Gravitational Acceleration inside a Planet

[whitetiger]

Consider a spherical planet of uniform density p. The distance from the planet's center to its surface (i.e., the planet's radius) is R_p. An object is located a distance R from the center of the planet, where R < R_p. (The object is located inside of the planet.)

Find an expression for the magnitude of the acceleration due to gravity, g(R), inside the planet.

density p = Me / Ve

where Me = (gR^2)/G and Ve = (4/3)piR^3

From the above equations, we try plug everything into the density equation and solve for g. My calculation is

p = ((gR^2)/G)/(4/3)piR^3 and solving for g, I get
g(R) = (4/3)p(pi^2)R(G)

and Rewrite your g(R) in terms of g(p), the gravitational acceleration at the surface of the planet, times a function of R.

I have the first part of the question, but I am not sure how to approach the second part by rewriting g(R) in terms of g(p)

Thank you

 

[OlderDan]

It can be shown, and I will assume you are supposed to use the fact that any mass that is outside of the radius from the center of the planet to the point in question does not contribute any net gravitational force. This is related to the fact that you can treat the mass of a spherical object as if it were located at its center when doing gravitity calculations. What you need to do is find the total mass that is within the distance R from the center of the planet.

 

[whitetiger]

It can be shown, and I will assume you are supposed to use the fact that any mass that is outside of the radius from the center of the planet to the point in question does not contribute any net gravitational force. This is related to the fact that you can treat the mass of a spherical object as if it were located at its center when doing gravitity calculations. What you need to do is find the total mass that is within the distance R from the center of the planet.

Thank you for the help. I have finally figured out the problem.

 

[cj07]

It can be shown, and I will assume you are supposed to use the fact that any mass that is outside of the radius from the center of the planet to the point in question does not contribute any net gravitational force. This is related to the fact that you can treat the mass of a spherical object as if it were located at its center when doing gravitity calculations. What you need to do is find the total mass that is within the distance R from the center of the planet.

Can you or someone please explain the solution in a better way? I'm stumped on part 2 of this problem, and this explanation made it more confusing.

Thanks!