Gravity Equations Formulas Calculator

Science Physics Newton's Law of Gravity

Solving for gravitational force exerted between two objects.
force exerted between two objects
G is the universal gravitational constant
G = 6.6726 x 10-11N-m2/kg2


object 1 mass (m1)
object 2 mass (m2)
distance between objects (r)
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object 1 mass (m1)
= 0
= 0
object 2 mass (m2)
= 0
= 0
distance between objects (r)
= 0
= 0


gravitational force (F)

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Newton's law of gravity
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What is Newton's law of gravity?

The Universal Law of Gravitation, Newton's law of gravity, is a fundamental physics principle governing the attractive force between two objects with mass. Sir Isaac Newton formulated this law in 1687, which helped our understanding of the universe. This law applies universally, from subatomic particles to celestial bodies, and helps explain phenomena such as planetary orbits, lunar motion, and ocean tides.
Newton's law of gravity has been a cornerstone of modern physics for over three centuries. This fundamental principle underlies our understanding of the universe and governs the behavior of all objects with mass. From explaining planetary orbits to predicting the motion of celestial bodies, Newton's law of gravity has provided us with critical insights into the workings of the cosmos. Moreover, it is an essential tool for scientists and engineers, enabling them to design and understand systems that function harmoniously with the gravitational forces shaping our world.

Historical Background

Before Newton, the general understanding of gravity was based on Aristotle's ideas, which stated that objects naturally moved toward their designated places, with heavier objects falling faster than lighter ones. Later, Galileo Galilei contributed significantly to understanding motion and gravity, demonstrating that things of different masses in a vacuum fall at the same rate.
Newton's breakthrough came when he realized that the same force causing an apple to fall from a tree is also responsible for keeping the Moon in orbit around the Earth. Newton formulated the Universal Law of Gravitation by combining his laws of motion with the concept of an attractive force between masses, forever changing our perception of the universe.

Mathematical Expression

Newton's law of gravity can be expressed mathematically as:
F = G (m1 X m2) / r^2
  • F - gravitational force between two objects
  • G - gravitational constant (approximately 6.674 × 10^-11 N(m/kg)^2)
  • m1 and m2 - two objects' masses
  • r - the distance between the two objects' centers
The equation reveals that the gravitational force is directly proportional to the product of the objects' masses and inversely proportional to the squared distance between them. This means that as the masses increase, the force increases, and the force decreases as the distance between objects increases.

Gravitational Constant

The gravitational constant (G) is a fundamental constant in Newton's law of gravity equation. It was first measured by physicist Henry Cavendish in 1798, over a century after Newton's original formulation. The constant represents the proportionality factor that relates the force of gravity to the masses of objects and the distance between them. Its value is approximately 6.674 × 10^-11 N(m/kg)^2. It remains constant throughout the universe, making it a critical value for understanding and predicting the behavior of celestial bodies and objects on Earth.

Applications and Examples

Newton's law of gravity has numerous applications central to our understanding of the universe. One such application is the explanation of planetary orbits. The law describes how planets are attracted to the Sun due to their mutual gravitational force, leading to their elliptical orbits.
Another application is the motion of the Moon around Earth. The gravitational force between Earth and the Moon keeps the Moon in orbit and causes ocean tides on our planet. The Moon's gravitational pull causes the ocean's water to bulge, leading to the high and low tides we experience daily.
Furthermore, Newton's law of gravity is essential in understanding the behavior of objects on Earth. For example, it helps us calculate the weight of an object, which is the force of gravity acting on its mass. The law also aids in the design of structures, vehicles, and other technologies, ensuring that they can withstand gravitational forces.text

References - Books:
Tipler, Paul A.. 1995. Physics For Scientists and Engineers. Worth Publishers. 3rd ed.
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