File:Aberrationlighttimebeaming.gif
From Wikimedia Commons, the free media repository
Jump to navigation
Jump to search
Aberrationlighttimebeaming.gif (400 × 220 pixels, file size: 126 KB, MIME type: image/gif, looped, 26 frames, 20 s)
File information
Structured data
Captions
Summary[edit]
DescriptionAberrationlighttimebeaming.gif |
English: Animation showing the relationship between the aberration of light, light-time correction, and relativistic beaming
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[edit]
Ahalda at English Wikipedia, the copyright holder of this work, hereby publishes it under the following licenses:
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.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
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[edit]
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]] |
The categories of this image need checking. You can do so here.
|
This plot was created with Matplotlib.
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 10:03, 5 February 2016 | 400 × 220 (126 KB) | Wiki LIC (talk | contribs) | Transferred from en.wikipedia |
You cannot overwrite this file.
File usage on Commons
There are no pages that use this file.
File usage on other wikis
The following other wikis use this file:
- Usage on ca.wikipedia.org
- Usage on en.wikipedia.org
- Usage on es.wikipedia.org