flux. (a) Flux lines emanate from bodies carrying positive charge. (b) Flux lines terminate on bodies carrying negative charge.
(2) The flux lines are directed parallel to the force exerted on a positive test charge.
(3) The total number of flux lines associated with a charged body is proportional to the flux density and test charge.
The flux lines are used to represent systematically the flux about a charged body. The flux and charge are really just two different ways to describing the same phenomenon. The charge q describes the properties at a point. The flux and flux density describe the properties some distance away from the point occupied by q. Thus flux and q are just different manifestations of the same physical quantity, so flux = q."

In the figure above
"A charge of +q coulombs is produced on one plate in vacuum, and a charge of -q coulombs on the other plate when a potential difference of V volts is established. If the potential difference is doubled it is found that the number of charges on each metal plate doubles. It appears that the ratio of the charge q to the potential difference V is a constant of the system. This constant is defined as the capacitance C. A physical structure having capacitance is called a capacitor."
C = q/V, charge2/energy, farads, coulombs/volt, a2*s4/(kg*m2),

"When some insulating material is included between the plates of a capacitor, the situation depicted above results. It is convenient to picture the insulator as being full of dipoles randomly oriented under normal conditions. When an electric field is applied, we assume that it causes the dipoles to rotate until they come into alignment with the electric field by an amount sufficient to bring them into alignment with the electric field. In so doing they produce new lines of flux, and induce additional charges on the capacitor plates. This causes the total accumulated charge q' on each plate to be larger than the vacuum case without the dielectric even though the potential difference remains the same. We spoke of dipoles rotating when the electric field was applied. Actually, all of the dipoles in the material may be induced and present only when the electric field is applied.
qi = induced charges
q' = q + qi, the new value of the charge.
C' = q'/V = (q + qi)/V, the new value of the capacitance.
This capacitance is larger than that obtained with vacuum between the plates.
You can easily see that the extent of increase of the capacitance is controlled by the character of the insulating material between the plates. The capacitance increases as the density of dipoles increase because this raises the number of induced charges.
P = n*p/v, the flux density added by dipoles, dielectric polarization, dipole moment per unit volume, coulombs per meter2, charge/area.
n is the number of dipoles in the material between the plates. n*p is the total dipole moment in coulombs*meters. v denotes the volume of the insulating material.
D = charge/area = q1/(4*pi*r2), the flux density imposed by q1, coulombs/meter2, a*s/m2, on the surface of a sphere which surrounds the charge q1.
F ~ q2*D, Force is proportional to the test charge q2 times the flux density,
F = q2*D/e0, force is proportional to the flux density imposed by q1 on q2, e0 is the dielectric constant of vacuum or the permittivity of vacuum.
F = q1*q2/(4*pi*e0*r2), substituted for D, this is Coulomb's law.
E = F/q2 = D/e0, force/charge, electric field intensity
Dv = e0*E, flux density in vacuum, charge/area = charge2/(force*area) *force/charge.
Dm = em*E, flux density in dielectric, em = dielectric constant of the material between plates.
flux density in dielectric = flux density in vacuum + flux density from dipoles
Dm = Dv + P,
em*E = e0*E + P,
em = e0 + P/E, divide through by E the electric field intensity.
kr = em/e0 = 1 + P/Dv, divide through by e0, dimensionless relative dielectric constant."
The ratio of the capacitance obtained with some insulating material between plates to the capacitance with vacuum insulation is the relative dielectric constant kr."
kr = C'/C = (q + qi)/q = 1 + qi/q = em/e0 = 1 + P/D
For vacuum the relative dielectric constant kr is equal to one. For water the relative dielectric constant kr is 78. The force between capacitor plates is divided by kr is 78 when the space between the plates is filled with water at zero frequency. At optical frequencies of 10E14 to 10E15 hertz the kr of water is 2. Conductors are infinitely polarizable so their kr approaches infinity at zero frequency. At the high frequencies of the atomic dipoles, 6E15 hertz, there is a force between the charges. Dielectric constants have no obvious relationship to mass.

We take from this that charge is induced by the presence of a dielectric in a potential field and that a dielectric induces these charges as the dielectric becomes polarized with dipoles. Some of these induced charges, those that are caused by the polarization of gravity, are the gravitational charges we have been looking for. Dipoles have an attractive force proportional to the inverse forth power of distance so dipoles can not be the source of gravity. Charges induced by dipoles have an attractive force proportional to the inverse square of distance and can therefore be the source of gravity.

