Are L4 and L5 Lagrange Points Stable with M1/M2 ≥ 24.96?

Thread starter E92M3
Start date Oct 23, 2009
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Points Stability

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L4 and L5 Lagrange points are stable only when the mass ratio of two bodies, M1/M2, is greater than or equal to 24.96. This stability condition is crucial for the formation of stable orbits around these points. The claim is supported by a citation that provides a complete proof, which can be found in the linked document from WMAP. Understanding this stability criterion is essential for applications in celestial mechanics and space mission design. The discussion emphasizes the importance of mass ratios in determining the stability of Lagrange points.

Oct 23, 2009

E92M3

I was reading this on wiki:
http://en.wikipedia.org/wiki/Lagrangian_point

In the stability section, it claimed that for L4 and L5 to be stable the following must hold:

\frac{M_1}{M_2}\geq24.96

Why is this the case? Where can I find proof?

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Oct 23, 2009

ideasrule

Homework Helper

That claim has a citation:

http://wmap.gsfc.nasa.gov/media/ContentMedia/lagrange.pdf

where you'll find the complete proof

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