# Equivalence Principles of Gravitation

by Ron Kurtus (revised 30 Janaury 2018)

There are several Equivalence Principles of gravitation.

The Weak Equivalence Principle states that objects fall at the same rate, provided that are freely falling. The equivalence of inertial and gravitational mass states that mass determined by inertia is the same as mass determined by gravitation. The Strong Equivalence Principle extends the equivalence of masses to state that observations of acceleration cannot be distinguished from gravity.

Questions you may have include:

• What is the Weak Equivalence Principle?
• What is the equivalence of inertial and gravitational mass?
• What is the Strong Equivalence Principle?

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

## Weak Equivalence Principle

The Weak Equivalence Principle (also called the Uniqueness of Free Fall Principle) states that the gravitational force from a larger body causes objects to fall or move toward the attracting body at the same rate, independent of their masses.

A major restriction is that there are no other forces acting on the objects.

## Equivalence of inertial and gravitational mass

There is an equivalence of inertial and gravitational mass. In other words, this principle states that mass determined by inertia is the same as mass determined by gravitation. You can see this by examining the forces for both inertial mass and gravitational mass.

## Strong Equivalence Principle

The Strong Equivalence Principle (also known as the Einstein Equivalence Principle) states that the effects of acceleration are indistinguishable from those of gravitation.

(See Artificial Gravity for an example of this.)

### Experiments by observer

This means that an observer cannot determine by experiment whether he or she is accelerating or in a gravitational field. In other words, results from experiments in an accelerating spaceship would be the same as those obtained from gravitation.

### Einstein's conclusion

Einstein concluded that gravitation and motion through space-time are related and that the Strong Equivalence Principle suggests that gravitation is geometrical by nature.

### Difference between strong and weak

The difference between the Strong Principle of Equivalence and the Weak Principle of Equivalence is that strong equivalence states all the laws of nature are the same in a uniform static gravitational field and the equivalent accelerated reference frame, while weak equivalence states all the laws of motion for freely falling particles are the same as in a reference frame that is not accelerated.

## Summary

The Weak Equivalence Principle states that objects fall at the same rate, provided that are much smaller than the attracting body and are freely falling.

The equivalence of inertial and gravitational mass states that mass determined by inertia is the same as mass determined by gravitation.

The Strong Equivalence Principle extends the equivalence of masses to state that observations of acceleration cannot be distinguished from gravitation.

Physics is amazing

## Resources and references

Ron Kurtus' Credentials

### Websites

Equivalence Principle - Laboratory Tests of Gravitational Physics

Equivalence principle - Wikipedia

Elevator, rocket, and gravity: the equivalence principle - Einstein online

Gravitation Resources

### Books

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gravitation_equivalence_principles.htm

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