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)
Note: Due to technical limitations, thumbnails of high resolution GIF images such as this one will not be animated.
This file is from Wikimedia Commons and may be used by other projects. The description on its file description page there is shown below.
Summary
DescriptionLagrangian points equipotential.gif |
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] |
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Source | Own work | |||
Author | cmglee | |||
Other versions |
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POV-Ray source code
Lagrangian_points_equipotential.pov | Lagrangian_points_equipotential.ini |
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#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}
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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
|
- ↑ ZF Seidov, "The Roche Problem: Some Analytics", The Astrophysical Journal, 603:283-284, 2004 March 1
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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 |
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File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 01:57, 23 October 2021 | 512 × 384 (2 MB) | wikimediacommons>Cmglee | Increase resolution and framerate, rotate around barycentre, reframe image and make bodies transparent |
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