What Does Δr Represent in the Roche Limit Formula?

In summary, Δr represents the radius of the primary in the Roche limit equation, which calculates the distance at which a satellite would be torn apart by tidal forces. It is also used to measure the distance between two particles or bodies on a smaller scale.
  • #1
PChar
11
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Relevant equations

[itex]r_{Roche}=(\frac{2M}{m})^{1/3}Δr[/itex]

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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  • #2
PChar said:
Relevant equations

[itex]r_{Roche}=(\frac{2M}{m})^{1/3}Δr[/itex]

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.
 

FAQ: What Does Δr Represent in the Roche Limit Formula?

1. What is the Roche Limit Formula?

The Roche Limit Formula is a calculation used to determine the distance at which a celestial object, such as a planet or moon, can orbit another object without being torn apart by tidal forces.

2. How is the Roche Limit Formula calculated?

The Roche Limit Formula takes into account the masses and densities of the two objects, as well as the gravitational constant and the radius of the larger object.

3. What is the significance of the Roche Limit Formula?

The Roche Limit Formula is important because it helps us understand the stability of planetary and satellite systems. It also has implications for the formation and evolution of these systems.

4. Can the Roche Limit Formula be used for objects other than planets and moons?

Yes, the Roche Limit Formula can also be applied to other objects, such as binary stars or even galaxies, to determine their stability and potential for tidal disruption.

5. Are there any limitations to the Roche Limit Formula?

While the Roche Limit Formula is a useful tool, it does not take into account other factors that can affect the stability of an orbit, such as atmospheric drag or collisions with other objects. It also assumes that the two objects are rigid and do not deform under tidal forces.

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