Universal law of gravitation formula

January 5, 2020

Law Of Gravitation

Since the 1700s, scientists noticed the similarity between gravitation and electrostatic forces. This led to speculation that the two forces were somewhat related. However, there are also differences that separate the forces.

In the early 1900s, equations indicated that moving charges and moving masses provide an analogy of gravitational and electromagnetic fields. This results in the concept of a gravitomagnetic force, where large rotating masses affect nearby small masses. However, measurements have not validated the concept.

Questions you may have include:

  • How are the force equations similar?
  • How are they different?
  • What is gravitomagnetism?

Force equations parallel

The gravitational force equation and the electrostatic force equation can be seen as parallel to each other.


The Universal Gravitation Equation states the force of attraction between two objects, where the mass is considered concentrated at their centers of mass:

F = GMm/R2


  • F is the force of attraction between two objects
  • G is the Universal Gravitational Constant
  • M and m are the masses of the two point objects
  • R is the separation between the centers of the objects


The electrostatic force equation is called Coulomb's Law and states the force of attraction between particles of opposite electrical charge. It also represents the force of repulsion for like charges:

F = keqQ/r2

  • F is the force of attraction or repulsion between two electrically charged particles
  • ke is the Coulomb force constant
  • q and Q are point charges of the two particles
  • r is the separation between the particles

Comparison of forces

There are similarities and differences between the two forces.


From looking at the two force equations, you can see the similarities and how gravitational force can be considered parallel to the force between two charges.

Besides being proportional to the inverse of the square of the separation, both forces extend to infinity. They also both travel at the speed of light.


One major difference is in the strength of the forces. The gravitational attraction between two electrons is only 8.22*10−37 of the electrostatic force of repulsion at the same separation. However, gravitation usually is concerned with large masses, while any large collection of charges will quickly neutralize.

Another difference between the two forces is the fact that gravitation only attracts, while electrical forces attract when the electrical charges are opposite and repel if the charges are similar. Thus, gravitation is considered a monopole force, while electrostatics is a dipole force.

However, the concept of dark energy, which seems to have an anti-gravitation force, may allow for gravitation to be both the attraction and repulsion of matter.

Source: www.school-for-champions.com
Law of Gravitation
Law of Gravitation
Law of Universal Gravitation
Law of Universal Gravitation
Universal Law of Gravitation
Universal Law of Gravitation

What is the law of universal gravition.

The Law of Universal Gravitation says that throughout the Universe, there is a force between two objects of matter,m and M, separated by a distance r. The force is mGM/r.

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