[SPACE] Rules considering Lagrange Points in Advanced Worldbuilding

Agemegos · 02-21-2010, 05:46 PM

Strictly speaking the stability limits of the Trojan points are unknown, since the Lagrangian solution holds only for test masses (i.e. if the mass of the third body is ignored). No analytical solution exists for that case of the three-body problem. As for numerical simulations, I understand that they always lead to a collision or the expulsion of the smaller body for any mass ratio that is tried.

Obviously the orbits are close enough to stable for really large mass ratios, since there are Trojan asteroids and analogues in the orbit of Saturn. But I don't know of any Trojan-analogues in the orbit of Earth, which suggests that the ratio of masses of Earth to an asteroid visible at 1 AU is not enough. One of the leading theories for the formation of the Moon is that an object about the size of Mars formed in one of Earth's Trojan points, where its orbit was unstable and led in time (only 20–30 million years) to a collision.

I can't be quite definite, but I would have to guess that having a planet in the Trojan point of another planet, even a gas giant, is a space opera conceit rather than a hard SF plausibility.

02-21-2010, 05:46 PM	#5
Agemegos Join Date: May 2005 Location: Oz	Re: [SPACE] Rules considering Lagrange Points in Advanced Worldbuilding Strictly speaking the stability limits of the Trojan points are unknown, since the Lagrangian solution holds only for test masses (i.e. if the mass of the third body is ignored). No analytical solution exists for that case of the three-body problem. As for numerical simulations, I understand that they always lead to a collision or the expulsion of the smaller body for any mass ratio that is tried. Obviously the orbits are close enough to stable for really large mass ratios, since there are Trojan asteroids and analogues in the orbit of Saturn. But I don't know of any Trojan-analogues in the orbit of Earth, which suggests that the ratio of masses of Earth to an asteroid visible at 1 AU is not enough. One of the leading theories for the formation of the Moon is that an object about the size of Mars formed in one of Earth's Trojan points, where its orbit was unstable and led in time (only 20–30 million years) to a collision. I can't be quite definite, but I would have to guess that having a planet in the Trojan point of another planet, even a gas giant, is a space opera conceit rather than a hard SF plausibility.