Gravity: What it is and what it isn’t.
Gravity is the attraction that occurs between any two bodies, anywhere, all the time. Sir Isaac Newton was the first to quantify this effect. His famous equation for the force of gravity is:
F = G x M1 x M2 / r^2
F is the force of gravity
G is a constant of proportionality
M1 is the mass of the first body.
M2 is the mass of the second body.
Gravity is the force that holds us to the surface of Earth and the Moon in orbit about Earth. M1 is the mass of our own body, and M2 is the mass of Earth. r is the distance between the centers of gravity of the two bodies. Even though gravity seems like a really strong force, it is very weak. For gravity to be felt, one of the bodies must be very large. Conversely, if both bodies are small, like one human’s gravitation pull on another human, or one car’s gravitational pull on another car, the gravity generated is negligible by several orders of magnitude.
The problem with gravity arises when we leave Earth and go into outer space, ending up either in orbit, where we are in a state of free fall, or far from Earth where its gravitational influence is minimal. The human body doesn’t do well in zero gravity (microgravity). And when someone must experience it for an extended period of time, methods of creating artificial gravity are highly desirable.
Artificial gravity generated by various techniques isn’t always what it seems or even what some people think it is. Generally, two methods are used to generate artificial gravity. The first and most frequently encountered is through space vehicle linear acceleration using a propulsion system. The second is the rotation of a structure so that at its interior wall the centripetal acceleration acts like gravity.
Gravity – Acceleration Equivalence
Einstein, in one of his famous thought experiments, demonstrated the equivalence between acceleration and gravity. To understand the equivalence, imagine you wake up in a small room the size of an elevator and you do not know where you are. You have no recollection of how you got there. However, one thing you believe you do know. You think you are on the surface of the Earth because you feel your weight as your feet push down on the floor. If you take a little jump, your feet immediately slam down against the floor, so you are certain your are on the surface of the Earth.
Then, quite unexpectedly, your weight vanishes and you start floating around in the room. But since the room is the size and shape of an elevator, you assume that the elevator is dropping, free falling, and that you will soon hit bottom. But you don’t. The weightlessness continues, and you don’t understand how this can be. An elevator can’t fall forever.
Then you notice a small window in the room, and when you look outside, you see that this room you are in isn’t an elevator at all. You are in a rocket in outer space. When the rocket is thrusting, you sense its acceleration as gravity. This is artificial gravity. It is not the attraction of one mass for another. This type of artificial gravity (acceleration) is used in Robot Dawn frequently to provide a comfortable passenger environment for travel about the Solar System.
Artificial Gravity from Rotation
Another method of generating artificial gravity is through centripetal acceleration by rotation. If you have ever ridden a Tilt-A-Whirl at the local fair, you are well aware of the effect. The passenger is strapped inside one of the seven spinning cars that are in turn attached to a large spinning platform. When the platform spins, the passengers are thrust against the back of the car through centripetal force. The cars also spin about their own axis providing a second level of centripetal acceleration that further increases or decreases the forces acting on the passengers.
This rotation-generated acceleration is also used in space to simulate Earth’s gravity, or at least engineers and scientists have proposed that it be used to provide a more livable environment for astronauts. However, no one has built a rotating habitat for astronauts. Not even the International Space Station has artificial gravity. So far, science fiction authors are the only ones to make effective use of it. Robot Dawn uses artificial gravity generated by rotation at both the DSO Torus and the O’Neill space colony.
The equation for determining centripetal acceleration is:
a = r x ω^2
a = the centripetal acceleration
r = the distance from the center of rotation to the cylinder surface
ω = the rotation rate of the cylinder
The rotation rate of the O’Neill colony is about one revolution every two minutes. This provides one-g at the internal surface of the cylinder. But this artificial gravity is much different that the gravity discovered by Sir Isaac Newton.
