File:Bi-elliptic transfer r-ratio14.svg

Summary

Description
English: A bi-elliptic transfer from a low circular starting orbit (dark blue), to a higher circular orbit (green). The spaceship is traveling in a counterclockwise direction during all segments of the orbital transfer as is indicated by the blue and green arrows. When the spacecraft arrives at point 1 it performs a prograde burn to enter the first portion of the transfer orbit (red segment). It then coasts until apoapsis of this transfer orbit located at point 2 where another prograde burn is performed to raise the point of periapsis until it coincides with the orbital radius of the desired orbit. The spacecraft then turns off its engine again and coasts along the orange segment until it arrives at point 3. The maneuver is completed by performing a retrograde burn at point 3 to slow the spacecraft down and lower apoapsis until the orbit is circular again. The image shows exactly computed trajectories of a bi-elliptic transfer with a ratio of orbit radii of 14, where the apoapsis is 26.10 times the smaller orbit radius. In this case the transfer is as efficient as a Hohmann transfer, for larger apoapses it is even more efficient. Source code below.
Date
Source Own work
Author Geek3
Other versions Bi-elliptic transfer.svg
SVG development
InfoField
Source code
InfoField

Python code

Python svgwrite code
#!/usr/bin/python3
# -*- coding: utf8 -*-

try:
    import svgwrite
except ImportError:
    print('requires svgwrite library: https://pypi.org/project/svgwrite/')
    # documentation at https://svgwrite.readthedocs.io/
    exit(1)

from math import *

# document
size = 800, 760
name = 'bi-elliptic_transfer_r-ratio14'
doc = svgwrite.Drawing(name + '.svg', profile='full', size=size)
doc.set_desc(name, name + '''.svg
https://commons.wikimedia.org/wiki/File:''' + name + '.svg')

# background
doc.add(doc.rect(id='background', insert=(0, 0), size=size, fill='white', stroke='none'))

r1 = 18
r2 = 14 * r1
rb = 26.10 * r1

g = doc.add(doc.g(transform='translate(500, 380)', fill='none'))

sun = g.add(doc.g(id='sun'))
nbeam = 12
rsun, rsun2 = 6, 5.5
rbeam = 10
p = []
for i in range(nbeam):
    phi0, phi1 = 2*pi*i/nbeam, 2*pi*(i+0.5)/nbeam
    p += [[rbeam*cos(phi0), rbeam*sin(phi0)], [rsun2*cos(phi1), rsun2*sin(phi1)]]
sun.add(doc.polygon(points=p, stroke='#f89c16', stroke_width=1, fill='#dbf816',
                    stroke_miterlimit=8))
grad = doc.defs.add(doc.radialGradient(id='grad', center=(0.5, 0.5), r=0.5,
                                       gradientUnits="objectBoundingBox"))
grad.add_stop_color(offset=0, color='#dbf816')
grad.add_stop_color(offset=1, color='#f89c16')
sun.add(doc.circle(center=(0, 0), r=rsun, stroke='#f89c16', stroke_width=1,
    fill='url(#grad)'))

arrow_d = 'M 0.3,0 L -0.8,0.5 Q -0.5,0 -0.8,-0.5 Z'
doc.defs.add(doc.marker(id='arrow1', refX=-0.3, refY=0, viewBox='-1 -1 2 2',
    orient='auto', markerWidth=8, markerHeight=8)).add(doc.path(
        d=arrow_d, stroke='none', fill='#0000c4'))
doc.defs.add(doc.marker(id='arrow2', refX=-0.3, refY=0, viewBox='-1 -1 2 2',
    orient='auto', markerWidth=8, markerHeight=8)).add(doc.path(
        d=arrow_d, stroke='none', fill='#00b956'))
doc.defs.add(doc.marker(id='arrow3', refX=0, refY=0, viewBox='-1 -1 2 2',
    orient='auto', markerWidth=8, markerHeight=8)).add(doc.path(
        d=arrow_d, stroke='none', fill='#333333'))
doc.defs.add(doc.marker(id='line_start', refX=0, refY=0, viewBox='-1 -1 2 2',
    orient='auto', markerWidth=8, markerHeight=8)).add(doc.path(
        d='M -0.07,0.5 H 0.07 V -0.5 H -0.07 V 0.5 Z', stroke='none', fill='#333333'))

