1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Gravitational Acceleration inside a Planet

  1. Nov 27, 2007 #1
    The problem:

    Consider a spherical planet of uniform density [tex]\rho[/tex]. The distance from the planet's center to its surface (i.e., the planet's radius) is [tex]R_{p}[/tex]. An object is located a distance [tex]R[/tex] from the center of the planet, where [tex]R\precR_{p}[/tex] . (The object is located inside of the planet.)

    Part A

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

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

    Part B

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

    Express your answer in terms of [tex]g_{p}[/tex], [tex]R[/tex], and [tex]R_{p}[/tex].

    My attempt at a solution:

    I determined the answer to Part A to be [tex]g(R)=(4/3)G\rho \pi R[/tex]. 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.
     
  2. jcsd
  3. Nov 27, 2007 #2

    Shooting Star

    User Avatar
    Homework Helper

    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.
     
  4. Nov 27, 2007 #3
    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.
     
  5. Nov 27, 2007 #4

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    What the question is asking you to do is to find some function [itex]f[/itex] such that

    [tex]g(R) = f(g_p,R_p,R)[/tex]

    In other words, somehow replace the [itex]G[/itex] and [itex]\rho[/itex] from the solution already at hand,

    [tex]g(R) = \frac 4 3 G \pho \pi R[/tex]

    with [itex]g_p[/itex] and [itex]R_p[/itex]. What is [itex]g_p[/itex]?
     
  6. Nov 28, 2007 #5

    Shooting Star

    User Avatar
    Homework Helper

    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.
     
  7. Nov 16, 2008 #6
    i'm doing the same question, got the first part right and i gotta 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.
     
  8. Nov 16, 2008 #7
    just worked it out, you gotta subsitute formulae and you should end up with R*g_p/R_p
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?