The strength of a gravitational field - also called the acceleration due to gravity - is the force per unit mass. Newton's Law of Universal Gravitation states that the force between point masses of mass
\[m_1, \: m_2\]
respectively separated by a distance \[r\]
is \[F=\frac{Gm_1m_2}{r^2}\]
.(
\[G=6.67 \times 10^{-11} m^3/kg/s^2\]
is the universal gravitational constant and is often called big G)Hence the gravitational field strength at the position of mass
\[m_1\]
due to the mass \[m_2\]
is \[\frac{F}{m_1}=\frac{Gm_2}{r^2}\]
and the gravitational field strength at the position of \[m_2\]
due to the presence of mass \[m_1\]
is \[\frac{F}{m_2}=\frac{Gm_1}{r^2}\]
.The gravitational field strength is given the label
\[g\]
at is actually equal to the acceleration of the body.The acvereration due to gravity on the Earth is
\[g=\frac{GM_{EARTH}}{R^2_{EARTH}}=9.8m/s^2\]