# Stationary Inter-planetary Satellite?

Is there a way to place a satellite in-between two planetary bodies such that the force from each gravitational pull is effectively nullified? In other words, is there any type of situation that would allow for us to place a satellite in-between orbits of two planets such that it wouldn't be moving at all? Is there any way to maintain this state for an extended period of time (the answer here can be in terms of any arrangement of planets, not in terms of our solar system).

I was thinking that if you had a planet orbiting closer to the star at a slower speed and one further from the star at a higher speed such that their orbits synchronized, you may be able to place a satellite between the two and maintain solar orbit indefinitely with no degradation, is this a dumb train of thought? Taking this further, I haven't read much about Lagrange points, but theoretically is there any planetary configuration that allows for a constant Lagrange point that never moves whereas most change with the orbit of the bodies in question?

• "wouldn't be moving at all" relative to what? – Organic Marble Apr 11 '18 at 23:15
• @OrganicMarble for the first half of the question, I assumed it would be able to maintain a stable solar orbit (E.G. the orbit around the star wouldn't degrade). For the latter half, I mean a stationary solar orbit. – Magic Octopus Urn Apr 11 '18 at 23:22

was thinking that if you had a planet orbiting closer to the star at a slower speed and one further from the star at a higher speed such that their orbits synchronized

That doesn't happen. Two orbits at different distances inevitably have different orbital periods (one orbit takes longer to complete than the other).

The exception is the Lagrange points L1 and L2, as described by uhoh, but then you're not talking about 2 planets, but 1 planet and a much smaller body (e.g. a satellite).

• I'm not sure what the mass limit is for a 1:1 resonance; that's a fascinating question! – uhoh Apr 12 '18 at 11:35
• – uhoh Apr 12 '18 at 12:17

This is an interesting question!

...if you had a planet orbiting closer to the star at a slower speed and one further from the star at a higher speed such that their orbits synchronized, you may be able to place a satellite between the two and maintain solar orbit indefinitely with no degradation.

That might describe the relative motion of a planet (say Jupiter) and a much smaller body like an asteroid, in a 1:1 resonance such as in a halo orbit around L1 (or L2 if you modify the wording slightly). While there are some halo orbits that are stable in the mathematical circular restricted three-body problem (CR3BP), in a real solar system with elliptical orbits and multiple planets, these orbits will probably not last a very long time.

There are other potential orbits with 1:1 resonance as well.

All of these are really heliocentric orbits.

However, is there yet another heliocentric orbit between Jupiter and one of these CR3BP resonances so that it would appear to be "fixed" to Jupiter, or at least somehow constrained to be roughly between Jupiter and the (presumably massive) asteroid? I've never heard of such an orbit. A non-existence proof is tough, but to date, I've never seen a discussion of such a thing.

The only other abstraction would be a body trapped at a Lagrangian point of a massive moon of Jupiter, but that will still orbit Jupiter, so it probably does not qualify as an answer to your question, not to mention that it would not likely be long-term stable either.

• I didn't understand half of that, but I'm wikipedia-ing as fast as I can. I was also thinking about asking this question as "what if there existed a planet as massive as the sun, how would the orbits between those two bodies work? What could make this scenario possibly exist?" Not quite the same, but the same spirit... – Magic Octopus Urn Apr 11 '18 at 23:23
• @MagicOctopusUrn take your time! This SE site is a bit more easy-going than some of the others. There's no rush. But try to ask one question at a time. If you would like to ask about a binary system of similar masses (two stars or a star and a planet of similar mass) I think that that would be a fundamentally different question. – uhoh Apr 11 '18 at 23:26
• Agreed, I just didn't really know how to ask it. I feel like any incoming asteroids between a star and planet of similar mass would almost be forcibly interjected between the two bodies after a single orbit of the outer body, or inner body depending on which it encountered first. Hence the similarity... But of course, I'm just speculating... I'm an amateur lol. Also I've read a lot of your answers, thanks for all of them. – Magic Octopus Urn Apr 11 '18 at 23:29
• After looking up the n-body problem I doubt this has a concrete answer, a far as I can tell. – Magic Octopus Urn Apr 11 '18 at 23:41