Newton's Law of Universal Gravitation

Physical Law

Every particle in the universe attracts every other particle with a force $F$ which is proportional to the square of the distance between them:

$\mathbf F \propto \dfrac {m_1 m_2} {r^2}$

The direction of the force on either particle is the same as the direction of the displacement vector to the other particle.

Using vector notation:

$\mathbf F \propto \dfrac {m_1 m_2} {r^2} \hat {\mathbf r}$

where $\hat {\mathbf r}$ is the unit vector from one particle to the other.

Also known as Newton's Law of Gravitation.

Gravitational Constant

The constant of proportion depends on the units used.

The value in SI units is referred to as $G$ and is approximately equal to $6.674 \times 10^{-11} \, \mathrm N \, \mathrm m^2 \, \mathrm{kg}^{-2}$.

Thus the equation becomes:

$\mathbf F = \dfrac {G m_1 m_2 \mathbf r} {r^3}$

Also see

• Gravitational Constant

Source of Name

This entry was named for Isaac Newton.

However, the idea behind it may have originated with Robert Hooke.

Sources

• Isaac Asimov: Understanding Physics (1966): $\text{I}$: Chapter $4$