Misconceptions Concerning Rotation Generated Artificial Gravity
In Robot Dawn, the O’Neill space colony at SE-L4 generates artificial gravity through rotation. The colony is a large cylinder five miles in diameter and twenty miles long. It spins at the rate of one revolution every two minutes about its longitudinal axis. This generates one-g of acceleration on the interior surface of the cylinder. Anyone standing on the interior surface of the cylinder will also experience the one-g and should be comfortable in that environment.
However, since the artificial gravity has its origin in centripetal acceleration due to the cylinder’s spin, it is much different from the gravity discovered by Newton. For example, assume that initially the empty (no atmosphere) cylinder is stationary and not spinning, and that an astronaut is inside the cylinder but floating in the zero-g environment a foot or so off the cylinder interior surface. Then spin up the cylinder to one revolution every two minutes. An accelerometer attached to the cylinder wall will measure one-g. But the astronaut floating one foot off the interior cylinder surface will feel nothing because he is not rotating with the cylinder. He is simply stationary inside. The cylinder wall is the only thing that experiences one-g. In a real gravitational field, gravitation permeates the space around the bodies. Not so with artificial gravity. As a matter of fact, our astronaut that is one foot off the wall can move around inside the cylinder to any place he wants (if he has a small propulsion pack). He can stop and stay there as long as he likes without being subjected to any form of gravity (except for microgravity effects which are very small).
Now lets say that our astronaut is standing on the wall and holding onto a cable that is fixed to the cylinder wall, so that he, the cable and the wall are rotating around the centerline of the cylinder at the rate of one cycle every two minutes. Our astronaut will now feel the full one-g gravity felt also by the wall. Say the cable is attached to the center (spin axis) of the cylinder (maybe the cylinder has an iron rod that goes along the centerline from one end of the cylinder to the other), so that this cable is actually a radius of the cylinder. Then let the astronaut climb the cable from the wall all the way up to the centerline. We can see from the equation a = r x ω^2 that he will initially feel one-g of acceleration, but that as he makes his way toward the centerline the acceleration will gradually drop off to zero at the centerline. This is because he is rotating with the cylinder, and the acceleration he feels is caused by his rotation about the cylinder centerline. His artificial gravity gradually decreases because his distance from the center of rotation, r, decreases as he climbs.
Now place an atmosphere inside the cylinder and raise the pressure to 14.7 psi, that which we experience at the surface of the Earth. Assume that the interior wall of the cylinder is so smooth that nothing sticks to it, not even the air. Now spin up the cylinder to one rotation every two minutes. The atmosphere inside the cylinder stays put, even that against the frictionless cylinder wall, and the internal pressure is still 14.7 psi and uniform throughout. In this situation, the wall is traveling at 691 feet per second relative to the air, but since we have stipulated that there is no friction between the air and the wall, the air remains still. Not only that. The artificial gravity is all within the cylinder wall, and the atmosphere experiences no gravity.
Now, increase the friction between the cylinder interior wall and the atmosphere by increasing the wall surface roughness. As the wall spins, the air in rough contact with it will move along with it. That air in direct contact with the wall will experience the same acceleration (gravity) as the wall, and this air will drag that air close to it along in the same direction but not the same velocity. A boundary layer will develop in the first few feet of air close to the wall, and within this boundary layer the velocity will be quite high but drop off quickly and dramatically at the upper edge of the boundary layer. This will also cause the air close to but above the boundary layer to start to move a little, and gradually all the air in the cylinder will start to move in the same circular path as the wall, rotating about the cylinder centerline. A velocity gradient will develop from the wall all the way to the center of the cylinder where it will go to zero and start traveling in the opposite direction along the radius until it reaches 691 feet per second at the wall opposite. This air velocity gradient will create a gravity gradient inside the cylinder that is totally dependent on air velocity. Any object in the air will experience the same gravity as the air if it keeps up with the air at that radius. But that actually won’t happen because friction between the object and the air will be the only thing keeping the object traveling in a circle. If the object is more dense than the air, it will not follow the air but will be slung out closer to the wall. The object will follow a trajectory to the wall where it will experience the full one-g, provided that it is able to keep up with the wall and doesn’t roll backward along it, pulled backward by wind resistance.
