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L4 and L5, the Lagrange points 60 degrees leading and trailing an orbiting body, are famous for being stable.

I will label the central mass S, orbiting mass J and the L4 mass T:

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It's said S/J needs to be equal to or greater than 24.96 for the system to be stable. For a stable system there's a ceiling on J, it can't be more than 4% of S.

My question: Is there a ceiling on mass T? If T were as massive as J, could the system still be stable?

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1 Answer 1

This wiki (moon creation theory) says at about 10% of your 'J' the orbit of an L4 or L5 (your 'T') destabilizes.

Possible origin of Theia

In 2004, Princeton University mathematician Edward Belbruno and astrophysicist J. Richard Gott III proposed that Theia coalesced at the L4 or L5 Lagrangian point relative to Earth (in about the same orbit and about 60° ahead or behind), similar to a trojan asteroid. Two-dimensional computer models suggest that the stability of Theia's proposed trojan orbit would have been affected when its growing mass exceeded a threshold of approximately 10% of the Earth's mass (the mass of Mars). In this scenario, gravitational perturbations by planetesimals caused Theia to depart from its stable Lagrangian location, and subsequent interactions with proto-Earth led to a collision between the two bodies.


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