Gravity/density equation? Giant ball of water

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SUMMARY

The discussion focuses on determining the equation for density in relation to an object's center of gravity, specifically for a spherical object like an Earth-sized volume of water. Participants highlight the necessity to account for increased density as one approaches the center of mass. Key references include the "adiabatic lapse" and "barometric formula" for understanding density changes, although the compressibility differences between water and atmospheric gases are noted as significant factors. A definitive equation for this specific scenario remains unspecified in the discussion.

PREREQUISITES
  • Understanding of basic physics concepts, particularly density and gravity.
  • Familiarity with spherical object properties and their implications on density.
  • Knowledge of the "adiabatic lapse" and "barometric formula" in atmospheric science.
  • Basic mathematical skills for manipulating equations related to density and gravity.
NEXT STEPS
  • Research the "adiabatic lapse" and its application to density changes in fluids.
  • Explore the "barometric formula" and its relevance to atmospheric density variations.
  • Investigate the compressibility of water compared to gases for a deeper understanding of density changes.
  • Study the principles of hydrostatics and how they apply to spherical objects and their centers of mass.
USEFUL FOR

Students of physics, engineers working with fluid dynamics, and researchers interested in gravitational effects on density in spherical bodies.

Vree
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Can you help me find the equation for determining density when also taking the object's own center of gravity into account?
For example, say I have an Earth-sized volume of water (or pick any simple spherical object). You have to account for the increase of density as you go closer to the center of mass. Is there a simple equation to determine the change of density from R distance from the center of mass in this case?

Thanks!
 
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Vree said:
Can you help me find the equation for determining density when also taking the object's own center of gravity into account?
For example, say I have an Earth-sized volume of water (or pick any simple spherical object). You have to account for the increase of density as you go closer to the center of mass. Is there a simple equation to determine the change of density from R distance from the center of mass in this case?

Thanks!

There are good analogies with calculating the change in density of the atmosphere with altitude. Google "adiabatic lapse" and "barometric formula". The difference between the atmosphere and a "big ball of water" is obviously two-fold -- the denisty and the compressibility are very different for the two.
 

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