A Force of Gravity

By J. Richard Jacobs

SOMEDAY IN THE NOT TOO FAR future, like in a few years from now, we are going to venture out into space on journeys encompassing long periods. Going to Mars is not a spin around the block. We want to see what is out there. We need to know. But doing that is going to put people into close quarters for months and years.

Much ado has been made about the psychological stresses that will be placed on those travelers. One way to help is to give them some semblance of normalcy during the trip. Something to take the stress off of living in a cramped ship where just moving around is a chore. What is that something? Gravity. At least something that acts like gravity.

In science fiction tales, one of the big problems is dealing with how people move around in ships in space. The most convenient solution is to utilize some material or combination of materials acted upon by a mysterious mechanism that miraculously provides normal gravity for all the occupants, wherever they happen to be.

The conundrum here is, how do you do this without introducing a fantasy element? Sorry folks, but the fact is, you can’t. The materials would have to be imaginezium, aintgonaworkium, or some alloy of the two, or the imaginezium requires four AAA batteries to activate it. Extrapolation from current technology and known physics is one thing. Just pulling something out of the air is quite another.

Let’s just say that “real” gravity from these sources is pure fantasy and isn’t being honest in your story building.

Of course, one could simply scoop up a cup of neutron star material and put that in the ship’s gut to provide natural gravity of a sort. However, with all that mass, the ship is not going to have enough acceleration to get from point A to point B in less than a gazillion years, nor will it be able to stop in less than half a gazillion years, either—but it would work—maybe.

Another difficulty here is, once the material is taken from the core of the neutron star, it is going to expand because it’s no longer under all that pressure, and it’s going to do it fast. It’s going to do it a lot. The ensuing explosion will rival an ordinary nova event. I guess that is not going to work, either.

Another fantasy with horrendous consequences. But wait ...! We have one more option. Magnetic fields, right? Wrong.

The application of intense magnetic flux can produce levitation, true enough. It is not the same thing as gravity by any stretch of the imagination. Although gravity is rather weak, it appears to have no limit to its reach. The mass of your body, for example, has an effect on the Andromeda galaxy. Okay, not much, but it does have an effect.

The strength of a gravitational field drops off by the inverse square law. That is to say, if there is a 1 g tug on an object at a specific distance and you increase that distance to double what it was, the tug will now be 1/4 g. A magnetic field at a distance follows the inverse cube law. That is, if the tug is equivalent to 1 g at a specific distance and that distance is doubled the effect will be 1/8 g. If we double the distance again the effect will be 1/16 g and 1/64 g respectively. It’s obvious that for a magnetic field to have any tangible effect, it needs to be pretty close.

One other thing we don’t know anything about is the effect on the human body when it is subjected to intense magnetic energy. Intense enough to have any effect. (The inverse cube law for magnetism is further complicated by the magnet having two poles.)

And there is the problem of generating those magnetic fields along with the power required to do so. If we could drag along a star on our voyage we could tap its energy to have enough power available to run our magnetic field on a trip of some duration. Well, that’s not too realistic, is it? Also, there is the mass of the machinery and hypothetical magnets themselves. We might just as well opt for that neutron star juice. Once again we are operating in the Wizard of Oz realm.

What’s left, aside from some magical Alice-in-Wonderland gravity source that is reasonably portable? Why, inertia, that’s what. We can take inertia with us anywhere and it doesn’t take incredible amounts of energy to make it happen. See, when something is spinning in a constant circular motion there is a constant acceleration imparted to anything at the perimeter. This acceleration is directed inward toward the center of spin and is frequently referred to as centripetal force. Some call the “force” applied to the body, causing it to want to move outward or away from the center, centrifugal force.

Neither of these are “forces” at all. Their names merely denote direction. It’s not real gravity, either, but the body would be affected in such a way that it would, for most purposes, respond to that acceleration in the same way it would respond to the presence of gravity. We could eliminate or substantially reduce bone mass loss and detrimental effects to the immune system and general bodily functions in that way. Our bodies have evolved in a gravity environment and apparently need some presence of gravity to operate properly.

Okay. That sounds reasonable, doable, practical, and realistic. Implying ... Do we have another fantasy getting ready to jump up and bite us in the butt? Thankfully, no, but there are some problems that must be considered before we spin up any old thing and call that a replacement for gravity.

Problem 1. People. What? That’s right, our number one difficulty and prime consideration in this wonderful project to help people cope with space travel is the people in our magnificent machine and how their bodies react to being in a slow-motion blender, and it all boils down to equilibrium and the tendency for humans to puke when that delicate issue is not quite right.

