Orbital Perturbations and Resonances 

Let's look at another example of the three body problem. Instead of the Earth, let's compare forces from Jupiter and the Sun on an object at R=3.28 AU (so between Mars and Jupiter. What objects live there?)
Bigger than for the Earth, but still not huge (< 1%). So why is this important?
Think about cumulative effects? What if this object continually felt this force?

This is referred to as an orbital perturbation -- a little nudge away from its current orbit.

But an object won't always feel that strong of a perturbing force (why not?). And the perturbing force it does feel, is constantly changing direction (why?)

Let's look again at our hypothetical object at R=3.28 AU. What is its period?

and remember Jupiter's period:

So notice that

So every second time around the sun, that asteroid "sees" Jupiter in the same spot. This is called an orbital resonance -- in this case a 2:1 resonance.

When you have a resonant perturbation, interesting things happen!

The Kirkwood Gaps: Gaps in the radial distribution of asteroids in the solar system.