Gravitational Acceleration inside a Planet

In summary, when an object is located a distance R from the center of a spherical planet, its gravitational acceleration is given by g(R) = (4/3)p(pi^2)R(G).
  • #1
whitetiger
22
0
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
 
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  • #2
It can be shown, and I will assume you are supposed to use the fact that any mass that is outside of the radius from the center of the planet to the point in question does not contribute any net gravitational force. This is related to the fact that you can treat the mass of a spherical object as if it were located at its center when doing gravitity calculations. What you need to do is find the total mass that is within the distance R from the center of the planet.
 
  • #3
OlderDan said:
It can be shown, and I will assume you are supposed to use the fact that any mass that is outside of the radius from the center of the planet to the point in question does not contribute any net gravitational force. This is related to the fact that you can treat the mass of a spherical object as if it were located at its center when doing gravitity calculations. What you need to do is find the total mass that is within the distance R from the center of the planet.

Thank you for the help. I have finally figured out the problem.
 
  • #4
OlderDan said:
It can be shown, and I will assume you are supposed to use the fact that any mass that is outside of the radius from the center of the planet to the point in question does not contribute any net gravitational force. This is related to the fact that you can treat the mass of a spherical object as if it were located at its center when doing gravitity calculations. What you need to do is find the total mass that is within the distance R from the center of the planet.

Can you or someone please explain the solution in a better way? I'm stumped on part 2 of this problem, and this explanation made it more confusing.

Thanks!
 

Related to Gravitational Acceleration inside a Planet

1.

What is gravitational acceleration inside a planet?

Gravitational acceleration inside a planet refers to the rate at which objects accelerate towards the planet's center due to the planet's gravitational pull.

2.

How is gravitational acceleration inside a planet calculated?

The formula for calculating gravitational acceleration inside a planet is g = G(M/r2), where g is the gravitational acceleration, G is the universal gravitational constant, M is the mass of the planet, and r is the distance from the object to the center of the planet.

3.

Does gravitational acceleration inside a planet vary?

Yes, the gravitational acceleration inside a planet can vary depending on the mass and radius of the planet. The higher the mass and the smaller the radius, the stronger the gravitational acceleration will be.

4.

How does gravitational acceleration inside a planet compare to that on the planet's surface?

Gravitational acceleration inside a planet is typically lower than that on the planet's surface. This is because as you move closer to the center of the planet, there is less mass pulling on the object.

5.

What factors can affect gravitational acceleration inside a planet?

The main factors that affect gravitational acceleration inside a planet are the planet's mass and radius. Other factors such as the planet's rotation and composition can also have an effect.

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