Here on old Mother Earth we have gravity pulling down on us all the time and the difference in the acceleration of gravity at our feet is infinitesimally different than it is at the point where our inner ear resides—the place where our sense of balance (equilibrium) is determined. I’m going to do some math (sorry, it’s unavoidable) to show you where the problem comes into play. Here’s a nifty little formula. I’ll give it to you in both metric and SES (Stupid English System):

a = v2 / r where r is radius in meters, v is the tangential velocity vector in meters/second, and a is the acceleration in meters/sec2.

It’s the same in SES, but r is given in feet, v is in feet/second, and a is in feet/sec2. Because size is important in this case, let’s choose a radius for our walking deck. We want to keep it as compact as possible to begin with so we can obtain highly exaggerated numbers for our illustration of the equilibrium problem. Let’s say we make the walking deck radius just 5 meters for our first example (that’s 16'−4.85" for the metrically impaired). There are other ways to do this, but let’s keep it as straightforward as possible. I mean, this isn’t a physics course, right?

Okay, let’s say we want 0.5 g for our acceleration. How fast do we have to be going to get that?

v = √(a×r) or √(0.5×9.81×5) which gives us 4.9523 meters/second. How fast is that in terms of revolutions/minute? Well, the total distance around our walking deck is 2×3.1416×5 and that is 31.4159 meters. Divide the circumference by the speed and we get 6.3437 seconds to travel that distance. So, 60/6.3437 = 9.4582 rpm. That doesn’t sound too bad, does it?

Now we will stand a 1.85 meter tall man on the rim deck. His feet are going to feel 0.5 g. Cool. Now let’s travel up to his inner ear. We now have a radius (r) of 3.3024 meters. How much gravity is the inner ear going to feel? Our velocity vector is now down to 2×3.1416×3.3024/6.3437 = 3.2709 meters/second and that is going to yield an acceleration of 0.3302 g. That is a difference of about 0.1698 g which is close to 34 percent less acceleration at the balance center than at the feet. Imagine what the effect is on the person trying to walk the length of the deck. It appears it would be an environment suited better to short people. A caterpillar would probably not even notice, unless it attempted to climb something vertical.

You may be asking yourself why the number 0.5 g was chosen. To be honest with you, it was arbitrary. See, we still don’t know how low we can go with gravity effects and still maintain bone mass and proper bodily functions. I think the number can be pretty low, say in the 0.25 g range, but I don’t know that and neither does anyone else—yet. Obviously, if it could be that low it would be an advantage because we could keep the spinning sections fairly compact. Also, from the foregoing, it is apparent that the largest radius possible for any given level of acceleration would be better than going too small. See, if we doubled our selected radius to 10 meters, the velocity differential between feet and inner ear would be substantially less and the puke factor would drop dramatically.

Our equilibrium problem does not end with the differential in acceleration between middle ear and feet. You feel a force on your feet and for all intents and purposes, the body thinks it’s gravity. The fact is, it is not gravity. If our person jumps straight up at a rate of 0.5 meters/second, he/she will continue to move toward the core at that rate until coming into contact with the deck again some distance from where the jump was initiated. I know it sounds weird. It is weird. When you finally make contact with the deck it probably won’t be with acceptably nice consequences, either.

Imagine, you jump up what you think was vertically, but when you made that leap toward the axis of rotation your feet were traveling at 4.9523 meters/second while your head was moving along at just a little over 3.27 meters/second. What does that mean? It means you are going to launch yourself into a backward tumble if you were facing in the direction of rotation. It also means you will be translating along the deck in reverse. Why reverse? Because the deck is moving away from you at the same rate in the direction of rotation but you are not. You are traveling upward at 0.5 meters/second and you have retained the decks speed at your feet and a slower speed at your head. The acceleration is not gravity and you have lost contact with the thing that was providing that “force.” You are now weightless and tumbling in something that is moving almost 5 meters/second away from you in the direction of rotation and toward you in the opposite direction, while you are traveling forward and up at a slightly reduced speed, your body rotating about your balance point (center of “gravity”).

[NASA’s Nautilus-X, pictured at right, would primarily be used for sleeping and lounging on long duration deep space voyages to preclude major bone deterioration.]

Also, if you drop something, it is not going to fall straight down. Actually, it is not falling at all. It is traveling along a line that is a combination of its tangential velocity vector and the outward force vector due to the acceleration at the point it was when it was released. Its path to the deck will appear, to a person standing there, slightly curved away from the direction of rotation. Lesson here, be careful when pouring hot coffee. Better to keep the spout close to the cup. This little phenomenon is known as the Coriolis effect and on our small radius deck it is strong. It is the reason that ping pong and pool tables will not be included for recreation. Also, be super careful when making cross rotation movements. Your feet can get tangled up and you’re then in for another type of tumble with possibly worse consequences than your jump.

