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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 R. An object is located a distance R from the center of the planet, where R < Rp. (The object is located inside of the planet.)

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

2) Rewrite your result for g(R) in terms of gp, the gravitational acceleration at the surface of the planet, times a function of R.

So, I have seen this question on the forum before, but I am still unsure about the concept.

For 1, I found $$g(R) = \frac{Gp(4/3)*π*R^3}{R^2}$$, which is the correct answer. However, I do not understand why R^3 in the numerator is R^3 and not (R_p)^3. In the equation $$g = \frac{GM}{R^2}$$ M is the entire mass of the planet or spherical body. Wouldn't that require $$M=p*(4/3)*π*R^3$$

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

2) Rewrite your result for g(R) in terms of gp, the gravitational acceleration at the surface of the planet, times a function of R.

**Relevant equations:**

$$g = \frac{GM}{R^2}$$$$g = \frac{GM}{R^2}$$

So, I have seen this question on the forum before, but I am still unsure about the concept.

For 1, I found $$g(R) = \frac{Gp(4/3)*π*R^3}{R^2}$$, which is the correct answer. However, I do not understand why R^3 in the numerator is R^3 and not (R_p)^3. In the equation $$g = \frac{GM}{R^2}$$ M is the entire mass of the planet or spherical body. Wouldn't that require $$M=p*(4/3)*π*R^3$$

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