Gravitational Acceleration inside a Planet

[Superfluous]

The problem:

Consider a spherical planet of uniform density $$\rho$$. 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 $$R\precR_{p}$$ . (The object is located inside of the planet.)

Part A

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

Express the acceleration due to gravity in terms of $$\rho$$, $$R$$, $$\pi$$, and $$G$$, the universal gravitational constant.

Part B

Rewrite your result for $$g(R)$$ in terms of $$g_{p}$$, the gravitational acceleration at the surface of the planet, times a function of R.

Express your answer in terms of $$g_{p}$$, $$R$$, and $$R_{p}$$.

My attempt at a solution:

I determined the answer to Part A to be $$g(R)=(4/3)G\rho \pi R$$. However, I am uncertain how to find the answer to Part B. I barely even understand what they are asking me to do. I could really use some hints to point me in the right direction.

Thanks.

 

[Shooting Star]

They want you to eliminate G, rho etc, and express the ans you got in terms of g at surface.

You do know that M = (4/3)pi*Rp^3*rho. Also, you should know g at surface using law of gravitation. Use all these to eliminate the unwanted stuff.

 

[Superfluous]

Ok, well I've tried to work this out, but I'm basically just guessing at everything--I'm that clueless. I don't even see how knowing M will help me. I don't know what to do.

 

[D H]

Express your answer in terms of $$g_{p}$$, $$R$$, and $$R_{p}$$.

What the question is asking you to do is to find some function $f$ such that

$$g(R) = f(g_p,R_p,R)$$

In other words, somehow replace the $G$ and $\rho$ from the solution already at hand,

$$g(R) = \frac 4 3 G \pho \pi R$$

with $g_p$ and $R_p$. What is $g_p$?

 

[Shooting Star]

Ok, well I've tried to work this out, but I'm basically just guessing at everything--I'm that clueless. I don't even see how knowing M will help me. I don't know what to do.

Put Rp in place of R in the formula you derived in our first post. Remember, g(Rp) is the g_p at the surface. So, you can write g(R) in terms of g_p and R.

 

[abiriax]

i'm doing the same question, got the first part right and i got to admit, i still don't get it, i know it has something to do with substiting the value of g_p but and that that can be obtained by using the universal law of gravitation, but after that i am stumped.

 

[abiriax]

just worked it out, you got to subsitute formulae and you should end up with R*g_p/R_p