Question

Topic: gravitational fields

The question says how much work is done by the gravitational field in moving a mass m of 2kg from infinity to a point A, 0.4m from a mass M of 30kg?

I know that gravitational potential is
Phi = -GM/r

The answer in the book is:
W = m phi(A) = -mGM/r

Now my question is why did they take phi(A) instead of g in the equation of work (W=mg)?
Are gravitational field strength and gravitational potential the same?

Thank you

Answer 1

No, they are not.
The answer took A as the work done was to move it from infinity to point .
Notice that g is a variable and is actually \(\frac{-GM}{r^2}\), and that W is work, not gravitational force (\(F_g =mg\)).

Answer 2

thank you