File:Bi-elliptic transfer r-ratio14.svg

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Original file (SVG file, nominally 800 × 760 pixels, file size: 4 KB)

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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
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This vector image was created with Python.
Source code
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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

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I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
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.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

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Date/TimeThumbnailDimensionsUserComment
current17:07, 29 May 2020Thumbnail for version as of 17:07, 29 May 2020800 × 760 (4 KB)Geek3 (talk | contribs)Uploaded own work with UploadWizard

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