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whitetiger

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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

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

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