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# Gravitational Speed

by Ron Kurtus (revised 22 January 2011)

Change in the separation of two objects results in a change in the gravitational force between them. *Gravitational speed* concerns the amount of time it takes the gravitational force to accommodate the change in separation over the given displacement. It is often carelessly called the *speed of gravity*.

Concepts about the mechanism of gravitation determine what scientists say is its reaction time or speed. The Newtonian model for gravitation states that the change in force is instantaneous and that the gravitational speed is infinite. However, some astronomical observations required a better explanation.

The *Theory of** General Relativity* stated that gravitation travels at the speed of light and is caused by the curvature of spacetime. The *Quantum Theory of Gravitation* states that gravitation is caused by the exchange of *graviton* particles, which travel at the speed of light.

Questions you may have include:

- What was the speed of gravitation according to Newton?
- What is the relativity gravitational speed?
- What is the speed of gravitation according to quantum physics concepts?

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

## Speed from Law of Universal Gravitation

In establishing the *Law of Universal Gravitation*, Isaac Newton said in 1687 that he was uncertain about the mechanism of gravitation, except that it was some sort of action-at-a-distance. His *Universal Gravitation Equation* shows the gravitational force between two objects at a given instance:

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 objects**R**is the separation between the objects, as measured from their centers of mass

Movement of one object, with respect to the other, results in a change in separation and thus a change in the force between the objects.

### Infinite speed

In order to satisfy *Kepler's Laws of Planetary Motion*—especially for elliptical orbits—Newton came to the conclusion that the gravitational force propagates instantaneously, irrespective of the separation between objects. In other words, Newton's concepts state that the gravitational speed is infinite. For example, the changing displacements due to elliptical orbits for any planets in the Solar System would make the orbits unstable if the gravitational force did not propagate instantaneously.

However, instantaneous propagation or infinite speed is counterintuitive to the way things work in the Universe. This had bothered scientists over the years. But the assumption was adequate to account for astronomical phenomena with the observational accuracy of those days.

### Searching for better solution

In 1847, French astronomer Leverier determined that the elliptical orbit of Mercury—the planet closest to the Sun—has a precession that was at a significantly different rate than was predicted by Newton's theory.

In searching for a solution scientists tried a new mechanism for gravitation, combining Newton's force law with the established laws of electrodynamics, placing the gravitational speed equal to the speed of light. Unfortunately, those theories provided insufficient.

## Speed from relativity

In 1915, Albert Einstein's *Theory of General Relativity* took a completely different approach, stating the gravitation was not a force but a result of the curvature of spacetime. With this mechanism of gravitation, a change in separation resulted in a change of the curvature of spacetime between the objects.

Since the *Special Theory of Relativity* stated that the speed of light, **c**, was a fundamental constant and was the ultimate speed for any physical interaction, the conclusion was that the gravitational speed was the speed of light. In other words, the change in curvature as a result of the change in separation of the object occurred at the speed of light. This also presented the possibility of gravitation waves.

Equations in the relativity theories showed that Kepler's Laws of Planetary Motion were approximations and explained the elliptical orbit of Mercury.

## Speed from quantum gravitation

In 1927, *Quantum Physics* formalized the various areas of *Quantum Mechanics* into one field. However, there was a disconnect between Quantum Physics and General Relativity. The recent development of *Quantum Gravitation*, along with *String Theory* and the *Theory of Everything* are efforts to unify Quantum Physics and Relativity.

The Quantum Gravitation mechanism for the gravitational force is the exchange of *graviton* particles, which travel at the speed of light. From the Quantum Physics wave-particle duality concept, those graviton particles could also be represented as gravitational waves.

Gravitation waves responding to change in separation

## Summary

Gravitational speed concerns the amount of time it takes the gravitational force to accommodate the change in separation over the given displacement. The mechanism of gravitation is a determining factor in its reaction time or speed.

The Law of Universal Gravitation did not define a mechanism for gravitation but stated states that the change in force is instantaneous and that the gravitational speed is infinite.

The Theory of General Relativity stated that gravitation travels at the speed of light and is caused by the curvature of spacetime. The Quantum Theory of Gravitation states that gravitation is caused by the exchange of *graviton* particles, which travel at the speed of light.

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## Resources and references

### Websites

**Does Gravity Travel at the Speed of Light?** - by Steve Carlip et al at Deutsches Elektronen-Synchrotron

**Speed of Gravity** - Wikipedia

**Measuring the Speed of Gravity** - MathPages.com

### Books

**Top-rated books on Gravitation**

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## Gravitational Speed