Artificial Gravity
Published on Dec 3, 2006 at 10:36 pm.
12 Comments.
Filed under physics, space exploration, space station.
One day we hope to send manned missions to Mars, or perhaps establish mining colonies on asteroids. We would even like to have a permanent moonbase. However, all of these ideas have one big problem. Gravity is weaker at all these places. In fact, the only place in the Solar System with gravity that is about the same strength as here on Earth is Venus, and Venus is quite hostile to our life, even with heavily shielded equipment. Now, gravity does all sorts of bad things to us, but our bodies are designed to work in an environment of 1g (the gravity here on Earth). We can tolerate somewhat higher or lower gravity for short durations. Slightly lower gravity may even be beneficial in some instances over short intervals (say recovering from surgery). But, too long in reduced gravity is very bad for the human body. Astronauts and cosmonauts who have been in space for extended periods of time have problems with their muscles and bones. In fact, the bones lose calcium in low gravity environments, and some cosmonauts who were in the Mir space station for nearly a year returned to Earth with symptoms similar to severe osteoporosis. So, in the long term, low gravity is bad. We were simply designed to live in the gravity of Earth.
In science fiction, this is an easy problem to solve — you use artificial gravity generators. Actually, I rather think that this is an invention of producers who wanted to keep special effects budgets down rather than any attempt to overcome physiological problems! But, once the idea was broached, then science fiction writers have been trying to come up with ideas for how gravity could be artificially generated. A favorite solution is to create directed gravitons, the hypothetical particle that mediates the gravitational force. The only problem is that we don’t know how to create gravitons on demand, and there are some theoretical reasons why it may not even be possible.
But, all is not lost. There is an idea that had been pushed by none less than Wernher von Braun for an artificial gravity system. It is simple and within our technology. You simply rotate the space station or spacecraft. Then, let centripetal force do the work for you. The principle is really pretty simple, but to understand it you need to know a few things about circular motion.
To start with, remember that Newton’s first law of motion states than any body in motion will remain in uniform motion (moving in a straight line at constant speed) unless a force acts on it. But, an object in circular motion must always be changing direction of motion, so there must be a force acting on it to make it move in a circle. This force is called the centripetal force. For our example, consider an astronaut standing in a large cylinder that is rotating. The outer edge of the cylinder, where the astronaut is standing is moving at some speed v. The walls of the cylinder must exert a force F on the astronaut to keep him moviing in a circle instead of flying of into space. This force, the centripetal force, is easily derived in first semester physics, and the formula is shown next to the diagram.
Now, comes the interesting part. For the person inside the cylinder, if they are standing still, all they feel is the wall of the cylinder pushing up on their feet. When you are standing on level ground, what you really feel is the ground pushing up on you to keep you from falling to the center of the Earth. Gravity pulls down, and unless you feel the ground pushing up then you feel weightless. This is the condition that astronauts experience in orbit. The Earth pulls down on them, but they are moving in orbit, always falling, but always missing the Earth. So, they feel weightless. On solid ground, the ground pushes up on you with a force equal to your weight, which is the product of your mass times the acceleration due to gravity: F = mg.
But, inside the space station, it turns out that if you are just standing there, then you can’t tell if it is level ground pushing you against gravity or if it is the wall of the cylinder pushing on you to make you go in a circle. Pushing is pushing. You feel the same. So, you feel like you have weight. If you want to feel like you weigh the same as you do on Earth, then you just spin the cylinder fast enough for the centripetal force to equal mg, your weight. But that may mean spinning the cylinder quite rapidly, which might put a lot of engineering stresses on it. So, perhaps you could get away with an apparent gravity of 1/2 or 1/3 of your normal weight. So, we’ll use the term f in our equation to represent the desired fractional weight that you want. The other thing is that we probably don’t really care so much for the actual speed of motion so much as the time that it takes to go around. This is the period, and it can be found by dividing the circumference of the circle by the velocity:
Plugging this into our earlier centripetal force equation, and using fmg as the fractional weight desired, and then doing a little algebra, we get:
Now, we know the rotational period in terms of the radius of the cylinder, the acceleration due to gravity, and the fractional weight desired. But, often what we want is to know the rotational rate in revolutions per minute. That is easy. You do a little more math and you get:
where g is measured in meters per second squared, and r in meters (or g in feet per second squared and r in feet), and the answer comes out in rpm. This tells you how fast to rotate your space station if you want to simulate gravity of a particular level. Unfortunately, we don’t know the minimum gravity needed for the human body to work properly over a long period of time. At best, we can just guess. But clearly, the closer that you want the fraction to be unity, the faster that you have to rotate the space station. But, also note that the bigger the radius, the slower that you will need to rotate your space station. So, perhaps you should just build it quite large.
But, if the space station has a very large radius, note that there is a lot of wasted empty space in the middle. The only part that has the desirable gravity is near the outer edge. So, a suggestion was made to build the living area as a large torus — essentialy making the space station into a giant spinning wheel.
For large space colonies, with a very big radius, the colony could be rotated at a comfortably gently rate, people living in the ring at the outer edge of the colony would feel just like they were on Earth (if f = 1). So, this is how we’d more likely generate artificial gravity, rather than with the graviton generators used in science fiction.