Tidal bulges
Tidal bulge equations and exposition, tides and other interesting items are at Johnson's website.
We calculate the tidal bulge of the Earth using accelerations. We calculate the accelerations both using mass and using gravitational charge. The accelerations have the same values. Tidal bulges in atoms, caused by charges, may use the same procedure.
mearth = 5.972E24_kg, the mass of the Earth.
rearth = 6.378E6_m, the radius of the Earth.
mmoon = 7.348E22_kg, the mass of the moon.
dmoon = 384.4E6_m, the distance from the center of the Earth to the center of the moon.
gcearth = mearth*(4*pi*e0*G).5 = 5.146E14_a*s, the gravitational charge of the Earth.
gcmoon = mmoon*(4*pi*e0*G).5 = 6.3317E12_a*s, the gravitational charge of the moon.

Accelerations using mass
ge = G*mearth/rearth2 = 9.79822007_m/s2, the gravitational acceleration of the Earth at the surface of the Earth, using mass.
ged = G*mearth/(rearth+Δr)2 = 9.79821898_m/s2, the gravitational acceleration of the Earth at the surface of the Earth +Δr.
gmd = G*mmoon/(dmoon-rearth-Δr)2 = 3.431742494E-5_m/s2, the gravitational acceleration of the moon at the surface of the Earth +Δr.
gms = G*mmoon/(dmoon-rearth)2 = 3.341742487E-5_m/s2, the gravitational acceleration of the moon at the surface of the Earth.

Accelerations using gravitational charge
ge = gcearth/(rearth2 )*(G/(4*pi*e0)).5, the gravitational acceleration of the Earth at the surface of the Earth, using gravitational charge.
ge = gcearth/(rearth2)*.77448_m3/(a*s3) = 9.7979_m/s2, since (4*pi*e0*G).5/(4*pi*e0) = (G/(4*pi*e0)).5 = .77448_m3/(a*s3), using gravitational charge.
ged = gcearth/(rearth+Δr)2*(G/(4*pi*e0)).5, the gravitational acceleration of the Earth at the surface of the Earth +Δr, using gravitational charge.
gmd = gcmoon/(dmoon-rearth-Δr)2*(G/(4*pi*e0)).5, the gravitational acceleration of the moon at the surface of the Earth +Δr, using gravitational charge.
gms = gcmoon/(dmoon-rearth)2*(G/(4*pi*e0)).5, the gravitational acceleration of the moon at the surface of the Earth, using gravitational charge.

Δg = ge-gms-(ged-gmd) = 1.09689E-6_m/s2, the net amount of acceleration applied to something on the surface of the Earth by the gravity of the moon when the moon is overhead. The moon overhead reduces your weight slightly. It pulls more on your head than your feet. Does this improve your posture?

ge - Δg = G*mearth/(rearth + Δrearth)2, the gravitational acceleration of the Earth and the pull of the moon above the surface of the Earth.
ge - Δg = gcearth/(rearth + Δrearth)2*.77448_m3/(a*s3), using gravitational charge.
(ge - Δg)/ge = G*mearth/(rearth + Δrearth)2*rearth2 /G*mearth, divided by ge.
(ge - Δg)/ge = gcearth/(rearth + Δrearth)2*.77448_m3/(a*s3)*rearth2 /(gcearth*.77448_m3/(a*s3)), using gravitational charge.
1 - Δg/ge = rearth2/(rearth + Δrearth)2, canceled mass or gravitational mass.
1 + Δg/ge = (rearth+ Δrearth)2/rearth2, inverted.
1 + Δg/ge = (rearth/rearth+ Δrearth/rearth)2,
1 + Δg/(2*ge) = 1+ Δrearth/rearth, square root.
_ We just used these two handy approximations which I discovered by accident.
_ Check these with your calculator.
_ (1.00008)-1 = 1+(.00008*-1) = 1-.00008, inverted
_ (1.00008).5 = 1+(.00008*0.5) = 1.00004, square root
_ The integer and fractional parts are separated which simplified this problem.

Δg*rearth/(2*ge) = Δrearth, canceled the ones.
Tidal bulge = Δrearth = 0.3570_m, This is the amount of the tidal bulge. The Earth is egg shaped or ellipsoid shaped by the pull of the moon. It is so small because the acceleration imposed by the moon, Δg is so small, 1.096E-6_m/s2. The Earth is also shaped by its spin on its axis producing a much larger equatorial bulge.

Equatorial bulge
The Earths equatorial radius is 6378165_m.
The Earths polar radius is 6356785_m.
The Earths equatorial bulge is 21380_m. The tidal bulge was a tiny 0.3570_m. The Earth rotation and centrifugal force makes it an oblate spheroid with an eccentricity of e = 0.08181.

Tidal bulge ratio
Δg/(2*ge) = Δrearth/rearth = 5.59750E-8 = Δratom/ratom,
5.59750E-8 *ratom = Δratom = 2.962E-18_m, tidal bulge, on each side of the atom. The atoms have a radius of about 5.292E-11_m so the tidal bulge of the Earth or atom is,
1/17.285E6, one part in 17 million. The Earth is ellipsoidal under the gravitational effects of the Sun and moon. The Earths atoms are ellipsoidal under the gravitational effects of the Sun and moon and their neighbor atoms and any other accelerations. This bulge in the atoms is too small to be seen with a scanning tunneling microscope. The atoms still appear spherical because they are egg shaped by only one part in 17 million. Both the atom and Earth are bulged a similar small proportional amount by the same external forces.

