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 gravitational force 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 $b$.

Universal 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.

Also see

 * Definition:Gravitational Field