Consider a spherical planet of uniform density ρ. The distance from the planet's center to its surface (i.e., the planet's radius) is Rp. An object is located a distance Rfrom the center of the planet, where R<Rp. (The object is located inside of the planet.)
Find a numerical value for ρearth, the average density of the earth in kilograms per cubic meter. Use 6378km for the radius of the earth, G=6.67×10−11m3/(kg⋅s2), and a value of g at the surface of 9.80m/s2.
Express your answer to three significant figures.
I answered the questions before this, and they go like this:
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 ρ, R, π, and G, the universal gravitational constant.
Rewrite your result for g(R) in terms of gp, the gravitational acceleration at the surface of the planet, times a function of R.
Express your answer in terms of gp, R, and Rp.
The Attempt at a Solution
To be quite honest, I do not know what to do. I need step by step instructions and explanations of why I had to do things that I should have.