Question

derive the relation between gravitational potential and gravitational field

Answer 1

Answer:

Relation between gravitational field and gravitational potential. The gravitational field is the negative differential of the gravitational potential. Now the gravitational potential due to a particle at a distance r is −Gm/r where m is the mass of the particle.

Answer 2

Small work done to displace a unit mass from A to B.

dw =-f×dx

dw =-E×dx. (E=f/m=f/1)

This work done is equal to gravitational potential difference so

dv =dw

dv = -E×dx

Hence E =-dv/dx

Where dv/dx is gravitational potential gradient.