Formula: Newton's Law of Gravity Force Distance 1st mass 2nd mass Gravitational constant
$$F_{\text g} ~=~ G \, \class{brown}{M} \, \frac{\class{brown}{m}}{r^2}$$
$$F_{\text g} ~=~ G \, \class{brown}{M} \, \frac{\class{brown}{m}}{r^2}$$
$$r ~=~ \sqrt{ G \, \frac{ \class{brown}{M} \, \class{brown}{m} }{ F_{\text g} } }$$
$$\class{brown}{M} ~=~ \frac{1}{G} \, \frac{ F_{\text g} }{\class{brown}{m}} \, r^2$$
$$\class{brown}{m} ~=~ \frac{1}{G} \, \frac{ F_{\text g} }{\class{brown}{M}} \, r^2$$
$$G ~=~ \frac{ F_{\text g} }{\class{brown}{M} \, \class{brown}{m}} \, r^2$$
Gravitational force
$$ F_{\text g} $$ Unit $$ \mathrm{N} = \frac{\mathrm{kg} \, \mathrm{m}}{\mathrm{s}^2} $$
It is the force that the mass \( \class{brown}{m_1} \) exerts on the mass \( \class{brown}{m_2} \) and vice versa.
Distance
$$ r $$ Unit $$ \mathrm{m} $$
Distance between the masses \( \class{brown}{m_1} \) and \( \class{brown}{m_2} \). The larger the distance, the smaller the gravitational force \( F_{\text g} \).
1st mass
$$ \class{brown}{M} $$ Unit $$ \mathrm{kg} $$
The mass of the first body.
2nd mass
$$ \class{brown}{m} $$ Unit $$ \mathrm{kg} $$
The mass of the second body.
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:
$$ G ~\approx~ 6.674 \, 30 ~\cdot~ 10^{-11} \, \frac{ \mathrm{m}^3 }{ \mathrm{kg} \, \mathrm{s}^2 } $$