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# Overview of Gravitation

by Ron Kurtus (updated 30 May 2023)

** Gravitation** is the force of attraction between objects that is proportional to the product of their masses and inversely proportional to the square of their separation.

Objects can range in size from sub-atomic particles to celestial masses, such as planets, stars and galaxies. Other properties of gravitation include attraction to the center or mass, escape velocity and gravity.

The concept that matter attracts other objects was formulated by Isaac Newton as the *Law of Universal Gravitation*. This theory has been superseded by newer theories of gravitation, such as Albert Einstein’s *Theory of General Relativity* and the *Theory of Quantum Gravitation*.

The *Universal Gravitation Equation* defines the force of attraction between two objects in ordinary situations. The equation can be simplified to give the gravity equation for objects near Earth.

Questions you may have include:

- What are the properties of gravitation?
- What are theories of gravitation?
- What is the gravitation equation?

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

## Properties of gravitation

All objects consisting of matter exhibit the property of gravitational attraction and tend to move toward each other. This property is considered universal and exists throughout the Universe.

### No shield

As far as we know, there is no way to shield the effect of gravitation. There are theories that there exists "dark matter" that repels standard matter, however dark matter has never been detected.

### Center of mass

There is a center of mass between disconnected objects, which is an average of the masses and their separations. When the objects move toward each other, the will meet at the center of mass. If one object seems to be revolving around another, as in the case of a moon around a planet, both objects are actually revolving around the center of mass.

### Escape velocity

It is possible for an object to be propelled at a sufficient velocity away from another object that it will overcome the gravitational attraction between the two. An example of this is when a rocket escapes the gravitation of the Earth.

### Gravity

The expressions *gravity* and *gravitation* are often commonly interchanged. However, the correct scientific terminology considers gravity as a special case of gravitation for objects near the Earth.

For gravitation close to other large objects, you should include the name of the object, such as: "gravity of the Moon" or "gravity of the Sun."

For astronomical situations, gravitation is the correct term to use.

## Gravitational theories

There have been several theories trying to explain the cause of gravitation.

### Law of Universal Gravitation

In 1687, Isaac Newton formulated the *Law of Universal Gravitation*, which states that all objects are attracted toward other objects, due to some force acting at a distance, called gravitation. The law and its equation apply to moderately-sized astronomical effects and is still the mainstay theory today.

### Theory of General Relativity

In 1915, Albert Einstein gave another interpretation of gravitation in his *Theory of General Relativity*. He stated that gravitation was the result of the curvature of space toward matter and not due to some force. General relativity applies best to very large gravitational fields and high velocities.

Anomalies in the orbit of the planet Mercury, which is closest to the Sun, could not be explained by the Law of Universal Gravitation. However, calculations using General Relativity equations correctly predicted the orbit and were used to verify the theory, as were the measurements of the effect of gravitation on deflecting light waves as they pass a star.

### Theory of Quantum Gravitation

Recent considerations in Quantum Physics say that gravitation is one of four fundamental forces in nature. The force of each is created by an exchange of special or virtual particles. In the case of gravitation, the particle is called the *graviton*. This interaction leads to an explanation of gravitation at very small separations.

### Dark matter and dark energy

Astronomical measurements on the rate of expansion of the Universe and measurements of the mass of galaxies showed discrepancies with predictions from general relativity. To explain the discrepancies, astronomers have speculated that there exists a form of dark matter and dark energy that they cannot detect.

These concepts fit to a degree in the Theory of Quantum Gravity.

## Gravitation Equation

Just as there are several theories about the cause of gravitation, likewise, there are several equations that define the force.

### Universal Gravitation Equation

Newton formulated the *Universal Gravitation Equation*, which allows the calculation of the force between two objects. The equation is:

F = GMm/R^{2}

where

**F**is the force of attraction between two objects in newtons (N)**G**is the universal gravitational constant in N-m^{2}/kg^{2}**M**and**m**are the masses of the two objects in kilograms (kg)**R**is the separation in meters (m) between the objects, as measured from their centers of mass

The value of **G** is 6.674*10^{−11} N-m^{2}/kg^{2}.

### Gravity equation

The gravity equation is a simplification of the gravitational equation for objects relatively close to the Earth:

F = mg

where

**F**is the force pulling objects toward the Earth in newtons (N) or pound-force (lbs)**m**is the mass of the object in kg or pound-mass**g**is the acceleration due to gravity in meters per second squared (m/s^{2}) or feet per second squared (ft/s^{2})

The value of **g** is 9.8 m/s^{2}.

### Other equations

The Theory of General Relativity provides a set of 10 complex equations to describe gravitation. Likewise, Quantum Mechanics and other newer theories explain gravitational force with sophisticated equations.

They are beyond the scope of our material.

## Summary

Gravitation is the attraction between objects because of their mass. Other properties of gravitation include attraction to the center or mass, escape velocity and gravity.

Theories of gravitation are the Law of Universal Gravitation, the Theory of General Relativity and the Theory of Quantum Gravity.

The Universal Gravitation Equation defines the force of attraction between two objects in ordinary situations. The equation can be simplified to give the gravity equation for objects near Earth.

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## Resources and references

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## Where are you now?

## Overview of Gravitation