Eccentricity of atoms and ellipses
a = ratom+Δratom = 5.292E-11_m +2.962E-18_m = 5.2920002962E-11_m, x radius of the elliptical atom,
b = ratom-Δratom = 5.292E-11_m - 2.962E-18_m = 5.2919997038E-11_m, y radius of the elliptical atom,
e = (a2-b2).5/a = 4.7316E-4, eccentricity or,
e = ((r+Δr)2-(r-Δr)2).5/(r+Δr), eccentricity or,
e = (4*Δr/r).5 = 4.7318E-4,
e = rapogee-rperigee/(rapogee+rperigee), 2*a*e/(2*a) = e
We can move on to discover the charge density at the ellipsoid ends of the atoms. This might relate to the gravitational charge of the atoms.

Charge separation
The red electron and blue proton ellipses share a common focus and eccentricity.
The radius of the Bohr atom is re + rp. The center of the red ellipse of the electron from the focus is re. The center of the blue ellipse of the proton from the focus is rp. The amount of charge separation is proportional to the eccentricity as is the amount of opposite charge on each end of the atom. e is the eccentricity of both ellipses but the electron ellipse is much bigger. e*(re + rp), is the separation of the centers of the electron and proton ellipses. If the eccentricity is zero then the atom is spherical and free of bipolar end charges.

Click figure to animate! Electron and proton binary atom with elliptical orbits r = a*(1-e2)/(1+cos(angle)*e), the polar form of the ellipse equation.
rapogee = a*(1-e2)/(1-e) = a*(1+e), when the angle is pi, r is maximum, at apogee, at its farthest from the center of mass focus.
rperigee = a*(1-e2)/(1+e) = a*(1-e), when the angle is 0, r is minimum, at perigee, at its nearest to the center of mass.
Kepler tells us planets sweep out equal areas in equal time. Their velocities must vary in elliptical orbits.
area = r2*angle/2, the area of each wedge of the ellipse is defined by r and angle.
angle = 2*area/r2, the angle advanced for a fixed area of wedge. A constant equal to 2*area can be used with the r from the ellipse equation to calculate an angular increment to trace out equal areas in equal times. This traces out the ellipse as it shows the changes in velocity along its orbit. See the figure above. This change in velocity as the proton and electron pair move around their elliptical orbits is what interest us with respect to polarized atoms. As the velocity varies so does the charge density. The positive and negative atomic charges are visible at the opposite ends of the atom. The atom is polarized.
See Orbit 101 for several methods of predicting future orbital locations.

Planets and electrons trace out equal areas in equal times in their orbits. Electrons on elliptical orbits tracing out equal areas in equal times have a variable velocity which leads to a variable charge density and polarization of the atom. The area is,
Δareaapogee = Δangleapogee*a2*rapogee2/2 = Δangleapogee*a2*(1+e)2/2, on the electron end of the atom.
Δareaperigee = Δangleperigee*a2*rperigee2/2 = Δangleperigee*a2*(1-e)2/2, on the proton end of the atom.
Δareaapogee = Δareaperigee
Δangleapogee*a2*(1+e)2/2 = Δangleperigee*a2*(1-e)2/2,
Δangleapogee*(1+e)2 = Δangleperigee*(1-e)2,
Δangleapogee*(1+e)2/(1-e)2 = Δangleperigee,
e = 0.0004732 for the tidal bulge of the Earth or the atom.
Δangleapogee*(1.001894) = Δangleperigee,
Δangleapogee*(1+e*4) = Δangleperigee, The electron traces out equal areas in equal time, but the angle the electron traces out at the proton end of the elliptical atom is bigger. The velocity is greater and the charge per angle or charge per radian is less. The charge per radian is greater where the electrons move slower, as they do, at the extended portions of the elliptical orbit where the electron radius is greater.

