Gravitational Force Formula, Definition & Examples

Understanding Gravitational Force

Gravitational force is the natural attraction that occurs between any two objects that have mass. It is one of the fundamental forces of nature and is responsible for keeping planets in orbit, the Moon around the Earth, and objects anchored to the ground. The concept of gravitational attraction was first clearly explained by Sir Isaac Newton in the late 17th century.

Newton's Law of Universal Gravitation states that every particle of matter in the universe exerts an attractive force on every other particle, which increases with the product of their masses and decreases with the square of the distance between their centers

Mathematically:

\(F = G \times (m_1 \times m_2) / r^2\)

• F = Gravitational force between two objects
• G = The universal gravitational constant, valued at \(6.674 \times 10^{-11}\, N.m^2/kg^2\)
• \(m_1\) and \(m_2\) represent the masses of the two interacting objects.
• r = The separation between the centers of the two masses

This concept applies everywhere, influencing objects from the tiniest particles to the most massive celestial bodies. For instance, the Sun’s gravity holds Earth and the other planets in their paths, while Earth’s gravity keeps the Moon revolving around it.

On Earth, the gravitational force near the surface gives rise to an acceleration of approximately 9.8 \(m/s^2\), which is why objects fall toward the ground when dropped. This acceleration is commonly known as the acceleration due to gravity, symbolized by g.

Gravity is essential in the creation of galaxies, stars, and planets, as it pulls matter together over time. Without it, the universe would have no structure as we know it.