Formula: Newton's Law of Gravity (Potential Energy of a Mass) Gravitational energy Distance Mass
$$W_{\text{pot}} ~=~ -G \, \class{brown}{M} \, \frac{\class{brown}{m}}{r}$$
$$W_{\text{pot}} ~=~ -G \, \class{brown}{M} \, \frac{\class{brown}{m}}{r}$$
$$r ~=~ -G \, \class{brown}{M} \, \frac{\class{brown}{m}}{W_{\text{pot}}}$$
$$\class{brown}{M} ~=~ \frac{ 1 }{ G } \, \frac{W_{\text{pot}} \, r}{ \class{brown}{m} }$$
$$\class{brown}{m} ~=~ \frac{ 1 }{ G \, \class{brown}{M} } \, W_{\text{pot}} \, r$$
$$G ~=~ \frac{1}{ \class{brown}{M} } \, \frac{ W_{\text{pot}} \, r }{ \class{brown}{m} }$$
Gravitational energy
$$ W_{\text{pot}} $$ Unit $$ \mathrm{J} $$
Gravitational energy is the potential energy of a mass \(m\) which is in the gravitational field of another mass \(M\) at a distance \(r\) from it. The gravitational energy is negative (see the minus sign in the formula) so that the mass \(m\) has a smaller (more negative) potential energy when it is closer to \(m\).
Distance
$$ r $$ Unit $$ \mathrm{m} $$
Distance of mass \( m \) from mass \( M \). The potential energy of the mass \( m \) goes from negative values to zero when the mass is further away from the mass \( M \).
Mass
$$ \class{brown}{M} $$ Unit $$ \mathrm{kg} $$
The mass of the first body, e.g. the earth.
Mass
$$ \class{brown}{m} $$ Unit $$ \mathrm{kg} $$
The mass of the second body, e.g. the moon.
Gravitational constant
$$ G $$ Unit $$ \frac{\mathrm{N} \, \mathrm{m}^2}{\mathrm{kg}^2} = \frac{\mathrm{m}^3}{\mathrm{kg} \, \mathrm{s}^2} $$
The gravitational constant is a physical constant that occurs in equations describing the interaction between masses. It has the following experimentally determined value:
$$ G ~\approx~ 6.674 \, 30 ~\cdot~ 10^{-11} \, \frac{ \mathrm{m}^3 }{ \mathrm{kg} \, \mathrm{s}^2 } $$