Elliptical velocity graph On the left is shown, the tangent velocity of an electron or proton on an elliptical orbit, at equal time intervals, around the center of mass of the electron-proton system. In the previous figure we saw both particles. Here we only look at one particle at a time. The particles slow down and speed up. They are accelerated. Like anything on an elliptical orbit there is an oscillating transfer between potential and kinetic energy of the particles along their orbit. There is equilibrium. Vp is the perigee velocity. Va is the apogee velocity. The apogee velocity is smaller than the perigee velocity. The orbiting particles spend more time near the apogee end of their orbits. The probability of an electron or proton being near the apogee end of its orbit is greater. The electron and proton each have their greatest charge per radian at the opposite ends of the atom. The atom is polarized. On the right is the hodograph. It is an interesting way of looking at velocity in elliptical orbits. The velocity is least at Va. The points along the orbit of equally spaced time intervals are closest together at Va. The charge density is greatest at Va. This charge density is much greater than at Vp. The atom is polarized by differences in charge density. See the original graph and papers by Butikov.
rperigee = a*(1-e), the minimum radius, closest to the center of mass focus.
rapogee = a*(1+e), the maximum radius, farthest from the center of mass focus.
vapogee*rapogee = vperigee*rperigee, this holds for all orbits.
vapogee*a*(1+e) = vperigee*a*(1-e), substituted for the radii.
vapogee*(1+e)/(1-e) = vapogee*(1+e)*(1+e) = vperigee, isolated vperigee.
vapogee*(1+2e+e2) = vperigee, another approximation where e is small.
Δv = vperigee - vapogee = vapogee*(1+2e+e2) - vapogee = vapogee*((1+2e+e2) - 1) = vapogee*(2e+e2)

Circle to ellipse
An electron in an circular orbit goes to an elliptical orbit by a change of velocity, Δv. This is an increase in momentum and energy as well as velocity.
rcircle = rperigee = a*(1-e), the minimum radius, closest to the center of mass focus.
rapogee = a*(1+e), the maximum radius, farthest from the center of mass focus.
vcircle*(1-e)/(1+e) = vapogee, isolated vapogee.
vcircle*(1-2*e+e2) = vapogee, or
vcircle/vapogee = (1+2*e+e2),
vcircle/vapogee = (1+Δv), substituted Δv = 2*e+e2,

Another clue
Atomic mass is measured in AMU, atomic mass units, 1.660E-27 kilograms, about the mass of a proton and electron dipole. Mass is proportional to the number of dipoles. Gravity is proportional to mass.

AMU
One AMU atomic mass unit = 1.66053886E-27 kilograms
Wiki says it is one twelfth of the mass of an isolated atom of carbon-12 (12C) at rest and in its ground state.
1 AMU or U = 1.660538782E-27 kg = 931.494028 MeV/c�
electron plus proton, (1.0078 amu) 1.6735E-27_kg = (1.0073 amu) 9.1094E-31_kg + (0.0005 amu) 1.6726E-27_kg
hydrogen atom, (1.00794 amu)*1.66054E-27_kg/amu = 1.67372E-27_kg,
neutron, (1.0087 amu), 1.6749E-27_kg,
1 amu or u = 1_gram/(Avogaodro's number) = 1_kg/ (1000*(Avogadro's number))
We noticed before that (c3*e0/hp).5 = 6.000359E23_a*s/(kg*m) is very close to Avogadro's number. Using it as Avogadro's number,
1_kg/ (1000*(Avogadro's number)) = 1.66656E-27_m/(A*s) = 1_AMU * 1_kg*m/(A*s)
This is at least an odd and interesting coincidence which links Avogadro's number, AMU and meters per charge.
The gravitational charge per AMU is,
1.66656E-27_kg * (4*pi*e0*G).5 = 1.4361E-37_A*s, or
1.66656E-27_kg*m/(A*s) * (4*pi*e0*G).5 = 1.4361E-37_m,

Earth in Bohr atoms
ratom = rc/(alpha2) = 5.292E-11_m, the minimum radius of the Bohr atom.
ratom*2 = 1.058E-10_m, the diameter of the atom or,
9.448E9_Bohr atoms/meter, if the atoms are cheek to jowl.
9.448E9_atoms/meter * 6.37E6_m (radius of the Earth) = rearth*alpha2/(2*rc) = 6.026E16_atoms, the radius of the Earth in diameters of series atoms or capacitors.
4/3*pi*6.018E163 = 9.133E50 atoms, the volume of the Earth in Bohr atoms.

What is the composition of the Earth?
32% iron * 55.845 amu = 17.8704 amu.
30% oxygen * 15.9994 amu = 4.79982 amu.
15% silicon * 28.0855 amu = 4.212825 amu.
14% magnesium * 24.305 amu = 3.4027 amu.
3% sulfur * 32.066 amu = 0.96198 amu.
2% nickel * 58.6934 amu = 1.173868 amu.
1.5% calcium * 40.078 amu = 0.60117 amu.
1.4% aluminum * 26.9815 amu = 0.377741 amu.
98.9% at 33.400 amu or
100% at an average of 33.7719 amu per atom for the Earth.
9.133E50 atoms at 33.7719 amu = 3.08438E52_amu or dipoles, the volume of the Earth in amu or dipoles.

