Can small objects have a gravity?

The force of gravity is

F_g = -GMm<r_hat>/r^2

where r_hat = the unit vector from M toward m.

Yes, if it were started out with the right velocity (~10 µm/s), the marble would go around the bowling ball in a circular orbit with a period of about 8 hr.

All objects have gravity.

A marble wouldnt orbit the bowling ball, you need something huge (like the size of a planet for instance) to see the effects of gravity.

In theory yes, but the escape velocity of the bowling ball would be so low that the marble would have to be barely moving.

From my understanding gravity is one of the biggest mysteries of our universe. some say it is the rotation of a large mass with an iron core but no one has proven much since the apple fell out of the tree. here on earth, when an object spins on an axis centrifugal force moves away from the mass but that law contradicts its self because the earth spins but we stay firmly glued to it. but!! if you set the bowling ball to spin it would spin forever (as long as no other opposing force interrupted its rotation).

hope this helps