Newton’s Law of Universal Gravitation

Statement

Every particle in the universe attracts every other particle with a force that is:

• Directly proportional to the product of their masses
• Inversely proportional to the square of the distance between them

Mathematical Form

$$ F = G \frac{m_1 m_2}{r^2} $$

Where:

• $G$ = universal gravitational constant
• $m_1, m_2$ = masses
• $r$ = distance between centers

Vector Form

$$ \vec{F} = -G \frac{m_1 m_2}{r^2} \hat{r} $$

The negative sign indicates that the force is attractive.