# Newton's Law of Universal Gravitation

on . Posted in Classical Mechanics

Newton's law of universal gravitation states that every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.  This law explains the force of gravity between any two objects in the universe, regardless of their size, shape, or location.  It is the basis for our understanding of the motion of planets, stars, and other celestial bodies in the universe.  This law is one of the fundamental laws of physics and has been validated by numerous experiments and observations.  It is a cornerstone of classical mechanics and played a crucial role in the development of modern astronomy and astrophysics.

### Newton's Law of Universal Gravitation formula

$$F_g \;=\; G \; ( m_1 \; m_2 \;/\; r^2 )$$     (Newton's Law of Universal Gravitation)

$$G \;=\; F_g \; r^2 \;/\; m_1 \; m_2$$

$$m_1 \;=\; F_g \; r^2 \;/\; G \; m_2$$

$$m_2 \;=\; F_g \; r^2 \;/\; G \; m_1$$

$$r \;=\; \sqrt{ ( G \;/\; F_g ) \; m_1 \; m_2 }$$

Symbol English Metric
$$F_g$$ = gravitational force  $$ft \;/\; sec^2$$  $$m \;/\; s^2$$
$$G$$ = universal gravitational constant $$lbf-ft^2 \;/\; lbm^2$$  $$N - m^2 \;/\; kg^2$$
$$m_1$$ = mass of object 1 $$lbm$$ $$kg$$
$$m_2$$ = mass of object 2 $$lbm$$ $$kg$$
$$r$$ = distance between centers of the masses $$ft$$ $$m$$