Now, lets populate the interior of the cylindrical colony with buildings. All these buildings rest upright with their foundations firmly fixed against the cylinder wall and spin with it. These buildings will experience the full one-g artificial gravity. They will also disrupt the airflow close to the wall, causing some air to travel with the wall, or at least create turbulence around the building. When you add trees bushes, etc., you get more turbulence up to and somewhat beyond the top of the buildings. This will increase the boundary layer and change to an extent the air velocity profile all the way to the center of the cylinder, and therefore, the gravity gradient of the air, such that it is.
The important thing to remember is that the one-g at the cylinder wall is not real gravity and that gravity does not propagate into the cylinder. This is centripetal-force artificial gravity and is only propagated to other objects that travel with the rotating wall.
Artificial Gravity Is Not Actually Gravity
I have seen several discussions on the Internet about whether artificial gravity is actually gravity. And of course, it is not. Real gravity comes from the attraction of masses. Artificial gravity that results from rocket acceleration may seem like real gravity because all objects within the rocket act as if they were on Earth if the acceleration is one-g. But this is not real gravity because it does not come from the natural attraction of one object for another. (F = G x M1 x M2 / r^2)
Artificial gravity generated by a spinning object is even less like real gravity than that generated by a rocket’s acceleration. A couple of the Internet message board I visited discussed the case of a spinning cylinder or torus where an astronaut on the inside surface, where the artificial gravity exists, jumps through a hole and falls through into outer space as if he were on earth. Some commenters said that this won’t happen. But I am here to tell you that it will. And you don’t need Einstein’s Theory of Relativity, either Special or General, to solve the problem. All you need is Newton’s three laws of motion:
First law: In an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force. [Note: velocity is a vector quantity having both magnitude (speed) and direction.]
Second law: In an inertial reference frame, the vector sum of the forces on an object is equal to the mass of that object multiplied by the acceleration of the object: F = ma.
Third law: When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.
Prior to his leap of faith into the hole in the wall of either a spinning torus or cylinder, the astronaut is traveling at the same speed as the wall along a circular path, and as mentioned above, that is about 691 feet per second. What gives the wall and the astronaut artificial gravity is the fact that the wall is constantly changing direction, as it must to maintain its circular motion. The astronaut is constantly being acted upon by the wall and also forced along the circular path, in accordance with Newton’s second law. When the astronaut jumps into the hole in the wall, he is no longer in contact with the wall and being forced along the circular path but is allowed to continue at a velocity of 691 feet per second but now along a straight-line path tangential to the wall, in accordance with Newton’s first law. So the astronaut is on a straight line trajectory from the point where he jumped, and the wall is on a curved path and is continuously pulled away from him. The wall continues to feel one-g, but the astronaut is in a state of free fall. The summation of forces acting on him are zero, so his acceleration is zero, according to Newton’s second law.
Work to do:
In my opinion, one of the critical issues of rotating space colonies is air turbulence. We have seen that the interior surface of the cylinder in the O’Neill colony is translating at 691 feet per second. If all the air in the colony isn’t rotating to keep up with cylinder rotation, air turbulence will result. How severe this is, I don’t know. I’m not sure that anyone else who really understands this problem has actually worked it out either. I have found no indication that Dr. Gerard K. O’Neill himself addressed this issue. I am an engineer with a BS in mechanical engineering from Arizona State University and an MS from Stanford University in astronautical engineering, and I did take several classes in fluid mechanics, but that was many years ago. I also worked as a flight mechanics engineer on many US Air Force and NASA projects. I’m not sure if I can solve this fluids problem, but I plan to look into it. I’ll keep you posted.