Collision Theory and Stable Orbits

[omnitom]

Given the extremely numerous and sometimes humongous craters observed all over the place, how big would an impact have to be to disrupt a planet or moon's orbit, seems like the slightest of changes should over time result in chaos over the system. Is there a mechanism to counter this or re-stabilize an orbit? Or would an impact of this magnitude shatter the body entirely so we will never observe such a change?

 

[yevaud]

That's actually two separate questions. So I'll answer one of them, the second:

To actually shatter a planetary body requires overcoming what's known as the binding energy of that body. A rule of thumb is that the impactor would need be as large as the body it impacts, or smaller but traveling at a god-awful relative velocity.

 

[DrRocket]

Given the extremely numerous and sometimes humongous craters observed all over the place, how big would an impact have to be to disrupt a planet or moon's orbit, seems like the slightest of changes should over time result in chaos over the system. Is there a mechanism to counter this or re-stabilize an orbit? Or would an impact of this magnitude shatter the body entirely so we will never observe such a change?

What I am about to tell you in no way contradicts what yevaud has said. His comment relates to actually breaking a body out of orbit entirely. and essentially escaping the system.

The problem of orbital mechanics involving many bodies is intractable for all but a few very special cases. That is, for three or more bodies there is no known closed-form solution for the orbits over time. It is not known whether the orbits of the planets around the sun are stable. They probably are not. But by virtue of simulations over very long periods of time you don't have to worry about the orbits becoming "chaotic" in your lifetime.

So, you are correct. Any small perturbation, or no perturbation at all, might result in a system that becomes unstable at some time in the distant future. The key is the interaction with other orbiting bodies, and not so much any solution to the ordinary two-body problem even with a significant perturbation -- that one is pretty well known from classical mechanics.

For the short term two-body approximations seem to work pretty well, so I wouldn't lose much sleep over any worry of a near-term issue of orbit de-stabilization.

A direct collision between the Earth and something relatively large is quite another thing -- but people are watching and plotting the orbits of potential bodies that might hit us. MeteorWayne can give you some details. So sleep soundly, if something is going to destroy the Earth you will probably have several hours notice, lperhaps even several years. The bad news is that we don't have much in the way of a plan for what to do if we are going to get hit -- but I bet the sales of booze go through the roof.

 

[DrRocket]

That's actually two separate questions. So I'll answer one of them, the second:

Your old avatar was better --- House, the genius with unexplainable penetrating insight and intuition.

You new avatar, the line drawing, looks like House the druggie.

But House on a bad day is better than most of us on a good one.