# Gravitational parameter

The gravitational parameter (symbol ${\displaystyle \mu }$ of a body (normally a planet, moon or star) is a value which represents the strength of its gravitational pull. This value is used in calculations involving other bodies which orbit it. For a body with mass ${\displaystyle M}$ and the universal gravitational constant ${\displaystyle G}$,

${\displaystyle \mu =GM}$

## Justification[1]

Experimental difficulties in determining ${\displaystyle G}$ makes it one of the most inaccurate of the fundamental constants. Since the mass of heavenly bodies is also calculated from ${\displaystyle G}$ according to the force equation for gravity (accurate to about 0.06%)

${\displaystyle F_{g}=G{{m_{1}m_{2}} \over {r^{2}}}}$

direct calculation of orbits using the force equation would be unacceptably inaccurate and prone to change whenever a better value for ${\displaystyle G}$ is found.
Because of this, it is better whenever possible to perform orbit calculations in terms of ${\displaystyle \mu }$ and the mass ratios of bodies. Astronomical observations can determine ${\displaystyle \mu }$ to very high precision.

## Values of interest for a Mars mission

Note: While most of these values are known to high precision, measurements still vary between observations and the less significant digits can change as the science advances. The table below gives the gravitational parameters to six significant digits or their full available accuracy (if less) when the source was published (2011). Anyone planning an actual or paper mission should search the literature for the most accurate and recent values.

Central body ${\displaystyle \mu }$[2]
Sol ${\displaystyle 1.327,12\times 10^{20}m^{3}s^{-2}}$
Earth ${\displaystyle 3.986,00\times 10^{14}m^{3}s^{-2}}$
Luna ${\displaystyle 4.902,80\times 10^{12}m^{3}s^{-2}}$
Mars ${\displaystyle 4.282,84\times 10^{13}m^{3}s^{-2}}$
Phobos ${\displaystyle 7.161\times 10^{5}m^{3}s^{-2}}$
Deimos ${\displaystyle 1.041\times 10^{5}m^{3}s^{-2}}$