What would cause a moon to not orbit around the center of the planet that has it as its satellite?

Question

There is no world or setting attached to this question but it does have me curious and might be useful for those who do actually want to build a world with this as a feature. Imagine a luna-like moon that orbits an earth-like planet but the moon does not orbit around the center of the planet, instead it orbits around the planet like how a marble might roll around a tennis ball on a flat floor. Its orbital ring is offset to be flatter and nearer to the 'floor' of the solar system but still orbits the planet that has it as a satellite.

What would cause a moon to orbit a planet like this?

Answer 1

I found a few possible causes for decentered, and even non-elliptic paths for moons,

• the moon is very far away from the planet, in this case the orbit will not become elliptical, it could follow a horse-shoe shaped path,

https://theconversation.com/earths-other-moon-and-its-crazy-orbit-could-reveal-mysteries-of-the-solar-system-38010

• the moon was not formed from planet matter, like Earth's moon, rather it was kept in orbit after a collision event, to get a new orbit around the planet/moon system. At first, it could have a very decentric orbit.

https://www.theguardian.com/science/2021/nov/11/near-earth-asteroid-is-a-fragment-from-the-moon-say-scientists

Eventually, depending on the mass (see L. Dutch answer), the object will impact, or its orbit will stabilize as a centered ellipse, or a wobbling centered ellipse, when other moons are near,

https://www.firstpost.com/tech/science/nasas-hubble-catches-a-pair-of-neptunes-moons-in-a-truly-bizarre-dance-of-avoidance-7669001.html

• there is a regular disturbance of the moon's orbit, due to a nearby planet or another, heavier moon in the same system. The decentricity of the orbit would become periodic, when the disturbance of the orbit will also be periodic.

https://solarsystem.nasa.gov/moons/saturn-moons/aegaeon/in-depth/

In any case, a decentered orbit is temporary. All orbits around a single center of gravity become elliptical and centered in due time.

Answer 2

A planet is defined as a body under hydrostatic equilibrium. In that condition, its center of mass will overlap with its geometrical center.

The only way for what you are asking to happen is to have a body not massive enough to be a planet but rather a potatoid like Ultima Thule

orbited by a body with an even lower mass.

In the configuration shown in the picture, if the biggest clump of the potatoid is also more massive, the center of mass will be located somewhere there, and the orbits would revolve around it, away from the geometrical center.