Why do small bodies stay in orbit around large bodies?

[Jireat]

I know this sounds like an elementary question with an easy answer.

However, I was thinking about chaos theory. Planets and stars are always changing so that their gravitational pulls towards other objects varies. Shouldn't the tiniest change between the pull of a star and a planet, or a planet and its moon (change due to rotation or distance [elliptical paths]) cause smaller objects to either get increasingly close or increasingly far from the large objects, per unit time?

Thank you in advance!

 

[Orodruin]

Shouldn't the tiniest change between the pull of a star and a planet, or a planet and its moon (change due to rotation or distance [elliptical paths]) cause smaller objects to either get increasingly close or increasingly far from the large objects, per unit time?

No. Why do you think this would be the case?

 

[A.T.]

However, I was thinking about chaos theory. Planets and stars are always changing so that their gravitational pulls towards other objects varies. Shouldn't the tiniest change between the pull of a star and a planet, or a planet and its moon (change due to rotation or distance [elliptical paths]) cause smaller objects to either get increasingly close or increasingly far from the large objects, per unit time?

The orbits you see today are those which happened to be stable enough to survive millions of years. They might be changing slightly over time, but those changes are constrained by energy and momentum conservation, so a planet cannot just fly off.

 

[Bandersnatch]

No.

Wouldn't you say that it's actually a yes, as long as you give n-body interactions enough time?

 

[Orodruin]

Wouldn't you say that it's actually a yes, as long as you give n-body interactions enough time?

I would say the OP deals with a two-body system:

the pull of a star and a planet, or a planet and its moon

 

[russ_watters]

Planets and stars are always changing so that their gravitational pulls towards other objects varies. Shouldn't the tiniest change between the pull of a star and a planet, or a planet and its moon (change due to rotation or distance [elliptical paths]) cause smaller objects to either get increasingly close or increasingly far from the large objects, per unit time?

First: How "tiny" is "tiniest"? Its pretty tiny: you can Google it for Earth.

Second, a lot of people have a misconception about orbits, that they are very unstable and that the slightest perturbation will cause the objects to spiral apart or together. In reality, they are very stable and even a major perturbation will only reshape them: To make two objects that are in a circular orbit crash into each other requires dissipating almost all of the orbital energy. Much less and you just change the shape into a more elliptical orbit.