SfC Home > Physical Science > Physics >
Explanation of Artificial Gravity - Succeed in Understanding Physics. Also refer to physical science, space station, spacecraft, acceleration, centrifugal force, radian, angular velocity, weightlessness, Ron Kurtus, 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:
- Why have artificial gravity?
- How can artificial gravity be created?
- How fast must a circular space station rotate?
This lesson will answer those questions. There is a mini-quiz near the end of the lesson.
Useful tools: Metric-English Conversion | Scientific Calculator.
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
where
- ω (lower-case Greek letter omega) is the angular velocity in radians per second
- A radian is the distance along a curve divided by the radius
Substituting 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", 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.
See the Side Menu for more Gravitation and Gravity topics
Think of ways to improve on nature
Resources
The following resources provide information on this subject:
Websites
Gravitation and Gravity Resources
Simulating Gravity in Space - From Batesville, Indiana HS Physics class
Books
Top-rated
books on Simple Gravity Science
Top-rated
books on Advanced Gravity Physics
Mini-quiz to check your understanding
If you got all three correct, you are on your way to becoming a Champion in Physics. If you had problems, you had better look over the material again.
What do you think?
Do you have any questions, comments, or opinions on this subject? If so, send an email with your feedback. We will try to get back to you as soon as possible.
Share link
Feel free to establish a link from your website to pages in this site.
Or use our form to send this link to yourself or a friend.
Students and researchers
The Web address of this page is:
www.school-for-champions.com/science/gravity_artificial.htm
Please include it as a reference in your report, document, or thesis.
Where are you now?
Artificial Gravity