Gravitational charge per AMU or dipole
gcearth = mearth*(4*pi*e0*G).5 = 5.146E14_a*s, the gravitational charge of the Earth.
gcamu = mamu*(4*pi*e0*G).5 = 1.430929E-37_a*s, the gravitational charge per AMU or dipole.
ce/gcamu = 1.6021E-19_a*s /1.430929E-37_a*s = 1.11962E18, The gravitational charge of the dipole is much, much smaller than the charge of the electron. Were does this tiny charge reside?
gcearth/gcamu = 5.146E14_a*s/1.430929E-37_a*s = 3.59626E51 gravitational charges or dipoles.
mearth*(4*pi*e0*G).5/(mamu*(4*pi*e0*G).5) =
mearth/(mamu) = 3.59626E51,
but this is only a ratio of masses.

3.08438E52 /3.5956E51 = 8.5782067, ratio of amu from volume to amu from gravitational charge. This is of the right magnitude.

Atomic dipoles
An electric dipole consists of two charges of equal magnitude separated by a distance.
q*d = electric dipole moment, q is one of the two charges. d is the distance between the charges. d is constant in a circular orbit. d varies in an elliptical orbit.
Torque = q*d*sin(angle)*E, a torque is created by the dipole as it tries to align itself with an external charge or electric field. This is the cross product of q*d and E. This torque is why objects tend to orbit in a plane and why solar systems and some galaxies form disks.
Ey = q*d/(4*pi*e0*y3), the electric field perpendicular to the dipole. y is the perpendicular distance far from the dipole.
Ex = 2*q*d/(4*pi*e0*x3), the electric field along the axis of the dipole. x is the distance far from the dipole. The electric field along this axis is twice that which is perpendicular to the axis. See Tatum.
Ex = 2*a/(b*x3), substituted a = q*d. b = 4*pi*e0.
dEx/dx = -(2*a*(b*(3*x2))/(b*x3)2,
dEx/dx = -(6*a/(b*x4),
q*d *dEx/dx = -(6*q2*d2/(4*pi*e0*x4), the force on a dipole in the x direction is proportional to q*d.
q*d *dEy/dy = -(3*q2*d2/(4*pi*e0*y4), the force on a dipole in the y direction is proportional to q*d.
The force between dipoles decreases with the inverse forth power of the distance between the dipoles. Gravitational force decreases with the inverse square of the distance between the masses. The interaction of solitary dipoles can not explain gravity. Long series of dipoles have large q*d products and proportionally large forces.

Magnetic forces on series of dipoles
Dipoles in rows stick together. The ends of rows of dipoles are oppositely charged. They are a larger version of a single dipole. The forces at the end of rows of dipoles are greater than with single dipoles. The attractive and repulsive forces between the ends of rows of dipoles are much greater. We will look at the force between rows of series magnets to try to understand the rules of series dipoles.

Calculations using inverse square force
force1 = m*m*k/x2 = m2*k/x2, for the force between two magnets. One m is a magnet on a scale. The other m is a magnet in a stack of magnets on a platform above the magnet on the scale. k is the constant of proportionality. x is the distance between the magnet on the scale and the first magnet on the platform. All the magnets appear the same but they vary somewhat in strength.
force2 = m2*k/(x)2 + m2*k/(x+d)2, for the first two magnets on the stack. d is the distance between the magnets on the stack. Each additional magnet is stacked and added at a greater distance in multiples of d from the scale as it is stacked onto the previous magnet. Each addition identical magnet adds a decreasing incremental force at the scale because it is at an increasing distance from the scale.
force4 = m2*k/(x+0*d)2 + m2*k/(x+1*d)2 + m2*k/(x+2*d)2 + m2*k/(x+3*d)2, for the first four magnets on the stack.

Using one inch for the distance between the magnet on the scale and the stack of magnets
force4 = m2*k/(4/4)2 + m2*k/(4/4+1/4)2 + m2*k/(4/4+2/4)2 + m2*k/(4/4+3/4)2, x = 4/4 and d = 1/4 for quarter inch magnets, for the first four magnets on the stack.
force4 = m2*k/(4/4)2 + m2*k/(5/4)2 + m2*k/(6/4)2 + m2*k/(7/4)2, collect terms.
force4 = m2*k*(4/4)2 + m2*k*(4/5)2 + m2*k*(4/6)2 + m2*k*(4/7)2, inverted the denominator and multiplied.
force4 = m2*k*16*( (1/4)2 + (1/5)2 + (1/6)2) + (1/7)2),
force10 = m2*k*16*(1/16 +1/25 +1/36 +1/49 +1/64 +1/81 +1/100 +1/121 +1/144 +1/169),
force10 = m2*k*16*0.20978 = m2*k*3.3565, collected terms for a calculated series, for a ten magnets stack.

