Gravitation (Preliminary Reference Earth Model)

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SUMMARY

The discussion focuses on deriving the equation for gravitational force as a function of radius, given the density of Earth as a function of radius, denoted as ρ(r). The approach involves considering the Earth as a series of hollow spheres and integrating to find the gravitational force. Key concepts include the volume of a hollow sphere and the relationship between mass, density, and volume. Participants share insights on the integration process and offer assistance for related problems.

PREREQUISITES
  • Understanding of gravitational theory and Newton's law of gravitation.
  • Knowledge of calculus, specifically integration techniques.
  • Familiarity with the concept of density as a function of radius.
  • Basic principles of spherical geometry and volume calculations.
NEXT STEPS
  • Research the derivation of gravitational force from density functions in astrophysics.
  • Study the integration of functions related to spherical coordinates.
  • Explore the implications of the Preliminary Reference Earth Model (PREM) on gravitational calculations.
  • Learn about the applications of gravitational equations in geophysics and planetary science.
USEFUL FOR

Students in physics or engineering, particularly those studying gravitational theories, geophysics, or anyone interested in the mathematical modeling of Earth's structure.

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Homework Statement



Assuming that we know the density of Earth as a function of radius, we have to derive the equation for gravity as the function of radius.

Homework Equations


The Attempt at a Solution



lets us choose density as [tex]\rho[/tex](r).
I know that within a hollow sphere there is no gravity.
We can assume sum of several hollow spheres with thickness dr, where r is the radius of the shell from center, and then we can integrate it.
I know its an easy question we used to do in undergraduate study, but I am missing something and i can't figure out how it was done? Please help!
 
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Hint: what is the volume of a hollow sphere, radius=r, thickness=dr?

Given the volume and density, what would be it's mass?
 
Thanks Redbelly98!

I did this problem. However I am having another problem in an associated problem with this question. I am working it out, however if I get stuck then i would ask you to help me.

Thanks once again!
 

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