## Gravitational Field Strength

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

\[g=\frac{GM_{EARTH}}{R^2_{EARTH}}=9.8m/s^2\]