Explanation of Artificial Gravity by Ron Kurtus - Succeed in Understanding Physics. Key words: physical science, space station, spacecraft, acceleration, centrifugal force, radian, angular velocity, weightlessness, School for Champions. Copyright © Restrictions

# Artificial Gravity

by Ron Kurtus (8 October 2009)

Artificial gravity is a force that simulates the effect of gravity but is not caused by the attraction to the Earth. There is a need for artificial gravity in spacecraft to counter the effect of weightlessness on the astronauts.

Acceleration and centrifugal force can duplicate the effects of gravity. Albert Einstein used the concept of artificial or virtual gravity in his General Theory of Relativity to give a different explanation of gravity.

A rotating circular space station can create artificial gravity for its passengers. The rate or rotation necessary to duplicate the Earth's gravity depends on the radius of the circle. Equations can be derived to determine the rotation rate and radius to simulate the effect of gravity.

Questions you may have include:

• When is artificial gravity needed?
• How can artificial gravity be created?
• How fast must a circular space station rotate?

This lesson will answer those questions.

Useful tool: Metric-English Conversion

## Artificial gravity needed

Artificial gravity is needed in spaceships that are in orbit around the Earth, as well as ones that are so far out that the effect of gravity or gravitation is negligible.

The International Space Station is in orbit around the Earth at approximately 350 km. Because the centrifugal force keeping the space station in orbit counters the force of gravity at that altitude, astronauts in the station do not feel the effect of gravity. Anything or anybody that is not tied down will float within the Space Station.

Astronauts in any spaceship that is far enough away from the Earth that the effect of gravity or gravitation is negligible will also feel the effects of weightlessness. The gravitation on a spaceship that is about 15,000 km from Earth is about 1/10 the gravity on the ground.

Thus, artificial gravity is needed to facilitate the tasks the astronauts must do, to make them more comfortable and to avoid negative health effects from weightlessness.

## Ways to create artificial gravity

Constant acceleration and centrifugal force are ways to create artificial gravity, such that a person could not tell the force was not gravity and all the laws of gravity hold.

### Acceleration

One way to simulate a gravitational force is to accelerate the spaceship. This is similar to the effect you feel when you are in an accelerating elevator, where you can feel heavier when the elevator is moving upward.

In developing his General Theory of Relativity, Albert Einstein noted that you could not tell the difference between gravity and constant acceleration. He used this example to state his theory that gravity or gravitation was not a force but an action related to inertia on moving objects.

Unfortunately, creating artificial gravity is impractical be depending on acceleration alone. There is a limit to the velocity of a spaceship.

### Centrifugal force

A better way to create this artificial gravity than constant acceleration is to use centrifugal force, which is an outward force caused by an object being made to follow a curved path instead of a straight line, as dictated by the Law of Inertia.

If a spaceship was in a large, circular shape that was rotating at a given speed, the crew on the inside could feel the centrifugal force as artificial gravity.

In the 1968 movie 2001: A Space Odyssey, a rotating centrifuge in the spacecraft provided artificial gravity for the astronauts. A person could walk inside the circle with his feet toward the exterior and his head toward the center, the floor and ceiling would curve upwards.

A rotating spacecraft will produce the feeling of gravity on its inside hull. The rotation drives any object inside the spacecraft toward the hull, thereby giving the appearance of a gravitational pull directed outward.

Rotating space station creates artificial gravity

## Rate of rotation to duplicate gravity

It is worthwhile to determine the radius of the space station centrifuge and its rate of rotation that will simulate the force of gravity.

### Centrifugal force equation

When you swing an object around you that is tied to a string, the outward force is equal to:

F = mv2/r

where

• F is the outward force of the object in newtons (N) or pounds (lb)
• m is the mass of the object in kilograms (kg) or pound-mass (lb)
• v is the linear or straight-line velocity of the object in meters/second (m/s) or feet/second (ft/s)
• r is the radius of the motion or the length of the string in m or ft

#### Verify units

It is a good practice to verify that the units you are using are correct for the equation.

F N = (m kg)(v m/s)2/r m

N = (kg)(m2/s2)/m

kg-m/s2 = kg-m/s2

A similar verification can be done using feet and pounds.

### Angular velocity equation

A better way to write the force equation is to use angular velocity, which will then lead to revolutions per minute.

ω = v/r

v = ωr

where ω (lower-case Greek letter omega) is the angular velocity in radians per second.

Note: A radian is the distance along a curve divided by the radius

Substituting for v in F = mv2/r, you get

F = mω2r

### Relate to gravity

Since the centrifugal force is F = mω2r and the force due to gravity is F = mg, you can combine the two equations to get the relationship between the radius, rate of rotation and g:

mg = mω2r

g = ω2r

Solving for ω:

ω = √(g/r)

Also, solving for r:

r = g/ω2

### Convert radians per second to rpm

The units for ω are inconvenient for defining the rate of rotation of the space station. Instead of radians per second, it would be better to state the units as revolutions per minute (rpm). Conversion factors are:

1 radian = 1/2π of a full circle (π is "pi", which is equal to about 3.14)

ω radians per second is ω/2π is revolutions per second

ω/2π revolutions per second is 60ω/2π revolutions per minute

60ω/2π = 9.55ω rpm

Let Ω (capital Greek letter omega) be the rate of rotation in rpm.

Ω = 9.55ω rpm

Thus:

Ω = 9.55√(g/r)

and

r = 91.2g/Ω2

### Example 1

Suppose the space station had a radius of r = 128 ft. How fast would it have to turn to create an acceleration due to gravity of g = 32 ft/s2?

Ω = 9.55√(g/r)

Ω = 9.55√(32/128) rpm

Ω = 9.55√(1/4) rpm

Ω = 9.55/2 rpm

Ω = 4.775 rpm

### Example 2

If you wanted the space station to rotate at only 2 rpm, how many meters must the radius be to simulate gravity?

r = 91.2g/Ω2

r = (91.2)(9.8)/(22) meters

r = 233.44 m

## Summary

Artificial gravity is a force that simulates Earth's gravity. There is a need for artificial gravity in spacecraft to counter the effect of weightlessness on the astronauts.

Acceleration and centrifugal force can duplicate the effects of gravity. A rotating circular space station can create artificial gravity for its passengers. The rate or rotation necessary to duplicate the Earth's gravity depends on the radius of the circle.

Think of ways to improve on nature

## Resources and references

Ron Kurtus' Credentials

### Websites

Artificial gravity - Wikipedia

Simulating Gravity in Space - From Batesville, Indiana HS Physics class

Artificial Gravity and the Architecture of Orbital Habitats - Theodore W. Hall - Space Future; detailed technical paper

Artificial Gravity - Technical resources from Theodore W. Hall -

The Physics of Artificial Gravity - Popular Science magazine

Simulated Gravity with Centripetal Force - Oswego City School District Exam Prep Center, New York

Gravity Resources

### Books

Do you have any questions, comments, or opinions on this subject? If so, send an email with your feedback. I will try to get back to you as soon as possible.

## Students and researchers

www.school-for-champions.com/science/gravity_artificial.htm

## Where are you now?

School for Champions

Gravity and Gravitation topics

## Gravitation

### Let's make the world a better place

Be the best that you can be.

Use your knowledge and skills to help others succeed.

Don't be wasteful; protect our environment.

### Live Your Life as a Champion:

Seek knowledge and gain skills

Do excellent work

Be valuable to others

Have utmost character

#### Be a Champion!

The School for Champions helps you become the type of person who can be called a Champion.