Weighing magnetic force
A gram scale may be used to determine the attractive and repulsive force between series magnets. Within the scale, a steel screw which supports a reference magnet is threaded into the small aluminum beam which measures forces by its deflection. When the small aluminum beam deflects it stretches a strain gage. The strain gage operates a digital display. The results are non-linear increases in force with increasing numbers of series magnets. First, put one magnet on the scale. Second, zero the scale with this magnet. Then, measure the force of attraction or repulsion, of a series of magnets stacked on a platform which is at a fixed distance above the magnet on the scale. Each additional magnet adds a decreasing force as it is stacked one quarter of an inch farther from the scale as they are stacked one quarter of an inch higher on the platform.
The internal batteries were wired and moved to a distance. The interaction of their steel ruined careful measurements of forces between magnets.

We measured the force between two magnets as 10.68_g using x = one inch as the distance between the magnets. The force between one magnet and a ten magnet stack equals 21.77_g.
force10 = 21.77_g = m2*k*3.3565, The total force is now correct but we seek the increment added by each magnet.
m2*k = 6.4859_g
m2*k*16 = 103.77_g
103.77_g *(1/16 +1/25 +1/36 +1/49 +1/64 +1/81 +1/100 +1/121 +1/144 +1/169),
103.77_g/16 +103.77_g/25 +103.77_g/36, for the first three terms in the series calculated.
6.48_g +4.15_g +2.88_g, for the three terms in the inverse square series calculated versus,
10.68_g +4.94_g +2.09_g, for the first three terms of the series measured with one inch as the distance between the magnets and the scale. Measurements enforce some reality in any process. The inverse square calculation does have pretty math but it does not seem to be a good fit to the measured reality. We must look for a better fit to the measurements.

Using a binary fraction
When you look at a binary number such as,
0.1111111111b, an integer which is zero, a "decimal point" and a fractional part in binary notation with ten ones, or
0. +1/2 +1/4 +1/8 +1/16 +1/32 +1/64 +1/128 +1/256 +1/512 +1/1024 = 1023/1024 = 210- 1/210, in decimal notation. The fractional part adds up to a little less than one depending on how close you want to go to one with a decreasing increment of the fraction by adding more ones on the right of the binary fraction.

We seek a simple rule to estimate the increment of force added by each magnet so that we might know the total force of a series of n magnets from the force between the first few magnets in the long series. The force on a series of magnets can be considered like a weight multiplied by a binary fraction which adds up to a little less than one.
21.77_g*(1/2 +1/4 +1/8 +1/16 +1/32 +1/64 +1/128 +1/256 +1/512 +1/1024) =
21.77_g *1023/1024,
21.77_g/2 +21.77_g/4 +21.77_g/8, for the first three terms of the series calculated using the binary procedure.
10.88_g +5.44_g +2.72_g, for the first three terms of the series calculated.
10.68_g +4.94_g +2.09_g, for the first three terms of the series measured with one inch as the distance between the magnets and the scale.

Twice the first measured term of 10.68_g estimates 21.36_g for the sequence of ten magnets. We see that this approach is near the correct overall force between a single magnet and a series of ten magnets with 21.77_g measured, but the first three calculated individual terms are a little too big so the last calculated terms will be too small. These last terms will be too small to measure. This approach is ongoing with gradual improvements in experimental technique.

The first magnet had a force of 10.68_g. The first ten magnet stack had a force of 21.77_g. The force with a twenty magnet stack equals 22.74_g. The force with a forty magnet stack equals 22.92_g. The second ten magnets only added 0.97_g. The second twenty magnets only added 0.18_g.

This is only a start in research by weighing magnetic repulsion using quarter inch cube magnets. I also have eighth inch cube magnets. Cylinder magnets may be better. This is a series with decreasing increments which too quickly become too small for my 0.01_g display scale and non-uniform neodymium magnets which vary by more than 0.25_g in force when separated by one inch.

Twenty magnets makes a dipole twenty times longer than a dipole made with one magnet. The first dipole had 10.68_g on one end and -10.68_g on the other end separated by one magnet and 6.35_mm. The dipole moment of one magnet q*d is 67.82_g*mm. Twenty magnets makes a dipole with a force of 22.74_g on one end and -22.74_g on the other end separated by twenty magnets and 127_mm. The dipole moment of twenty magnets q*d is 2888_g*mm. This force is more complex than the analysis of isolated dipoles would suggest. A long series of dipoles has an accumulated force on their oppositely charged ends and a lot of distance between their ends for a large q*d.

Capacitors When the two parallel plates of a capacitor are connected across a battery they store energy. The plates become charged and attract each other with an electric field between them. Some say the energy is stored in the electric field between the plates. If you disdain the abstraction and distraction of the field then the forces between the plates may be analyzed just as well as any fields.
Q*E = Q2/(4*pi*e0*r2), the electrical force equals the Coulomb force.
The charged plates are only held apart by some type of mechanical structure so the electrical force, Q*E measures the force of attraction of the plates. The actual force between the plates is measured in this electric forces between charged plates lab and in this Coulomb balance lab.