I should also throw in a little note about one of the rarely thought of problems in low g environments. Traction. Traction, or frictional resistance, is a function of “weight” and surface area and the coefficient of friction at the interface of two objects. If it is determined we can function and maintain proper bone mass and not suffer any deleterious effects to our immune system at low g, then it would be wise for us to surface the deck, shoe soles, bottoms of cups and other things with high friction coatings, or several other forms of accidents will be waiting in the shadows.

Anyway, the Vomit Comet can’t hold a candle to the weird, nausea breeding effects that one will encounter in a rotating habitat with a small radius and high rate of spin. Small radius rotating habitats would probably be just fine for sleeping and/or lounging but would be lousy for track and field events. There are some other interesting problems in this rotating chamber of horrors, but we’ve covered the major ones.

Problem 2. Structure. When anything tall is built on Earth, we can save some weight as we go upward because the lowest columns are holding up all the weight above them and as we travel skyward, each column in the structure is supporting progressively less weight. That’s the nature of compression. Now, what about the spokes or cables that hold our rotating habitat together. They have to have the same strength at the hub as they do at the far end. Why is that? Because they are in tension. If you measure the tensile load at one end of a string, then measure it at the other, you’ll find that the numbers are the same. We can’t do any tapering because the load is the same throughout for a structure in free space that is not being acted upon by anything more than the load of the rim and some incidental, off axis loading from other sources.

It is understood there will be some lateral loads applied, but they are insignificant and can be minimized by applying the rotational force on the outer side of the rim and stringing cables like bicycle wheel spokes. Some loading will be generated due to bearing friction at the hub where it connects to the ship. Such loads can be greatly reduced through the use of magnetic bearings rather than mechanical systems. Precession loading can be minimized through the use of contrarotating habitats. Spinning up the entire ship would preclude that, but it would be impractical and in some way impossible. Traveling counterweights can be employed to keep off-balance vibrational loading in check.

Probably the simplest and safest configuration would involve short habitat pods suspended from a cable system that can be retracted when necessary or convenient. NASA has proposed something along those lines, though to the best of my knowledge nothing of the sort is actually on the boards (well, the computers). I think, all things considered, that the most difficult part of the rotating habitat is building one that is better than tolerable for human frailties while keeping the structural aspects in balance and, at the same time, keeping the assemblage as compact as is consistent with purpose.

There is nothing new about spin “gravity.” There is also nothing unique about it. It has been used in circuses and carnivals for over a hundred years to thrill people and make them suddenly sick. Konstantin Tsiolkovsky wrote about using rotation to create artificial gravity in space in 1903. Herman Potočnik introduced the idea of spinning up a space station with a 30 meter diameter toroid (15 meter radius) in his paper Problem der Befahrung des Weltraums (“The Problem of Space Travel”). He also suggested it would be a good idea to put it in a geostationary orbit.

When I was a kid, my mother gave me a book that had been made from the collected articles of Werner von Braun and Willy Ley that had appeared in Colliers Magazine. That was about 1952, as I recall. Their space station concept used a 76 meter wheel revolving at 3 rpm. It was intended to provide about 0.3 g to the passengers. It would have had three decks and a permanent crew of eighty. What they outlined as main purpose was as a staging area for ships moon-bound and Mars-bound and other destinations in the future.

NASA has a proposal a vehicle called Nautilus-X that would be equipped with an inflatable, rotating habitat and would be used in deep space. An identical habitat has been proposed as an add-on for the ISS.

Since the mandate for “the moon and beyond” by the current administration in Washington, the U.S. is beginning to get serious about issues arising from long term exposure to zero-g. Several programs are currently either active or gearing up. So far the projected launch of the Bigelow Aerospace prototype experimental space habitat is 2015.

Because of budget issues and ongoing debates over the “value” of space exploration among the members of Congress who don’t seem to understand the “gravity” of the situation, it is going to be an uphill struggle with “acceleration“ inhibited by the “mass” of all those wise individuals who are always making decisions for us because they know we are not capable of such difficult things on our own. Once we shake off the deadweight, things will begin to move. All of those who do understand what is at stake are champing at the bit and few question the solutions now being proposed. But take heart, there are several large donuts in our future and Mars is well within reach of the twentysomethings of today. 

J. Richard Jacobs has lectured on NEOs (Near Earth Objects), PHAs (Potentially Hazardous Asteroids), Mars, the possibility of life in the Universe, and other observational astronomy topics. He also writes science fiction stories and novels.