The law of universal gravitation says that every object in the universe pulls on every other object with a gravitational force that depends on their masses and how far apart they are.

Core idea

Isaac Newton’s law states: any two masses attract each other with a force that is:

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

In words: if you increase either mass, the force gets stronger; if you move them farther apart, the force decreases very quickly (because of the distance squared).

The formula

The mathematical form of the law is:

F=Gm1m2r2F=G\frac{m_1m_2}{r^2}F=Gr2m1​m2​​

  • FFF: magnitude of the gravitational force between the two objects.
  • m1,m2m_1,m_2m1​,m2​: the masses of the two objects.
  • rrr: distance between the centers of the two masses.
  • GGG: universal gravitational constant.

The constant GGG is the same everywhere in the universe (as far as experiments show) and has a very small value, which is why you mainly notice gravity from very massive bodies like Earth.

What “universal” means

“Universal” means the law applies:

  • Between any two masses: planets, stars, people, apples, spacecraft, etc.
  • Both in space and on Earth—it unifies falling apples and orbiting moons under one rule.

For example, the same law that makes an apple fall also governs the Moon’s orbit around Earth and Earth’s orbit around the Sun.

Everyday example

Near Earth’s surface, Newton’s law can be simplified to the familiar equation F=mgF=mgF=mg, where ggg (about 9.8 m/s²) is the gravitational field strength of Earth. This is just a special case of the universal law when one mass is Earth and the distance is roughly Earth’s radius.

Information gathered from public forums or data available on the internet and portrayed here.