The shortest or longest path in curved space between two points is geodesic . What about a body having no potential energy was put in geodesic near earth , what makes it move , May be it is about the space , what does it something to do with motion ,"if question sounds nonsense please ignore
Once things are moving, they just keep moving with the same velocity. This is part of what we mean by “inertia”, and it’s just Newton’s First Law. There doesn’t need to be an explanation for why things keep the same velocity. There only needs to be an explanation when they don’t.
Geodesic motion is just the generalization of this idea to curved spacetime. Geodesic motion keeps the velocity constant. In curved spacetime one has to decide how to compare vectors such as velocity at different points as something moves. This is done with a procedure called “parallel transport”. One definition of a geodesic is that it parallel-transports its tangent vector, and this means the velocity doesn’t change.