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

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Discussion Overview

The discussion revolves around calculating the gravitational acceleration on the surface of a planet composed of a core and a shell, with specific focus on the equations and methods to use given the radii and densities of each component.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant seeks guidance on which equation to use for calculating gravitational acceleration, expressing uncertainty about how to approach the problem.
  • Another participant references Newton's shell theorem, suggesting that the planet can be treated as a point mass at the center for the purpose of calculating gravitational acceleration.
  • Questions arise regarding how to account for changes in density when calculating gravitational acceleration.
  • Clarification is provided that if the planet is spherical and the focus is on surface gravity, the density change may not need to be considered.
  • A participant expresses confusion about which density to use, noting that they have only been given the density and radius, and seeks confirmation on the method for calculating mass.
  • It is suggested that both densities should be used to find the mass of the core and shell separately before summing them to find the total mass.
  • A participant acknowledges their lack of clarity in understanding the process.

Areas of Agreement / Disagreement

Participants express uncertainty and confusion regarding the appropriate methods and equations to use, indicating that multiple competing views remain on how to approach the calculation of gravitational acceleration.

Contextual Notes

There are limitations regarding the assumptions made about density and the spherical nature of the planet, as well as the dependence on the definitions of core and shell in the context of gravitational calculations.

jrw
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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.
 
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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.
 
but how do I account for the density change?
 
jrw said:
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.
 
Janus said:
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?
 
jrw said:
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.
 
Janus said:
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 :)
 
Evidently I lack clarity.
 

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