Editing Roche limit (section)

=== Rigid satellites ===
The ''rigid-body'' Roche limit is a simplified calculation for a [[spherical]] satellite. Irregular shapes such as those of tidal deformation on the body or the primary it orbits are neglected. It is assumed to be in [[hydrostatic equilibrium]]. These assumptions, although unrealistic, greatly simplify calculations.

The Roche limit for a rigid spherical satellite is the distance, <math>d</math>, from the primary at which the gravitational force on a test mass at the surface of the object is exactly equal to the tidal force pulling the mass away from the object:<ref>see calculation in Frank H. Shu, ''The Physical Universe: an Introduction to Astronomy,'' p. 431, University Science Books (1982), {{ISBN|0-935702-05-9}}.</ref><ref>{{cite web | url=http://www.asterism.org/tutorials/tut25-1.htm | title=Roche Limit: Why Do Comets Break Up? | access-date=2012-08-28 | archive-date=2013-05-15 | archive-url=https://web.archive.org/web/20130515200347/http://www.asterism.org/tutorials/tut25-1.htm | url-status=dead }}</ref>

:<math> d = R_M\left(2 \frac {\rho_M} {\rho_m} \right)^{\frac{1}{3}} </math>

where <math>R_M</math> is the [[radius]] of the primary, <math>\rho_M</math> is the [[density]] of the primary, and <math>\rho_m</math> is the density of the satellite. This can be equivalently written as

:<math> d = R_m\left(2 \frac {M_M} {M_m} \right)^{\frac{1}{3}} </math>

where <math>R_m</math> is the radius of the secondary, <math>M_M</math> is the [[mass]] of the primary, and <math>M_m</math> is the mass of the secondary. A third equivalent form uses only one property for each of the two bodies, the mass of the primary and the density of the secondary, is

:<math> d = 0.7816 \left( \frac {M_M} {\rho_m} \right)^{\frac{1}{3}} </math>

These all represent the orbital distance inside of which loose material (e.g. [[regolith]]) on the surface of the satellite closest to the primary would be pulled away, and likewise material on the side opposite the primary will also go away from, rather than toward, the satellite.