What Does Δr Represent in the Roche Limit Formula?

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Δr in the Roche Limit formula represents the radius of the primary body, not the diameter. The formula r_{Roche}=(\frac{2M}{m})^{1/3}Δr calculates the distance at which a smaller body can orbit without being torn apart by tidal forces. The confusion arises from its explanation in textbooks, which often use particle examples. For planetary scales, it is crucial to interpret Δr as the radius of the larger body involved in the interaction. Understanding this distinction is essential for applying the Roche Limit correctly.
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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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