What Does Δr Represent in the Roche Limit Formula?

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SUMMARY

Δr in the Roche Limit formula, represented as r_{Roche}=(\frac{2M}{m})^{1/3}Δr, specifically denotes the radius of the primary body in a two-body system. This clarification is essential for understanding the gravitational interactions between celestial bodies. The discussion confirms that Δr does not refer to the diameter but rather the radius, which is crucial for accurate calculations in astrophysics.

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  • Understanding of gravitational interactions in celestial mechanics
  • Familiarity with the Roche Limit concept
  • Basic knowledge of mathematical equations involving mass and distance
  • Ability to interpret astrophysical formulas
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Relevant equations

r_{Roche}=(\frac{2M}{m})^{1/3}Δr

I can't seem to find a good explanation of what Δr is. My textbook uses an example of two particles, with that being the distance between their centers, but on the planetary scale, does Δr represent the orbiting body's radius or diameter?
 
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PChar said:
Relevant equations

r_{Roche}=(\frac{2M}{m})^{1/3}Δr

I can't seem to find a good explanation of what Δr is. My textbook uses an example of two particles, with that being the distance between their centers, but on the planetary scale, does Δr represent the orbiting body's radius or diameter?

Δr is the radius of the primary. Wikipedia has a derivation.
 

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