Is it possible to have a small planet to have a larger moon orbiting it?

I dont think this is possible because mass is proportional to gravity. Therefore, a larger mass equals larger gravity. Also, electrons orbit the nucleus not because of gravity but electrostatic forces.

Mass is the key determining factor as to where the center of gravity is located.

In order for an object with greater volume to orbit one of lesser volume, the one with lesser volume would need to have more mass... if it has more mass and less volume, then it has a much greater density. All the objects in our solar system fit the model of the larger object having greater mass as well, and with very few exceptions, this barycenter is located within the surface of the primary, while the secondaries orbit around the larger body.

If you could somehow find a way to condense the mass of the Earth into a volme less than that of the Moon, and kept the mass of both objects the same, the Moon's orbit would not change. But this smaller Earth of equal mass would have a smaller radius. If this radius was too small, the barycenter would lie closer to the 'New Earth' but not necessarily inside of its surface.

The two would orbit the barycenter, just like they do now. But in the case of Pluto and Charon, the barycenter lies outside of both objects.

The center of rotation for the Earth and Moon system is the common center of mass, which is a couple thousand miles from the center of the Earth. In every case, a planet and its moon(s) orbit around their common center of mass, which will be within the more massive object.

Take Pluto and Charon -- see the link below -- each of which orbits around their common center of mass, which is outside either body (but nearer to Pluto).

Size is not really the issue, but mass. A gas giant might be larger in diameter, but less massive than a rocky planet, for example. We still have to consider the common center of mass as the axis of rotation.

actually the terms 'planet' and moon ' are often arbitrary. In such cases there is a Primary and a Satellite. The satellite is usually taken to be the secondary body and is referred to as the 'moon'. The primary is called the planet. The difference in terminology derives from which is considered to revolve around which. The moon is considered to revolve around the primary. By and large, unless there exists a definition (which I hav never seen) then it may be taken that such terms are purely arbitrary and depndent upon perception and preference.

What if you had two bodies of equal size and mass revolving about each other? which would you call the planet and which the moon? You would be obliged to refer to them as constituting a double-planet system. In fact our own Earth-Moon system is sometimes called a double-planet system.

The object with the greater mass is always orbited by the object with less mass because of the conservation mass, energy. and momentum in a two or three body system. Of course, IF you choose the body with less mass to be the fixed reference point of your inertial frame of reference, then the the larger body can and does orbit the smaller body without violating any laws of physics

In any orbiting pair, they always actually orbit their barycentre, the average centre of their masses. This is always within or close to the larger of the two objects, so the effect is _always_ that the smaller object orbits the larger, and so would be called the "moon" of the pair.

Usually, bigger things have bigger gravity. That's why smaller things will orbit around bigger things. The planet is the rock that is bigger and thus has a larger gravity than the moon which is the rock that is smaller and has a puny gravity.

If the planet was small and heavy and the moon was big and light perhaps it would work

If there was a moon as big as Saturn orbiting the Earth, the gravity from the moon would pull the Earth in and then the moon would eat it. :)

The object with the greater mass will attract a moon. So technically possible.