-Astroprof
(Future space colony images courtesy of NASA)
A Ler…-- Rastos de Luz on December 4, 2006 at 5:20 pm: 1
[…] “Artificial Gravity“, no Astroprof’s Page. Um tema sempre na berlinda quando se fala em assuntos desde futuras missões a Marte, até ficção cientÃfica. […]
Quasar9 on December 4, 2006 at 6:37 pm: 2
Wow - a bit of synchronicity
I posted the same pic today (Monday)
I’ll link up this artificial gravity post, if that’s ok - Thanks!
Darnell Clayton on December 4, 2006 at 7:33 pm: 3
Great post! I hope our bodies will be able to adapt to a little as 1/6th Earth gravity as that would enable us to live on the moon!
If not, I wonder if construction “orbital towers” on the lunar surface would work as well (or just simply wearing extra heavy suits).
PS
I linked to you article but I didn’t see a trackback.
J. Donahue on February 15, 2007 at 2:10 pm: 4
Many thanks for this. I have recommended it to my high school physics students both for the content and the excellent illustrations.
Astroprof’s Page » Astronaut Bone Loss on March 12, 2007 at 12:33 pm: 5
[…] The Skylab missions sought to mitigate this trend in bone loss by providing astronauts with exercises. The Skylab interior was mostly like a bit cylinder, and in part of that cylinder, astronauts could run along the walls of the space station, with the force of the walls providing a centripetal force on their body, which acted as a weak sort of artificial gravity. On a much larger scale, one suggestion for providing artificial gravity in space stations or on a long duration spaceflight is to rotate the vehicle itself. Unfortunately, that is an expensive proposition and poses numerous engineering issues (particularly in maintaining antenna alignment with Earth as well as docking of spacecraft) as well as safety concerns for astronauts in extravehicular activities (if they lose their grip, they hurl off into space). […]
yilmaz on March 14, 2007 at 6:55 am: 6
Not possible? look at the website below
http://www.esa.int/SPECIALS/GSP/SEM0L6OVGJE_0.html
Astroprof’s Page » Space Settlement Art Contest on December 1, 2007 at 4:42 pm: 7
[…] About a half century ago, Wernher von Braun proposed that one day soon, there would be vast orbiting space stations. He envisioned giant cylinders and toruses slowing spinning to produce artificial gravity through centripetal forces. With the rapid progress in space travel and space exploration of the 1960s and early 1970s, it seemed that his vision would come to pass. An early scene of Stanley Kubric’s 1968 movie 2001: A Space Odyssey shows just such a station. But, such a feat is difficult and expensive. It seemed just out of reach at that time. Arthur C. Clarke, who originally wrote the novel that Kubric’s movie was based on, stated once that fantastic ideas of this sort go through three stages on their way to fruition. First, it is said that such an endeavor can’t be done. Then, people realize that it can be done, but that it probably isn’t worth the effort: it is too expensive, it won’t bring enough of a return for the investment, etc. Then, finally, once the idea is put into practice, everyone agrees that it was really a wonderful idea in the first place. Geosynchronous satellites are such an idea. At first, the idea of putting a satellite into orbit over one spot on Earth seemed fantastic and unrealistic. The, rockets developed that could do the job, but no one saw any need for such a satellite. Now, geosynchronous satellites are essential for communication and commerce, and society as we know it depends upon them. Currently, space settlements, as envisioned by von Braun and others, are in the second stage. We now know that they can likely be done, but only at great cost, and the average person believes that the cost is too great and the return too small. However, many people in space exploration believe that such settlements are inevitable, and that the ultimate return would be far greater than the impact that geosynchronous satellites would bring. I may blog about that in a later entry. […]
Anthony Smales on April 23, 2008 at 3:05 am: 8
If you wanted to have more gravity on the moon, you could do it like so:
1/ build a shell around the moon
2/ apply a spin to the moon to create the centrepital force (use rockets on opposite sides of the shell, facing in opposite directions) (extra rockets may also be useful, in case you want to reposition the moon in space)
Now you can walk on the inside of the shell!!
next thing to do would be to use, probably nanotechnology, to terraform the inside of the shell and introduce oxygen to the enclosed area. I’d also suggest that the shell should be coated to prevent penetration of cosmic rays.
Elvan Knight on June 12, 2008 at 12:16 am: 9
Until such time that experiments carried out in the vacuum of space where gravity of an type is absent, show that simulated gravity can be created by centripetal forces I just do not believe it will work.
My belief is that centripetal forces exist because of gravity so therefore can not be created in it’s absence.
Astroprof on June 12, 2008 at 1:03 pm: 10
Actually, this is first semester physics stuff. And, of course, they did simulate artificial gravity in Skylab. Only, in that case, the astronauts ran around the interior of the space station rather than the space station rotating.
David on August 11, 2008 at 8:46 pm: 11
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Astroprof on August 11, 2008 at 10:03 pm: 12
Unfortunately, you can’t just “create” gravity. The best that you can do is to simulate it in the fashion described in this post. But, you can’t just build a mini-gravity generator at home.