Roche Limit Query

[GeeKay]

If I may quote Wikipedia here: "The Roche limit is the distance within which a celestial body, held together only by its own gravity, will disintegrate due to a second celestial body's tidal forces exceeding the first body's gravitational self-attraction."

 

This being so, in the case of a Solar-mass body, does its Roche limit, as it applies to a given satellite, remain the same, regardless of its diameter? In other words, would the limit stay put, even if the Sun were magically shrunken into a white dwarf, while retaining its original mass? Many thanks.

 

 

[swansont]

The gravitational force from the sun does not depend on its diameter. The mass is what's important.

[GeeKay]

Thank you. That's what I wanted to hear

[Janus]

To clarify, The Roche limit is going to fall somewhere between

 

[math]d = 1.26 R\sqrt[3]{\frac{\rho M}{\rho m}}[/math]

 

and

 

[math]d = 2.44 R\sqrt[3]{\frac{\rho M}{\rho m}}[/math]

 

Where

 

[math]\rho M[/math] Is the density of the primary object

[math]\rho m[/math] Is the density of the secondary object

R is the radius of the primary object.

 

depending on the rigidity of the secondary object.

A rocky body will tend to the first value and a fluid object tends toward the second value.

 

Note that while the Roche limit does go up by the radius, it also goes up by the cube root of the density.

 

So if the Sun maintained its mass and decreased its radius by a factor of x, its density increases by a factor of x^3. The two changes cancel each other out and you get no change in the Roche limit.

[GeeKay]

So I take it then that even if the primary body was a white dwarf, or something even denser - a neutron star, say - the same Roche limit rules apply, as they pertain to a far less dense satellite in orbit round the above object. . . a water-ice comet, to take an extreme example?

 

I mention this because some commentators on the internet, in discussing the Roche limit, referred to relative densities. Unfortunately, for whatever reason, it all left me feeling confused, rather than enlightened.

[imatfaal]

So I take it then that even if the primary body was a white dwarf, or something even denser - a neutron star, say - the same Roche limit rules apply, as they pertain to a far less dense satellite in orbit round the above object. . . a water-ice comet, to take an extreme example?

 

I mention this because some commentators on the internet, in discussing the Roche limit, referred to relative densities. Unfortunately, for whatever reason, it all left me feeling confused, rather than enlightened.

 

The talk of relative densities allows predictions of roche limits without knowledge of the mass of the objects just knowledge of what they were constituted. Saturn's rings might be (in truth I think the consensus is this is not the case) the remains of moons that were within the roche limit - but we know this cannot be the whole answer as E-ring is too far out for a satellite ( we don't need to know mass just that it was made up of the same stuff as the e-ring) to be within Roche Limit of a gas-giant. The use of relative densities allow us to say what the roche limit (albeit as a multiple of the Radius of the primary) is for any water ice comet in orbit around any white dwarf - because whilst we are not given the masses we are given the densities