universal gravitation

Question

Calculate the force of gravity on a 95 kg person at the surface of the Earth. The acceleration of gravity is 9.8 m/s2 . Answer in units of N.

a) Calculate force of gravity- that's completed

Need help on:

b)What force of gravity exists at two times the Earth’s radius? Answer in units of N.

c)What force of gravity exists at four times the Earth’s radius? Answer in units of N.

Answer 1

The universal force of gravity is used to determine the gravitational force between any two objects based on the distance between them.

F_g = G m₁m₂ / r²

The answer to b involves using the radius of the earth r_e times 2, that will be our r in the above equation.

F_g = G m₁m₂ / (2*r_e)²

The interesting bit of physics is how this answer compares to the answer in part a. In part a we had:

F_g^a = G m₁m₂ / (r_e)²

If we divide the answer to a and b we get that basically everything cancels

[F_g^a = G m₁m₂ / (r_e)²] / [F_g^b = G m₁m₂ / (2*r_e)²]

F_g^a_/F_g^b = [G/G] [m₁m₂ /m₁m₂] [(r_e)² / (2*r_e)²]

The only terms that are not 1 are F_g^a_/F_g^b and [(r_e)² / (2*r_e)²].

The first term is the ratio of the value of the force of gravity in part a and b and the second term is 1/4. So the answer to b will scale by 1/4 compared to your answer in a.

You can make the same arguments for part c or use the same equation and plug in the relevant 4*r_e