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Artificial gravity in a space station

How can we create a kind of ‘artificial gravity’ with circular motion?

Recall our unit on inertia (objects in motion tend to stay in motion, in a straight line)

inertia car GIF

recall our unit on centripetal force:
objects would fly off in a straight line, unless an inward-directed forced kept them held in a circle

uniform-circular-motion

What happens when we combine inertia with circular motion?

For a fast-moving object trapped in a circular track,
it wants to fly off in a straight line
but the track has an inward-pointing FN  (normal force)
which prevents the car from flying out
so the car is stuck moving along the track

g-forces-on-a-roller-coaster

A person inside this car feels as if their is a gravitational force,
pulling them towards the tracks
keeps them safely inside the car, even when upside down.

What if we did the opposite? Run in circular bowl (as below)
your body wants to fly off in a straight line
but the bowl (the ground!) has an inward-pointing FN  (normal force)
which prevents you from flying out
so you’re stuck moving along the surface

man-in-hole-centripetal-force-normal-force

From Conceptual Physics, Hewitt:

Now apply this to spaceships!

Consider a ladybugs living inside a bicycle tire.
Drop the tire from an airplane high in the sky
The ladybugs float freely, zero g, while the wheel is in free fall.

But now spin the wheel: they’ll experience something that feels like gravity.

Ladybugs in space station circular

From within a rotating frame of reference,
there seems to be an outwardly directed centrifugal force.

Gravity is {almost} simulated by centrifugal force.

To the ladybugs:

“up” is toward the center of the wheel.

“Down” is what we call “radially outward”

Today we live on the outer surface of our spherical planet, held here by gravity. Earth has been the cradle of humankind. But we will not stay in the cradle forever. We are on our way to becoming a spacefaring people. In the years ahead many people will likely live in huge lazily rotating space stations where simulated gravity will be provided so the people can function normally

Occupants in today’s space vehicles feel weightless because they lack a support force.

They’re not pressed against a supporting floor by gravity, nor do they experience a centrifugal force due to spinning. But future space travelers need not be subject to weightlessness. Their space habitats will probably spin, like the ladybugs’ spinning bicycle wheel, effectively supplying a support force and nicely simulating gravity.

The interaction between the man and the floor of a space habitat, as seen at rest outside the rotating system.

Floor presses against the man (action) – and the man presses back on the floor (reaction).

Only force exerted on the man is by the floor. It is directed toward the center and is a centripetal force.

As seen from inside the rotating system, in Figure 12.20b, in addition to the man-floor interaction, there is a centrifugal force exerted on the man at his center of mass. It seems as real as gravity.

Hewitt

Hewitt

Yet, unlike gravity, it has no reaction counterpart—there is nothing out there that he can pull back on.

Centrifugal force is not part of an interaction, but results from rotation. It is therefore called a fictitious force.

Challenges of Simulated Gravity

The comfortable 1 g we experience at Earth’s surface is due to gravity. Inside a rotating spaceship the acceleration experienced is the centripetal/centrifugal acceleration due to rotation. The magnitude of this acceleration is directly proportional to the radial distance and the square of the rotational speed.

For a given RPM, the acceleration, like the linear speed, increases with increasing radial distance. Doubling the distance from the axis of rotation doubles the centripetal/centrifugal acceleration. At the axis where radial distance is zero, there is no acceleration due to rotation.

Small-diameter structures would have to rotate at high speeds to provide a simulated gravitational acceleration of l g. Sensitive and delicate organs in our inner ears sense rotation. Although there appears to be no difficulty at a single revolution per minute (1 RPM) or so, many people have difficulty adjusting to rotational rates greater than 2 or 3 RPM (although some people easily adapt to 10 or so RPM).

To simulate normal Earth gravity at 1 RPM requires a large structure— one almost 2 km in diameter. This is an immense structure compared with the size of today’s space shuttle vehicles.

Space Station 2001 A Space Odyssey

What might it look like inside such a space station?

https://www.youtube.com/watch?v=qD3GMwg4qZo

Economics will probably dictate that the size of the first inhabited structures be small. If these structures also do not rotate, the inhabitants will have to adjust to living in a seemingly weightless environment. Larger rotating habitats with simulated gravity will likely follow later. Imagine yourself living in a rotating space colony such as the one shown in Figure 12.21.

