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File:Aberrationlighttimebeaming.gif

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Aberrationlighttimebeaming.gif (400 × 220 pixels, file size: 126 KB, MIME type: image/gif, looped, 26 frames, 20 s)

Summary

Description
English: Animation showing the relationship between the aberration of light, light-time correction, and relativistic beaming
Other information

Made using the following script:

#!/usr/bin/env python2
from pylab import *
rcParams['savefig.dpi'] = 100
lightcolor = '#ffc22a'
beamcolor = '#234781'
velocitycolor = '#aaaaaa'
def squigglyarrow(x,y,xp,yp, amplitude, ax, wavelength=1, color='b'):
dx, dy = xp-x, yp-y
L = sqrt(dx ** 2 + dy ** 2) or 1
rot = array([[:en:dx/L, -dy/L],
             [dy/L,  dx/L]])
tailL = L - 3*amplitude
t = r_[arange(0, tailL ,wavelength/50.0), tailL]
xy = c_[t, amplitude*sin(2*pi*t/wavelength)]
rxy = rot.dot(xy.T).T
line = Line2D(rxy[:,0] + x, rxy[:,1] + y, color=color, lw=2, zorder=-1)

arrowpath = rot.dot(array([[:en:tailL, 2*amplitude], 
                           [L,0], 
   [tailL, -2*amplitude]]).T).T
arrowhead = Polygon(arrowpath + array([x,y]), color=color, ec='none')
ax.add_artist(line)
ax.add_patch(arrowhead)
def drawframe(axobs, axlit, t):
axobs.add_patch(Circle((0,12), radius=1, color=lightcolor, ec='none'))
axobs.add_patch(Circle((-8 + 8*t,0), radius=1, color='w', ec='k', lw=1))
squigglyarrow(0,12-t*7,-0,12-4-t*7, 0.2, axobs, wavelength=1.13, color=beamcolor)
axobs.set_xticks([])
axobs.set_yticks([])
axobs.set_xlim(-12,8)
axobs.set_ylim(-5,15)
axobs.set_title("Source's rest frame")
axlit.add_patch(Circle((0-8*t,12), radius=1, color=lightcolor, ec='none'))
axlit.add_patch(Circle((-8,0), radius=1, color='w', ec='k', lw=1))
lx, ly = 4.0*8/sqrt(8*8+12*12), 4*12/sqrt(8*8+12*12)
squigglyarrow(0-(8-lx)*t,12-(11-ly)*t,-lx-(8-lx)*t, 12-ly-(11-ly)*t, 0.2, axlit, wavelength=1.13, color=beamcolor)
axlit.set_xticks([])
axlit.set_yticks([])
axlit.set_xlim(-15,5)
axlit.set_ylim(-5,15)
axlit.set_title("Observer's rest frame")
def drawfigaxes(ax):
ax.set_xlim(0,1)
ax.set_ylim(0,1)
ax.set_xticks([])
ax.set_yticks([])
ax.add_artist(Line2D([0.5,0.5], [0,1], color='#888888', zorder=-1))
def drawframes():
fig = figure(figsize=(6,3*1.1), facecolor='white')
axobs = Axes(fig,[0,0,0.5,0.9],yticks=[],xticks=[],frame_on=False)
axlit = Axes(fig,[0.5,0,0.5,0.9],yticks=[],xticks=[],frame_on=False)
figAxes = Axes(fig, [0,0,1,1], yticks=[], xticks=[], frame_on=False)
fig.add_axes(axobs)
fig.add_axes(axlit)
fig.add_axes(figAxes)
drawfigaxes(figAxes)
drawframe(axobs, axlit, 0)
axobs.arrow(-6,0,3,0, width=1, head_width=2, head_length=1, color=velocitycolor, ec='none')
axlit.arrow(-2,12,-3,0, width=1, head_width=2, head_length=1, color=velocitycolor, ec='none')
savefig('init.png')

figAxes.arrow(0.35,0.49,0.22,0, width=0.25, head_width=0.4, head_length=0.1, color='#c0e8cf', ec='none')
figAxes.text(0.5,0.5, 'Lorentz Transform', horizontalalignment='center')
figAxes.text(0.5,0.43, '(Beaming)', horizontalalignment='center')
savefig('init2.png')

figAxes.clear()
drawfigaxes(figAxes)
for t in range(21):
axobs.clear(); axlit.clear()
drawframe(axobs, axlit, t/20.0)
savefig('t{:02d}.png'.format(t))
axobs.arrow(2,0,3,0, width=1, head_width=2, head_length=1, color=velocitycolor, ec='none')
axlit.arrow(-10,12,-3,0, width=1, head_width=2, head_length=1, color=velocitycolor, ec='none')
figAxes.arrow(0.35,0.49,0.22,0, width=0.25, head_width=0.4, head_length=0.1, color='#c0e8cf', ec='none')
figAxes.text(0.5,0.5, 'Lorentz Transform', horizontalalignment='center')
figAxes.text(0.5,0.43, '(Aberration)', horizontalalignment='center')
savefig('end1.png')

axlit.add_patch(Circle((0,12), radius=1, color=lightcolor, ec='none', alpha=0.5))
axlit.text(0,8, 'Apparent\nposition', alpha=0.5, horizontalalignment='center')
savefig('end2.png')
drawframes()
#convert -delay 200 init.png -delay 300 init2.png -delay 10 t* -delay 100 t20.png -delay 200 end1.png -delay 1000 end2.png -loop 0 out.gif
Date
Source matplotlib
Author BlankAxolotl

Licensing

Ahalda at English Wikipedia, the copyright holder of this work, hereby publishes it under the following licenses:
GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
Attribution: Ahalda at English Wikipedia
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.
You may select the license of your choice.

Original upload log

The original description page was here. All following user names refer to en.wikipedia.
Date/Time Dimensions User Comment
2013-05-20 04:46 400×220× (129425 bytes) Ahalda Uploading a self-made file using [[Wikipedia:File_Upload_Wizard|File Upload Wizard]]


 
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20 May 2013

image/gif

429e9e2440d5eac2d1921b70daa499eeaa5896ec

129,425 byte

20.099999999999994 second

220 pixel

400 pixel

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Date/TimeThumbnailDimensionsUserComment
current10:03, 5 February 2016Thumbnail for version as of 10:03, 5 February 2016400 × 220 (126 KB)Wiki LICTransferred from en.wikipedia

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