File:Lagrangian points equipotential.jpg

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$Image showing the relationship between the five Lagrangian points (red) of a planet (blue) orbiting a star (yellow), and the effective potential (gravitational + rotational) in the plane containing the orbit (grey surface with purple contours of equal potential). The potential was computed in POV-Ray using Ψ ( x , y , z ) = ( x − q 1 + q ) 2 + y 2 + 2 ( 1 + q ) x 2 + y 2 + z 2 + 2 q ( 1 + q ) ( x − 1 ) 2 + y 2 + z 2 {\displaystyle \Psi (x,y,z)={\Big (}x-{\frac {q}{1+q}}{\Big )}^{2}+y^{2}+{\frac {2}{(1+q){\sqrt {x^{2}+y^{2}+z^{2}}}}}+{\frac {2q}{(1+q){\sqrt {(x-1)^{2}+y^{2}+z^{2}}}}}} for q = 0.1 and z = 0.[1]$

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Summary

Description

Image showing the relationship between the five Lagrangian points (red) of a planet (blue) orbiting a star (yellow), and the effective potential (gravitational + rotational) in the plane containing the orbit (grey surface with purple contours of equal potential). The potential was computed in POV-Ray using

$\Psi (x,y,z)={\Big (}x-{\frac {q}{1+q}}{\Big )}^{2}+y^{2}+{\frac {2}{(1+q){\sqrt {x^{2}+y^{2}+z^{2}}}}}+{\frac {2q}{(1+q){\sqrt {(x-1)^{2}+y^{2}+z^{2}}}}}$

for q = 0.1 and z = 0.^[1]

Source

Own work

Author

User:cmglee

Other versions

↑ ZF Seidov, "The Roche Problem: Some Analytics", The Astrophysical Journal, 603:283-284, 2004 March 1

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Original upload log

This image is a derivative work of the following images:

File:Lagrangian_points_equipotential.gif licensed with Cc-by-sa-3.0, GFDL
- 2013-02-15T23:41:06Z Cmglee 256x192 (362667 Bytes) {{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

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File history

Click on a date/time to view the file as it appeared at that time.

	Date/Time	Dimensions	User	Comment
current	01:52, 23 October 2021	1,024 × 768 (256 KB)	Cmglee	Reduce artifacts and noise
	00:56, 23 October 2021	1,024 × 768 (256 KB)	Cmglee	Rerender to match GIF animation and rotate to clearly show L1
	16:48, 17 February 2013	768 × 512 (128 KB)	Cmglee	Improve crop.
	10:22, 16 February 2013	768 × 512 (128 KB)	Cmglee	Increase size and quality.
	23:56, 15 February 2013	384 × 256 (64 KB)	Cmglee	== {{int:filedesc}} == {{Information \|Description={{en\|1=Visualisation of 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 sur...