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# Similarity Between Gravitation and Electrostatic Forces

by Ron Kurtus (updated 30 May 2023)

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?

This lesson will answer those questions. Useful tool: Units Conversion

## Force equations parallel

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

### Gravitation

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/R^{2}

where

**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

### Electrostatic

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 = k_{e}qQ/r^{2}

where

**F**is the force of attraction or repulsion between two electrically charged particles**k**is the Coulomb force constant_{e}**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.

### Similarities

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.

### Differences

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.

## Gravitomagnetism

An analogy of gravitational and electromagnetic fields is seen by comparing the *Einstein Field Equations* from the *General Theory of Relativity* with *Maxwell's Field Equations* for electrical and magnetic fields.

Einstein's equations state that the gravitational field produced by a rotating object can be described by equations that have the same form as Maxwell's equations.

Note: Both sets of equations are beyond the scope of our material.

Just as a rotating or moving electrical charge creates a magnetic field, general relativity predicts that a huge rotating mass will cause a small nearby free-falling object to rotate. This is called a *gravitomagnetic effect*. Unfortunately, this prediction of general relativity has yet to be directly tested or proven to be true

## Summary

There is a similarity between gravitation and electrostatic force equations. Although this led to speculation that the two forces were somewhat related, differences were seen that separated the forces.

Einstein's and Maxwell's equations indicate that moving charges and moving masses provide an analogy of gravitational and electromagnetic fields, called *gravitomagnetics*. The result is that large rotating masses affect nearby small masses. However, measurements have not validated the concept.

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## Resources and references

### Websites

**Parallels between electrostatics and gravity** - Wikipedia

**Gravitomagnetism **- Wikipedia

### Books

(Notice: The *School for Champions* may earn commissions from book purchases)

**Top-rated books on Gravitation**

## Students and researchers

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gravitation_electrostatic.htm**

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## Similarity Between Gravitation and Electrostatic Forces