Equation for Solid Planet Structure

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Discussion Overview

The discussion centers around finding a radial equation to determine the pressure or density within a solid planet or moon, with references to concepts such as Young's modulus and Poisson's ratio. Participants explore various models, including hydrostatic equilibrium and elastic mediums, and express interest in advancing their understanding of planetary structure beyond basic equations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant seeks a radial equation for pressure or density in solid planetary structures, mentioning Young's modulus or Poisson's ratio.
  • Another suggests starting with the equation of hydrostatic equilibrium, applicable to both fluid and elastic medium models, and questions if a Newtonian model is desired.
  • A participant expresses frustration with the suggestion to refer to geophysics books, indicating they have already solved hydrostatic equations for spheres and are looking for more advanced topics.
  • A participant provides a link to a resource, expressing uncertainty about the mathematical content and asking for assistance in applying the formulas to find density and temperature.
  • There is a discussion about the next steps after understanding fluid balls in hydrostatic equilibrium, with suggestions to explore rotation and references to McLaurin spheroids and Chandrasekhar's work.
  • One participant mentions having Chandrasekhar's "Stellar Interiors" and is trying to understand composite polytropes, indicating a desire for examples and clarity on solid planet equations similar to Emden's equation.

Areas of Agreement / Disagreement

Participants express differing views on the appropriate next steps in their studies, with some focusing on hydrostatic equilibrium and others suggesting more advanced topics. No consensus is reached on a specific equation or approach for solid planet structures.

Contextual Notes

Participants reference various models and texts, indicating a range of familiarity with the subject matter. There are unresolved questions regarding the application of certain equations and the understanding of composite polytropes.

Who May Find This Useful

Individuals interested in planetary structure, geophysics, and stellar interiors may find the discussion relevant, particularly those looking to advance their understanding of equations governing solid and fluid planetary models.

Helios
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I'm looking for an radial equation to find the pressure or density of the interior of a moon or rock planet. It would involve Young's modulus or Poisson's ratio or something like. Any help?
 
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Well, you should probably start with something more basic: the equation of hydrostatic equilibrium. This is relevant to models in which you model a planet or star as a ball of fluid, but also to models in which you model it as an (isotropic, inhomogeneous) elastic medium. I take it you are looking for a Newtonian model? There are many books on Newtonian models of stellar structure, also many books on geophysics.
 
There are books on geophysics? Really? Your reply is kind of a downer. I've solved hydrostatic eq'ns for spheres and I'm looking for a next thing to do.
 
Hi Helios!

Maybe this one is what you are looking for: http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1980LPSC...11.1999A&data_type=PDF_HIGH&type=PRINTER&filetype=.pdf
I'm not so good at math and physics, so I don't really understand everything in the text. If you can use the formulas in the text to find density (and temperature), please tell me how!
 
Last edited by a moderator:
The next thing after fluid balls in hydrostatic equilibrium?

Hi, Helios,

Helios said:
There are books on geophysics? Really? Your reply is kind of a downer. I've solved hydrostatic eq'ns for spheres and I'm looking for a next thing to do.

Sorry if I underestimated your previous experience. Should I infer from your handle that you are particularly interested in stellar interiors? Would adding rotation whet your appetite? If so, if you know about McLaurin spheroids, I suppose the obvious next question is: have you studied Chandrasekhar, Selected Papers, esp. Vols 1, 4? That should keep you happy for a while!
 
Last edited:
Hi Chris. I have Chandra's book "Stellar Interiors" and that's it. Out of it I'm trying to understand his explanation of composite polytropes. I don't get it and there are no examples.
Anyway I'm looking for a solid planet equation that might resemble Emden's eq'n.
 

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