'This program draws a binary system of an electron and
    'proton in an elliptical orbit. We follow the laws
    'of Kepler. They sweep out equal areas in equal times.
    'Each position of the electron and proton are separated
    'by equal areas and time periods.

    nomainwin

    WindowWidth = 900
    WindowHeight = 800

    open "ellipse.txt"for graphics as #1
     #1 "color black ; down ;  size  1 "
    ' #1 "rule "; _R2_NOTXORPEN

    for zzz=1 to 10:gosub [main]
    if zzz<10 then #1 "cls ":gosub [delay]
    next zzz
    goto [exit]
'*********************************************
[delay]
for z=0 to 3000:next z
    '#1 "cls "
return
'*********************************************
[main]
    fr = .4'eccentricity
    x0=600'right focus
    y0=360
    pi = asn(1) * 2
    circleR= 750'200 'width of ellipse
    a=circleR/2  'a=half width of ellipse
    outer = circleR/2*(1-fr) '=140 focus to right side of ellipse
    eccx = fr
    eccy = sqr(1 - eccx^2)
    b=a*eccy
    areaellipse=pi*a*b
    dfoci = circleR*fr/2' =60 half distance between foci
    divider=31:dec=6.28*.1/divider
    area=areaellipse/divider '11  using constant area triangles
    '**************************************************
     r = outer+.05
     angle =0
      #1 "color blue ":#1 "backcolor blue"
      #1 "place "; x0 ; " "; y0
      #1 "goto "; x0 - outer/5 ; " "; y0 'top circle
      #1 "circlefilled 2 "
      #1 "color red ":#1 "backcolor red"
      #1 "place "; x0 ; " "; y0
      #1 "goto "; x0 + outer ; " "; y0 'top circle
      #1 "circlefilled 8 "
      gosub [delay]
 while angle< 3.14159 - dec
     #1 "color red ":#1 "backcolor red"
     gosub [doCosAngle]
      #1 "place "; x0 ; " "; y0
      #1 "goto "; x0 + (r*cosAngle) ; " "; y0 + (r*sinAngle)'top circle
      #1 "circlefilled 8 "
      #1 "color blue ":#1 "backcolor blue"
      #1 "place "; x0 ; " "; y0
      #1 "goto "; x0 + -1*(r/5*cosAngle) ; " "; y0 + -1*(r/5*sinAngle) ;
      #1 "circlefilled 2 "
      gosub [delay]
 wend

while angle < 6.28 - (20*dec)
    gosub [doCosAngle]
     #1 "color red ":#1 "backcolor red"
     #1 "place "; x0; " "; y0
     #1 "goto "; x0+r*cosAngle ; " "; y0+ (-1*r*sinAngle) ;'bottom circle
     #1 "circlefilled 8 "
     #1 "color blue ":#1 "backcolor blue"
     #1 "place "; x0 ; " "; y0
     #1 "goto "; x0 + -1*(r/5*cosAngle) ; " "; y0 + (r/5*sinAngle) ;
     #1 "circlefilled 2 "
      gosub [delay]
wend
return
'**************************************************
[doCosAngle]
    'angle = ACS(((circleR/2*(1 - fr^2)/r) - 1)/fr)'r sets the angle
    anginc=area/r^2
    r1 =circleR/2*(1 - fr^2)/(cos(angle+anginc)*fr+1)
    anginc=area/(r*r1)
    r1 =circleR/2*(1 - fr^2)/(cos(angle+anginc)*fr+1)
    angle=angle+anginc
    cosAngle =cos(angle)'((circleR/2*(1 - fr^2)/r1) - 1)/fr
    sinAngle = sin(ACS(cosAngle))  'why does this work
    r = r1
return
'**************************************************
[exit]
  #1 "flush "
  'gosub [save]
  wait
  ' #1 "discard"'no redraw info kept
  close #1
  end
'**************************************************
[save]
     #1 "getbmp drawing 1 1 "; 800;" ";800
    ' #1 "place 1 1 ";
    ' #1 "box "; 286; " "; 284;
    ' #1 "flush"
    filedialog "Save as...", "test", filename$
    if filename$ = " " then wait
    filename$ = filename$ + ".bmp"
    bmpsave "drawing", filename$
return
'**************************************************