The O’Neill cylinder (also called an O’Neill colony) is a space settlement design proposed by American physicist Gerard K. O’Neill in his 1976 book The High Frontier: Human Colonies in Space.  O’Neill proposed the colonization of space for the 21st century, using materials extracted from the Moon and later from asteroids.

An O’Neill cylinder would consist of two counter-rotating cylinders. The cylinders would rotate in opposite directions in order to cancel out any gyroscopic effects that would otherwise make it difficult to keep them aimed toward the Sun.

Each would be 5 miles (8.0 km) in diameter and 20 miles (32 km) long, connected at each end by a rod via a bearing system. They would rotate so as to provide artificial gravity via centrifugal force on their inner surfaces. {Wikipedia}

A pair of O'Neill cylinders. NASA ID number AC75-1085

A pair of O’Neill cylinders. NASA ID number AC75-1085

Rick Guidice, NASA Ames Research Center; color-corrector unknown

Rick Guidice, NASA Ames Research Center; color-corrector unknown

If the structure rotates so that inhabitants on the inside of the outer edge experience 1 g, then halfway between the axis and the outer edge they would experience only 0.5 g. At the axis itself they would experience weightlessness at 0 g.

The possible variations of g within the rotating space habitat holds promise for a most different and as yet unexperienced environment. We could perform ballet at 0.5 g; acrobatics at 0.2 g and lower g states; three-dimensional soccer and sports not yet conceived in very low g states. People will explore possibilities never before available to them.

This time of transition from our earthly cradle to new vistas is an exciting time in which to live—especially for those who will be prepared to play a role in these new adventures.12.6
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What happens if you let go of an object?

Then we will see that the forces are not like real gravity.

http://spiff.rit.edu/classes/phys211/lectures/orbit/orbit_all.html

http://spiff.rit.edu/classes/phys211/lectures/orbit/orbit_all.html Copyright © Michael Richmond. This work is licensed under a Creative Commons License.

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http://spiff.rit.edu/classes/phys211/lectures/orbit/orbit_all.html

http://spiff.rit.edu/classes/phys211/lectures/orbit/orbit_all.html Copyright © Michael Richmond. This work is licensed under a Creative Commons License.

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O’Neill Cylinder Simulator

David Kann, Math and Physics teacher working with IB students in Australia.

“In our discussion we came across the thought of what it might look like to throw a ball in the air in a zero-gravity rotating space station. I was stumped so I brought the question to my colleagues. They were stumped. Eventually I was able to make a pair of parametric equations for position in time to model the motion of the ball but it didn’t tell me much unless I could visualize the graph of the equations. The next logical step was to simulate the equations in software. Enter the O’Neill Cylinder Simulator:”

“When I saw the parametric equation animated (like above) it blew my mind a little. Here we see someone throwing a ball up and to the left, it circles above their head, and returns to them from the right. Throwing a ball in an O’Neill Cylinder apparently is nothing like on Earth. You can do some really sweet patterns:”

Spiral space station 1

Videos

Visions Of The High Frontier Space Colonies of 1970

Rama

In his 1973 science fiction novel Rendezvous with Rama, Arthur C. Clarke provides a vivid description of a rotating cylindrical spaceship that is about 50% larger than the classic 20-mile long O’Neill Cylinder. Artist Eric Bruneton has created this striking 3D animation of Rama.

http://www.nss.org/settlement/space/rama.htm

Rama video YouTube

Rama video – artist’s homepage and resources

Ringworld

(to be added)

Ringworld video

External links

Throwing a ball in a rotating space station

Would you be able to tell the difference between centrifugal force and normal gravity?

Gravity in the Elysium Space Station – Rhett Allain

http://www.bogan.ca/physics/coriolis.html

Artificial Gravity in Spacecraft by Ron Kurtus

NASA Skylab running track YouTube

Learning Standards

SAT Subject Test in Physics
Circular motion, such as uniform circular motion and centripetal force

2016 Massachusetts Science and Technology/Engineering Curriculum Framework
HS-PS2-1. Analyze data to support the claim that Newton’s second law of motion is a
mathematical model describing change in motion (the acceleration) of objects when
acted on by a net force.

HS-PS2-10(MA). Use free-body force diagrams, algebraic expressions, and Newton’s laws of motion to predict changes to velocity and acceleration for an object moving in one dimension in various situations

Massachusetts Science and Technology/Engineering Curriculum Framework (2006)
1. Motion and Forces. Central Concept: Newton’s laws of motion and gravitation describe and predict the motion of most objects.
1.8 Describe conceptually the forces involved in circular motion.

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