Acceleration due to gravity is given by:
Gravitational Acceleration inside a Planet
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 R from the center of the planet, where R<Rp. (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.
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.
Frequently Asked Questions
What scientific concept do you need to know in order to solve this problem?
Our tutors have indicated that to solve this problem you will need to apply the Universal Law of Gravitation concept. You can view video lessons to learn Universal Law of Gravitation. Or if you need more Universal Law of Gravitation practice, you can also practice Universal Law of Gravitation practice problems.