Compactness (mass)

The dimensionless compactness of a mass in astronomy is the ratio of the gravitational radius to the geometric radius : ${\displaystyle {\mathcal {C}}}$ ${\displaystyle r_{G}}$ ${\displaystyle R}$

${\displaystyle {\mathcal {C}}:={\frac {r_{G}}{R}}={\frac {GM}{R\,c^{2}}}}$

With

• the gravitational constant ${\displaystyle G}$
• the mass of the object ${\displaystyle M}$
• the speed of light . ${\displaystyle c}$

A mass is considered compact if relativistic effects are very pronounced: ${\displaystyle {\mathcal {C}}\geq 0{,}01}$

Compactness must not be confused with density , which is defined differently for spherical objects.

Examples

The compactness of a neutron star is  , but that of the earth is only  . ${\displaystyle 0{,}16}$ ${\displaystyle 7\cdot {10}^{-10}}$

Web links

• Lexicon of Astronomy
• Compact star in the English Wikipedia