Transfer angles for every circular orbit

transfer.py

#! /usr/bin/python

#
# ----------------------------------------------------------------------------
# "THE BEER-WARE LICENSE" (Revision 42):
# <Gnonthgol@gmail.com> wrote this file. As long as you retain this notice you
# can do whatever you want with this stuff. If we meet some day, and you think
# this stuff is worth it, you can buy me a beer in return Gnonthgol
# ----------------------------------------------------------------------------
#

from math import pi, sqrt, sin, cos

def ang(r):
	if r == 0:
		return 0.0
	return -pi*(1-(1/(2*sqrt(2))*sqrt((1/r+1)**3)))

def xy(r):
	if r == 0:
		return (0.0, 0.0)
	a = ang(r)
	return (cos(a)*r, sin(a)*r)

r = (0.001*400)**2

co = [xy((0.001*i)**2) for i in range(400, 2500)]

path = "M " + " ".join(["%.4f %.4f"%(x,y) for (x,y) in co])

print """<?xml version="1.0" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN" 
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg width="1080px" height="1920px" viewBox="0 0 1.1 1.1"
     xmlns="http://www.w3.org/2000/svg" version="1.1">
  <title>Transfer angles</title>
  <desc>Hohman transfer angles in any system</desc>
  <style type="text/css"><![CDATA[
    .Graph {{ fill:none; stroke:green; stroke-width:0.01 }}
    .Sun {{ fill:none }}
    .Earth {{ fill:#000000 }}
    .Orbit {{ fill:none; stroke:#888888; stroke-width:0.01 }}
    .Cross {{ fill:none; stroke:grey; stroke-width:0.005 }}
  ]]></style>

  <g transform="translate(0.5,1) scale(0.5)">
    <path class="Graph" d="{path}" />
    <circle class="Graph" cx="0" cy="0" r="{r}" />
    <circle class="Sun" cx="0" cy="0" r="0.1" />
    <path class="Cross" d="M -0.1 0 L 0.1 0 M 0 -0.1 L 0 0.1" />
    <circle class="Orbit" cx="0" cy="0" r="1" />
    <circle class="Earth" cx="1" cy="0" r="0.03" />
    <path class="Cross" d="M 0.97 0 L 1.03 0 M 1 -0.03 L 1 0.03" />
  </g>
</svg>""".format(path=path, r=r)

transfer.svg

<?xml version="1.0" standalone="no"?>
<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN" 
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
<svg width="1080px" height="1920px" viewBox="0 0 1.1 1.1"
     xmlns="http://www.w3.org/2000/svg" version="1.1">
  <title>Transfer angles</title>
  <desc>Hohman transfer angles in any system</desc>
  <style type="text/css"><![CDATA[
    .Graph { fill:none; stroke:green; stroke-width:0.01 }
    .Sun { fill:none }
    .Earth { fill:#000000 }
    .Orbit { fill:none; stroke:#888888; stroke-width:0.01 }
    .Cross { fill:none; stroke:grey; stroke-width:0.005 }
  ]]></style>

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