g.add(doc.path(d='M {0},0 A {1},{1} 0 0 0 {1},0 A {1},{1} 0 0 0 {0},0'.format(-r1, r1),
      stroke='#0000c4', stroke_width=4, marker_end='url(#arrow1)'))
g.add(doc.path(d='M {0},0 A {1},{1} 0 0 0 {1},0 A {1},{1} 0 0 0 {0},0'.format(-r2, r2),
      stroke='#00b956', stroke_width=4, marker_end='url(#arrow2)'))

a1 = (r1 + rb) / 2
b1 = sqrt(a1**2 - (a1 - r1)**2)
a2 = (r2 + rb) / 2
b2 = sqrt(a2**2 - (a2 - r2)**2)

g.add(doc.path(d='M {},0 A {},{} 0 0 0 {},0'.format(-rb, a1, b1, r1),
      stroke='#dc0d0d', stroke_width=2, stroke_dasharray='2,4'))
g.add(doc.path(d='M {},0 A {},{} 0 0 0 {},0'.format(r2, a2, b2, -rb),
      stroke='#ff991b', stroke_width=2, stroke_dasharray='2,4'))
g.add(doc.path(d='M {},0 A {},{} 0 0 0 {},0'.format(r1, a1, b1, -rb),
      stroke='#dc0d0d', stroke_width=5))
g.add(doc.path(d='M {},0 A {},{} 0 0 0 {},0'.format(-rb, a2, b2, r2),
      stroke='#ff991b', stroke_width=5))

dv1 = sqrt(2/r1 - 1/a1) - sqrt(1/r1)
dv2 = sqrt(2/rb - 1/a2) - sqrt(2/rb - 1/a1)
dv3 = sqrt(2/r2 - 1/a2) - sqrt(1/r2)
l1 = 220

g.add(doc.line(start=(r1, 0), end=(r1, -l1),
      stroke='#333333', stroke_width=3,
      marker_start='url(#line_start)', marker_end='url(#arrow3)'))
g.add(doc.line(start=(-rb, 0), end=(-rb, l1*dv2/dv1),
      stroke='#333333', stroke_width=3,
      marker_start='url(#line_start)', marker_end='url(#arrow3)'))
g.add(doc.line(start=(r2, 0), end=(r2, l1*dv3/dv1),
      stroke='#333333', stroke_width=3,
      marker_start='url(#line_start)', marker_end='url(#arrow3)'))

# text
g.add(doc.text('1', font_size='48px', stroke='none', fill='black',
      text_anchor='middle', transform='translate(50, 18)',
      font_family='Bitstream Vera Sans'))
g.add(doc.text('2', font_size='48px', stroke='none', fill='black',
      text_anchor='middle', transform='translate(-435, 18)',
      font_family='Bitstream Vera Sans'))
g.add(doc.text('3', font_size='48px', stroke='none', fill='black',
      text_anchor='middle', transform='translate(218, 18)',
      font_family='Bitstream Vera Sans'))

doc.save(pretty=True)

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
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You are free:
  • to share – to copy, distribute and transmit the work
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Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
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Category:CC-BY-SA-4.0#Bi-elliptic%20transfer%20r-ratio14.svgCategory:Self-published work
Category:Celestial mechanics Category:SVG spaceflight Category:Orbits of spacecraft Category:Photos by User:Geek3
Category:CC-BY-SA-4.0 Category:Celestial mechanics Category:Orbits of spacecraft Category:Photos by User:Geek3 Category:SVG spaceflight Category:Self-published work Category:Valid SVG created with Python code