If you have an object that is moving with a constant velocity around a planet the force gravity would be greater then the normal force. Why?

The force of gravity acts downward; the normal force acts upward. Assuming there are no other forces acting on the object, the sum of those forces must equal $mvec a$.

If the planet is spherical then the only way the acceleration can be purely vertical while the object is confined to the surface is if it's moving at constant speed on a great circle. In that case the net force is the centripetal force which points downward, so the gravitational force must be larger than the normal force (unless the speed is zero in which case they're equal).

In a way, the object is falling. In fact if the speed is just right then the normal force is zero, and the object is in a freefall orbit just above the surface.