Question

The energy of a system depwnds upon mass and acceleration due to gravity and length derive a relation

Answer 1

Given an object of mass m in a gravitational field due to a body of mass M, the force upon either would be GMm/(r^2) where G is the Gravitational constant, and r is the distance between the two masses.

Since Force = (mass)(acceleration), hence you can see that:-

Acceleration of mass m due to gravity = GM/(r^2)

Acceleration of mass M due to gravity = Gm/(r^2)

So the acceleration of a given mass due to gravity does not depend upon the said mass.

Addendum (just to cover all the bases):-

However, if your question is/was whether the acceleration due to gravity depends upon the mass exerting the gravitational force, then Yes.

Hope this helps.