What is the gravitational field strength formula?

A gravitational field is a region in space where a mass will experience a gravitational force. The gravitational field strength at a location is defined as the force per unit mass experienced by a small test mass placed at that location. The field strength can be expressed as an equation as follows:

$\hspace{3em} g = \dfrac{F}{m}$

Where:
$\hspace{3em}$ $g$ is the gravitational field strength in units of N kg$^{-1}$
$\hspace{3em}$ $F$ is the gravitational force experienced by the mass in units of N
$\hspace{3em}$ $m$ is the mass of the object experiencing the gravitational force in units of kg.

Any object with mass will create a gravitational field in the region around it. This field extends an infinite distance away; however, it decreases proportionally with the square of the distance. We can use Newton’s Law of Gravitation to develop the formula for the gravitational field strength at a given distance from an object. The law states that the force of gravity between two masses is directly proportional to the product of the masses and inversely proportional to the square of the distance of the separation of their centres of mass:

$\hspace{3em} F_g = G\dfrac{m_1m_2}{r^2}$

Where:
$\hspace{3em}$ $F_g$ is the force of gravity in units of N
$\hspace{3em}$ $G$ is the gravitational constant 6.67 x 10$^{-11}$ N m$^2$ kg$^{-2}$
$\hspace{3em}$ $m_1$ and $m_2$ are the masses of the two objects in units of kg
$\hspace{3em}$ $r$ is the separation of their centers of mass in m.

We can substitute this equation for gravitational force into the first question for gravitational field to derive a new equation

$\hspace{3em} g = \dfrac{F}{m}$

$\hspace{3em} g = \dfrac{G\dfrac{m_1m_2}{r^2}}{m}$

$\hspace{3em} g = \dfrac{Gm_1}{r^2}$

This formula gives the gravitational field strength at a distance $r$ from a the centre of a mass $m_1$ . This mass is normally a planet, star or moon.