Is falling in vacuum reversible or irreversible process? Process is reversible if

*

*you can return to initial state through the same intermediate equillibrium states and

*cause infinitesimaly small changes in surrounding area.

Does that mean that falling in vacuum is reversible or irreversible process? Please explain, even if it's a reversible process how can falling body return to initial state through the same intermediate states as before?
 A: The word “reversible” has (at least) two different meanings in physics. We must distinguish between time reversibility and thermodynamic reversibility.
As the orbit and frictionless roller coaster examples in the comments show, falling in vacuum is time reversible. We can travel around a closed loop in phase space (in actual space we return to the same position with the same momentum) with no input of external energy. So if we reverse our momentum vector we have demonstrated time reversibility - the “backwards” version of our trajectory is also physically feasible.
Thermodynamic reversibility - which is what the definition that you quote refers to - is different. A thermodynamically reversible process must proceed through a series of equilibrium states that have infinitesimally small effects on
the surrounding environment. A true thermodynamically reversible process would therefore take an infinite amount of time. It is a theoretical abstraction which is useful in thought experiments but not physically realisable.
A spacecraft or a satellite orbiting in vacuum is not thermodynamically reversible because it causes small but finite changes in the position and momentum of the primary body. Gravity assist manoeuvres exploit this non-reversibility to exchange energy between a spacecraft and a planet. The Moon’s orbit is not thermodynamically reversible because it is gradually moving away from the Earth due to tidal forces, which dissipate energy.
