Artificial gravity in spinning space ship conumdrum

[atyy]

I was pleased that someone mentioned Mach's Principle, which caused me to find the wikipedia discussion on the same. I am content to learn that Einstein grappled with the issue and decided that inertia originates in a kind of interaction between bodies. That is, (as I understand it) the presence of other matter (I guess all matter in the universe) determines what is and is not spinning.

I think even in General Relativity, rotation is absolute, in the sense that it produces a gravitational field without a matter source. The other common absolute motion in GR texts is the uniformly accelerating rocket, which also produces a gravitational field without a matter source.

 

[Nick666]

For anyone planning to check in at the Centrifugal Space Station, remember to sit your *** and put your furniture on the far ends of the space station.

 

[Shooting Star]

Spinning? Who says the carnival ride is spinning and not the Earth? Who nominated the Earth to be the center of the universe?

It's easy to slip into classic absolute space thinking. Though the question isn't absolutely answered yet, I'm still pleased enough by what was said earlier.

It is also easy to simplify the matter to an extent where metaphysics takes precedence over Physics. Mach’s Principle, though a guiding light for Einstein, need not be last word. In addition, the principle itself indicates that nearby masses should have an appreciable effect on the motion of a body. Taking the view that the carnival ride can be described completely by considering relative rotations would be too simplistic.

I think even in General Relativity, rotation is absolute, in the sense that it produces a gravitational field without a matter source. The other common absolute motion in GR texts is the uniformly accelerating rocket, which also produces a gravitational field without a matter source.

Please remember that all these results apply to our universe, where there is a background of matter, distant or otherwise. Otherwise, what would we measure the rotation against? (Please don't say with accelerometers.) That is the whole spirit behind Mach’s Principle. We have to find a different universe and conduct some experiments before conclusively stating how much of an effect the distant or nearby matter have on the motion with respect to any frame of reference.

(As far as I remember vaguely, there are matter-free solutions to the GR Equations, though I must admit that I am not familiar with their status in accepted science.)

[About "Shooting star is the Man! or woman?", please look up my profile, which contains a single entry. However, due to the way language and society have evolved, "name_of_woman is the the woman!" doesn't quite deliver the original connotation...]

 

[atyy]

Please remember that all these results apply to our universe, where there is a background of matter, distant or otherwise. Otherwise, what would we measure the rotation against? (Please don't say with accelerometers.) That is the whole spirit behind Mach’s Principle. We have to find a different universe and conduct some experiments before conclusively stating how much of an effect the distant or nearby matter have on the motion with respect to any frame of reference.

Well, it's a bit unclear what Mach's Principle is. General Relativity respects some form of Mach's Principle in the sense that the local gravitational acceleration of a test particle is inertial (ie. an accelerometer measures zero). I'm not sure I'm recalling correctly, but I believe "General Relativity" by Hobson, Efstathiou, and Lasenby actually exclude rotated frames from being considered inertial, and call this "Mach's Principle"!

 

[schroder]

Shooting Star, Like other have explained, I think the coriolis effect will be at play in a rotating spaceship (and on earth). But, I'm wondering if the magnitude of the effect is a greater in space, and how it is calculated in space or on land (moon, earth, etc).

From reading this one cannot avoid the conclusion that there is a lot of confusion concerning gravity and centripetal acceleration. This is understandable since gravity is a centripetal acceleration, but generally when we speak of centripetal acceleration we are not speaking about gravity! Gravity, as far as we know, is not related to rotation, but is directly proportional to mass and indirectly proportional to the square of the distance. Centripetal acceleration is directly proportional to the velocity of rotation and the inversely proportional to the distance from the axis of rotation. The idea of utilizing centripetal acceleration to simulate the force of gravity does certainly have it’s merits. Since the earliest days of orbital space flight it became apparent that humans who are removed from the force of gravity as well as electromagnetic fields suffer biological consequences. The excuses which were used in the 1960’s, such as, “He slipped and fell in the shower”, for returning astronauts, are no longer offered or accepted. But a great deal more research needs to be done to determine if this form of “gravity substitute” is indeed viable, as it may well have serious long-term health consequences. The first thing to realize is that the force of centripetal acceleration due to rotation, while generating a similar force magnitude, is not the same as the force of gravity. On the surface of the earth, the force of gravity can be calculated from the equation: g = G x M / r^2 Where G is the gravitational constant of 6.67 x 10^-11, M is the mass of the Earth 5.98 x 10^24 kilograms and r is the radius of the Earth 6.37 x 10^6 meters. This results in a gravitational acceleration of ~ 9.8 m/s^2. Now, for an astronaut, or any human, who has the height of 2 meters, this gravitational force will vary along his height, from head to toe, by a factor of only one part in ten million. So essentially, there is no variation in gravity along the height/length of a human on the surface of the earth. However, the centripetal acceleration, and thus centripetal force, exerted on this same astronaut who is inside a spacecraft which employs rotational centripetal acceleration to simulate the force of gravity will experience quite a bit of variation along his 2 meter height. If we assume a spacecraft of one kilometer in length, from the axis of rotation, it will need to have an angular velocity of 0.099 rad per second to achieve a centripetal acceleration which is the same as gravity, 9.8 m/sec^2. Due to the astonauts’ height of 2 meters, the radius from the axis is now 998 meters and with the same angular velocity the centripetal acceleration will be only 9.78 m/sec^2. This may not seem to be much of a variation, but it certainly is not a trivial consideration! This represents a variation of 2 parts in one thousand, compared to the one part in ten million on the surface of the earth. No one can say what the possible biological consequences may be of this increased variation of about five orders of magnitude over a long length of time. Obviously, much more research needs to be done in this area.