How to Calculate Gravitational Acceleration on a Planet with Core and Shell?

[jrw]

I am trying to figure out a gravitational acceleration of a planetary surface with two parts; a core and shell, radius and densities for each are given. I am not sure which equation to use to get started, will I find the gravitational acceleration of the core and then the shell? I just am not sure where to start off. Thanks for any advice that can be shared.

 

[Nabeshin]

Well, by Newton's shell theorem you know that you can consider the entire planet to be a simple point mass at the center. So one way to solve the problem would be to compute the total mass, that is core + shell, and use this to solve for gravitational acceleration on the surface from the familiar equation.

 

[jrw]

but how do I account for the density change?

 

[Janus]

but how do I account for the density change?

If you are just concerned about the surface gravity and your planet is spherical, you don't have to.

 

[jrw]

If you are just concerned about the surface gravity and your planet is spherical, you don't have to.

I guess then I am confused on which density I should use. I am given only the density and radius, so I found the volume of the planet using the total radius, but then to find the mass I need density * volume right?

 

[Janus]

I guess then I am confused on which density I should use. I am given only the density and radius, so I found the volume of the planet using the total radius, but then to find the mass I need density * volume right?

You use both densities. You have to find the mass of the core and shell separately, and then sum them together to find the total mass.

 

[jrw]

You use both densities. You have to find the mass of the core and shell separately, and then sum them together to find the total mass.

Oh I see thank you very much :)

 

[Nabeshin]

Evidently I lack clarity.