How reliant is the Solar System on being exactly the way it is?

Question

We know that all objects with mass exert forces on all other objects of mass such that

$$ F = \frac{GMm}{R^2}.$$

And as others have discussed the planets do interfere with each other gravitationally to a small degree.

My question is how reliant the solar system is on its exact structure. If a planet were to change its alignment or orbit or gravitational effect on other planets, through gain of a mass through an asteroidal collision for example.

Would a deviation in the structure of the solar system as it is cause it to collapse? e.g planets change orbits significantly enough to drift away from the sun or drift into it?

Answer 1

This is something I played with while testing a n-body code I wrote during college. Unfortunately I don't have any animations, or even the original code anymore - but I can report qualitative results.

Removing Jupiter and Saturn does indeed have a significant destabilizing effect -- an a chaotic one at that (i.e. depending on precise initial conditions, and varying on numerical accuracy) -- leading to the dynamical instability of numerous planets.

Removing the other planets had no effect on dynamical stability, but there were some small changes to periods, etc.

This result should be expected as the gravitational effects of planets other than Jupiter (and saturn to a lesser degree) are almost entirely negligible on the dynamics of other planets.