Useful details are in this current balance lab..
A circuit is not necessary for electrostatic gravity
Polarized atoms storing their tiny gravitational charge do not need to be wired together. If there is a conductive path their electrostatic gravity is unimpeded. The bipolar atoms are like capacitors and are arranged in series, along each row, so
Qseries = Q1 = Q2 = Q3, they all have the same small gravitational charge.
Cseries = 1/(1/C1 + 1/C2 + 1/C3), 1/(n*(1/C)) = C/n, since n, the number of capacitors is very large, the capacitance of the row is very low.
Vseries = V1 + V2 + V3, This is a voltage divider over a very large number of capacitors where there is a conductive path.
The capacitors are arranged in parallel rows, so
Qparallel = Q1 + Q2 + Q3, is the sum of the charge in all the rows, which is the sum of all the charge. The total charge is undiluted by series or parallel effects. All the individual atomic gravitational charges participate in the gravitational effect if there is a conductive path or not.
Cparallel = C1 + C2 + C3, this is the sum of the capacitance of the rows. A large sum of small capacitance is what? The capacitance is unknown.
Vparallel = V1 = V2 = V3, The voltage drop along the parallel rows is the same where there is a conductive path.

Capacitors
Spherical capacitor
Q*E = Q2/(4*pi*e0*r2), the electrical force equals the Coulomb force.
E = Q/(4*pi*e0*r2) = volts/meter = force/charge = kg*m/(a*s3), divided by Q.
V/r = Q/(4*pi*e0*r2), substituted V/r for E.
V = Q/(4*pi*e0*r) = volts = energy/charge = kg*m2/(a*s3), multiplied by r.
Q/V = 4*pi*e0*r = C = Farads = charge2/energy = a2*s4/(kg*m2), this is the capacitance of a isolated sphere with a radius r. As r increases the capacitance goes up.

Parallel plate capacitor using force and charge
Q = C*V, charge = charge2/energy * energy/charge, energy = Q*V
Q = C*E*d, substituted E*d for V, V = E*d, E = V/d, charge = charge2/energy * force/charge * distance, energy = Q*E*d
Q = C*d*Q/(area*e0), substituted Q/(area*e0) for E, E = D/e0 = charge density/permittivity: D = charge density = Q/area: E = Q/(area*e0), so force/charge = charge/(area)* force*area/(charge2), so e0 = charge2/(force*area) = a2*s4/(kg*m3)
C = e0*area/d, canceled Q, charge2/energy = charge2/(force*area) *area/(distance), capacitance in a plate capacitor. If the area goes up, or the distance between the plates decreases, the capacitance goes up.
Q = e0*area *V/d, substituted e0*area/d for C, in Q = C*V, charge = charge2/(force*area) *area *energy/(charge)*1/(distance), Combined the above equations. Even something as complex as the capacitor can be understood in terms of charge, force, energy, distance and action-at-a-distance without any reference to electric fields.

Atoms as capacitors
Two oppositely charged ellipsoid ends of polarized bipolar atoms, work the same as the parallel plate capacitors. If the voltage (energy/charge) is constant, while the area of the plates or the charged area of the ellipsoid ends increases, then the charge goes up. As an atom becomes more polarized the opposite charges at each end of the ellipsoid increases as the atoms charges become more separated. The charged area increases. The distance between the ends of neighbor atoms decreases as the atoms become more ellipsoid. An increase in the area of the charge or a decrease in the distance apart of the charges on neighbor atoms both increase the capacitance. The energy required is converted to additional charge stored between the plates or ellipsoids. Where we see forces or accelerations we see charge. Charge is starting to look like a placeholder for force on the plates. Energy is conserved.

Charged concentric spherical shell atoms
Binary orbits in a plane are stable in isolation. Stable atoms, which we see in photos, require the spherical symmetry which they acquire by the precession of their orbits out of the plane. The electrons and protons are not confined to the two dimensions of a plane. They orbit in three dimensions. Atoms are spherical spinning precessing dipoles. This is how medical scanners and microwave ovens work. In a proton-electron binary atom, the proton is close to the center of mass where it orbits and precesses. This is seen as a charge spread over a spherical surface traced out by the orbiting and precessing proton. The electron across the center of mass from the proton and farther out but orbiting with the same angular velocity as the proton is also like a charge spread over a spherical surface traced out by the orbiting and precessing electron. Is this an electron cloud? How can a cloud-like electron become a negative ion particle? What you see depends on the metaphors you use. The surface of the atom, the electron orbit, is negative for circular orbits. Negative spherical surfaces of atoms repel each other and do not clump together without being polarized. The positive surface of a positive ion would be attracted and pulled into the negative surface of an atom. They would merge until the ion and atom were at equilibrium, until the ion reached the region of charge neutrality within the atom which is halfway between the electron spherical surface and the much smaller proton spherical surface. The positive ion would be repelled by the proton within the atom beyond the region of charge neutrality. This leaves us with the familiar image of bonding as overlapping spherical atoms.

