File:Lagrangian points equipotential.gif

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Lagrangian_points_equipotential.gif (512 × 384 pixels, file size: 2 MB, MIME type: image/gif, looped, 72 frames, 7.2 s)

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Summary

[edit]
Description
English: Animation showing the relationship between the five Lagrangian points (red) of a planet (blue) orbiting a star (yellow), and the gravitational potential in the plane containing the orbit (grey surface with purple contours of equal potential). The potential was computed in POV-Ray using

for q = 0.1 and z = 0.[1]
Source Own work
Author cmglee
Other versions
Lagrangian points equipotential.png
Lagrangian points equipotential.jpg
Roche potential.stl

POV-Ray source code

[edit]
Lagrangian_points_equipotential.pov Lagrangian_points_equipotential.ini 
#declare rotation = clock;
// #declare rotation = -28;
#declare bounding_radius = 8;
#declare q = 0.1;
#declare q_plus_1 = q + 1;
#declare q_divide_q_plus_1 = q / q_plus_1;
#declare two_divide_q_plus_1 = 2 / q_plus_1;

union {
 isosurface {
  function {
   y + (pow(x-q_divide_q_plus_1,2) + z*z + two_divide_q_plus_1 * (q / sqrt((x-1)*(x-1)+z*z) + 1 / sqrt(x*x + z*z)))
  } 
  accuracy     0.001
  max_gradient 200 // increase to reduce artifact in funnel
  contained_by {sphere{0,bounding_radius}} open
  pigment {
   gradient <0,1,0>
   color_map {                                               [0.01 color rgb <0.5,0,0.75>][0.02 color rgb 1]
              [0.18 color rgb 1][0.19 color rgb <0.75,0.5,1>][0.21 color rgb <0.75,0.5,1>][0.22 color rgb 1]
              [0.38 color rgb 1][0.39 color rgb <0.75,0.5,1>][0.41 color rgb <0.75,0.5,1>][0.42 color rgb 1]
              [0.58 color rgb 1][0.59 color rgb <0.75,0.5,1>][0.61 color rgb <0.75,0.5,1>][0.62 color rgb 1]
              [0.78 color rgb 1][0.79 color rgb <0.75,0.5,1>][0.81 color rgb <0.75,0.5,1>][0.82 color rgb 1]
              [0.98 color rgb 1][0.99 color rgb <0.75,0.5,1>]                                               }
   scale 0.5
   translate <0,0.03,0>
  }
  scale     <1,0.5,1>
  translate <0,1.42,0>
 }
 union {
  sphere {0,0.2          pigment {rgbt <1,1,0,0.5>}   interior {ior 1} finish {specular 1 roughness 0.1} }
  sphere {<1,0,0>,0.1    pigment {rgbt <0,0.5,1,0.5>} interior {ior 1} finish {specular 1 roughness 0.1} }
  sphere {<q/2,0,0>,0.05 pigment {rgb  <0.5,0,0>} }
  union {
   torus    {1-q/2,0.02 translate <q/2,0,0>}
   cylinder {<-0.95,0,0>,<1.35,0,0>,0.02}
   cylinder {<q/2,0,0>,<0.5,0,0.866>,0.02}
   cylinder {<q/2,0,0>,<0.5,0,-0.866>,0.02}
   pigment  {rgb <0,0.75,0>}
  }
  union {
   union { sphere {0,0.05} cylinder {0,<0,-9,0>,0.02} text {ttf "arlrdbd.ttf" "L1" 0.2, -0.1 scale 0.4 translate <-0.15,0.05,-0.1> rotate <55,rotation,0> no_shadow} translate <0.72,0,0> }
   union { sphere {0,0.05} cylinder {0,<0,-9,0>,0.02} text {ttf "arlrdbd.ttf" "L2" 0.2, -0.1 scale 0.4 translate <-0.15,0.05,-0.1> rotate <55,rotation,0> no_shadow} translate <1.35,0,0> }
   union { sphere {0,0.05} cylinder {0,<0,-9,0>,0.02} text {ttf "arlrdbd.ttf" "L3" 0.2, -0.1 scale 0.4 translate <-0.15,0.05,-0.1> rotate <55,rotation,0> no_shadow} translate <-0.95,0,0> }
   union { sphere {0,0.05} cylinder {0,<0,-9,0>,0.02} text {ttf "arlrdbd.ttf" "L4" 0.2, -0.1 scale 0.4 translate <-0.15,0.05,-0.1> rotate <55,rotation,0> no_shadow} translate <0.5,0,0.866> }
   union { sphere {0,0.05} cylinder {0,<0,-9,0>,0.02} text {ttf "arlrdbd.ttf" "L5" 0.2, -0.1 scale 0.4 translate <-0.15,0.05,-0.1> rotate <55,rotation,0> no_shadow} translate <0.5,0,-0.866> }
   pigment {rgb <1,0,0>}
  }
 }
 translate <-q/2,-0.14,0>
 rotate    <0,-rotation,0>
}
sky_sphere {pigment {rgb 1}}
light_source {<0,1,0>    color rgb 0.5 parallel point_at 0}
light_source {<0,10,-10> color rgb 1   shadowless}
camera {orthographic location <0.05,7.8,-10> look_at <0.05,-0.1,0> angle 13.8}

Antialias=off
Antialias_Threshold=0.01
Antialias_Depth=2

Input_File_Name="Lagrangian_points_equipotential.pov"

Initial_Frame=0
Final_Frame=71
Initial_Clock=0
Final_Clock=360

Cyclic_Animation=on
Pause_when_Done=off
  1. ↑ ZF Seidov, "The Roche Problem: Some Analytics", The Astrophysical Journal, 603:283-284, 2004 March 1

Licensing

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I, the copyright holder of this work, hereby publish it under the following licenses:
w:en:Creative Commons
attribution share alike
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  • 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.
  • 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.
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.
You may select the license of your choice.

File history

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Date/TimeThumbnailDimensionsUserComment
current23:57, 22 October 2021Thumbnail for version as of 23:57, 22 October 2021512 × 384 (2 MB)Cmglee (talk | contribs)Increase resolution and framerate, rotate around barycentre, reframe image and make bodies transparent
10:35, 16 February 2013Thumbnail for version as of 10:35, 16 February 2013256 × 192 (709 KB)Cmglee (talk | contribs)Use 6-bit GIFs.
10:06, 16 February 2013Thumbnail for version as of 10:06, 16 February 2013256 × 192 (574 KB)Cmglee (talk | contribs)Fix shifting background colour.
09:51, 16 February 2013Thumbnail for version as of 09:51, 16 February 2013256 × 192 (574 KB)Cmglee (talk | contribs)Orbit around barycentre instead of Sun, darken every fifth contour and double number of frames.
23:41, 15 February 2013Thumbnail for version as of 23:41, 15 February 2013256 × 192 (354 KB)Cmglee (talk | contribs){{Information |Description ={{en|1=Animation showing the relationship between the five Lagrangian points (red) of a planet (blue) orbiting a star (yellow), and the gravitational potential in the plane containing the orbit (grey surface with purple c...

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