Newton's Law of Universal Gravitation

Physical Law
Let $a$ and $b$ be particles with mass $m_a$ and $m_b$ respectively.

Then $a$ and $b$ exert a force upon each other whose magnitude and direction are given by Newton's law of universal gravitation:


 * $\mathbf F_{a b} \propto \dfrac {m_a m_b {\mathbf r_{b a} } } {r^3}$

where:
 * $\mathbf F_{a b}$ is the force exerted on $b$ by the electric charge on $a$
 * $\mathbf r_{b a}$ is the displacement vector from $b$ to $a$
 * $r$ is the distance between $a$ and $b$.

Thus it is seen that the direction of $\mathbf F_{a b}$ is specifically towards $a$.

By exchanging $a$ and $b$ in the above, it is seen that $b$ exerts the same force on $a$ as $a$ does on $b$, but in the opposite direction, that is, towards $b$.

Gravitational Constant
Thus the equation becomes:
 * $\mathbf F_{a b} = \dfrac {G m_a m_b \mathbf r_{b a} } {r^3}$

Also presented as

 * $\mathbf F_{a b} \propto \dfrac {m_a m_b \hat {\mathbf r}_{b a} } {r^2}$

where $\hat {\mathbf r}_{a b}$ is the unit vector in the direction from $b$ to $a$.

Also known as
Newton's Law of Universal Gravitation is also known as just Newton's Law of Gravitation.

Some sources refer to it as the inverse square law of gravitation.