An atom as a concentric spherical capacitor
This is another approach to charge separation. Aren't the electron and proton in the Bohr atom somewhat like the oppositely charged parallel plates of a capacitor? Or the oppositely charged concentric spherical plates of a capacitor? The proton orbit is like a sphere of charge surrounded by the much larger sphere of charge of the electron orbit. While they are neutral they are spherical and concentric. As the charges separate the spheres become ellipsoids. The ellipsoid ends become oppositely charged. Their area increases. Their capacitance increases.
The electron orbit is considered as a negatively charged sphere with a radius of re = 5.2889E-11_m.
The proton orbit is considered as a positively charged sphere with a radius of rp = re*me/mp = 2.8804E-14_m.
The distance between the spheres is re-rp = 5.28602E-11_m apart.
Q/V = C = Farads = 4*pi*e0*r = charge2/energy = a2*s4/(kg*m2), This is the capacitance of a isolated spherical capacitor. We can use this formula for a concentric spherical capacitor with r defined in a special way. Here,
r = 1/(1/(rp) - 1/(re)) = re*rp/(re-rp) = re*me/(mp-me) = 2.88159E-14_m, this r is only slightly larger than the proton sphere rp.
C = 4*pi*e0*r = 4*pi*e0*2.88159E-14_m = 3.2061E-24_Farads, additional charge could be imposed by electrostatic gravity with or without a change in geometry.

Charged ends of atoms
The positive end of an atom has a positive _a*s charge and the negative end of an atom has a negative _a*s charge. This is the very small polarized charge of the atom. This is the slight separation of the much larger charges of the electron and proton in the atom.

Force between the ends of the polarized atom
Q*E = Q2/(4*pi*e0*d2) = _kg*m/s2,
E = Q*E/Q = _kg*m/s2/(_a*s) = _volts/meter,

Gravitational energy stored between the ends of the polarized atom
Q2/(4*pi*e0*D) = _kg*m2/s2,

Voltage drop across the gravitational capacitor
Q = e0*a *V/d, formula for a plate capacitor.
V = Q*d/(e0*A), isolate V. We are solving for the voltage drop across each gravitational capacitor.
Q = _a*s, gravitational charge of an atom.
d = ratom*e = 2 *5.292E-11_m * e = _m, spacing of the capacitor plates is the distance between the foci. This is the separation between the centers of the electron and proton ellipses. The centers are no longer concentric.
ratom2*pi/2 = 5.292E-11_m2*pi/2 = 4.3987E-21_m2, area of a ellipsoid end or plate is half the surface of the Bohr atom.
V = Q*d/(e0*A) = _kg*m2/(a*s3), volts/atom

Capacitance of an atom:
Q/V = C =_a*s/(_volts) = _Farad per atom. These tiny capacitors depend on the electro negativity and electro positivity of the atoms to work. A very small eccentricity, in an almost perfectly circular orbit, allows atoms to become polarized.
Useful equations
me = 9.1094E-31_kg, mass of the electron
ce = 1.6021E-19_a*s, charge of the electron
mp = 1.6726E-27_kg, mass of the proton
c = 299792458_m/s, speed of light
alpha = .007297 or 1/137.036, fine structure constant
hp = 2*pi*me*c*rc/alpha = 6.626E-34 _kg*m2/s, Plank's constant
e0 = 1E7/(4*pi*c2)_a2*s2/(kg*m) = 8.854E-12_a2*s4/(kg*m3), e0 = charge2/(force*area) , permittivity of vacuum.
Avogadro's number? = (c/(u0*hp)).5 = (c3*e0/hp).5 = 6.000359E23_a*s/(kg*m)
G = 6.6739 E-11_m3/(kg*s2) is the gravitational constant.
rc = ce2/(4*pi*e0*me*c2) = 2.82E-15_m, the classical radius of the electron or
me*c2 = ce2/(4*pi *e0 *rc), The rest energy of the electron equals the energy associated with the charge of the electron of ce and a radius of rc. If the rest energy increases then rc decreases.

These papers go some way in the right direction
Accelerating superconducting disk produces reversing pulses of gravitation
Spinning super conductors - Gravitational attraction when accelerated in one direction and repulsion when accelerated in the other has been experimentally detected by Tajmar.

Electromagnetic drive
emDrive - This looks like the drive which will be used in space craft of the future. It is an impulse drive where microwaves in a truncated cone magnetron push harder on the small end of the cone than the larger. I hope this is real and can compete with plasma drive. New Scientist magazine had a wonderful article showing a flying car on the cover a few years ago. http://www.emdrive.com/

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