# How does the shape of a planetary body affect the orbit of its moon?

More specifically, would the distortion from a sphere of the planetary body lead to shifts in angular momentum for the moon.

• Depends on how the distortion and the axis of orbit are arranged relative to each other. – Jon Custer Oct 19 '18 at 16:07

If you are dealing with a closed system (a planet and its moon only), then the orbital motion is due to gravitational force, which is a central force. The total angular momentum of the system will remain constant.

The angular momentum may be transferred back and forth between the planet and the moon, depending on the spherical aberrations of each, but the angular momentum about the center of mass of the system will be constant.

So, yes, it's possible that the angular momentum of the moon could change and its orbit about the center of mass of the planet be non-elliptical. But it would be a repetitive pattern.

This is actually how we have mapped the spherical aberration of Earth using a pair of satellites, one behind the other. Their relative velocities are mapped as they travel in a common orbit. NASA's version was/is called GRACE.

• Just one more thing, if the object were not to be a sphere then the orbit would still be spherical or would this not be conserved? (in a closed system) – John Miller Oct 19 '18 at 17:47
• Which object is not a sphere? The planet or the satellite? And there isn't a spherical orbit. It's elliptical. Maybe you're thinking circular, which is a special case of an ellipse. – Bill N Oct 19 '18 at 21:36
• Sorry the planet, I'm actually applying this to something else that's why I'm not being very specific. Just imagine the planet is perfectly spherical, in which case you'd assume the orbit of the satellite is perfectly circular, and then how does the imperfect shape of the planet affect the shape of the orbit. Sorry if I'm being a bit vague. – John Miller Oct 20 '18 at 10:04
• Even with a spherically symmetric planet the orbit may not be circular. It would be elliptical, depending on the total energy and angular momentum. An irregular mass distribution would make for a non-elliptical orbit, but the system angular momentum would be constant. – Bill N Oct 20 '18 at 22:22
• To get the specific orbit on the non-symmetric mass would require some fancy numerical simulation. – Bill N Oct 20 '18 at 22:23