The other thing to consider is that your golf balls are able to move at different velocities because there are two objects with no fixed center of mass between them. With your moon, the gravity is centered 100,000 km from the planet's center. The diameter of the moon isn't really all that important as far as the orbit goes.
Now, if your golf balls were bound together with a fixed point, like a thin rod, you need to look at the gravitational pull for each individual mass, as well as the whole. Because of the inverse square law of gravity, the lower golf ball will have more pull on it than the upper one. As it tries to rotate due to torque, the energy needed to raise it up will be more than the energy pulling the other down. This will keep the low end always pointing at the planet.
At least, this is my understanding.
See below for any corrections.
I'm Not Evil.
An evil person would do the things that pop into my head.