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The nature of gravity

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brianvds
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« on: November 17, 2013, 05:18:04 AM »

This is a bit of a long story, so bear with me.

I have been rereading one of my favourite SF books, namely Iain M. Banks' "Consider Phlebas." (I still have no idea what the title means, but that's another story).

Anyway, in it the protagonist, along with a ragtag group of pirates, visit a structure called an orbital, where they want to strip an abandoned megaship of a few things that may be of use to them. An orbital is basically a gigantic ring in space, spinning so that an artificial gravity is created on its inner surface.

Some of the pirates are outfitted with antigravity units in their space suits. But their captain warns them not to try using these on an orbital, because they only work in "real" gravity where they cancel out the effect of mass rather than the effect of acceleration.

Now of course this is all fiction, so the author can postulate whatever he likes, and as far as I know there isn't such a thing as antigravity anyway. But if I understand Uncle Albert correctly, if AG works on a planet, it should work just as well on an orbital, because the effects of acceleration and mass are exactly equivalent.

Or are they? My knowledge of physics is almost non-existent. But I'm sure our resident physicists will have fun speculating about the notion of AG and how it may or may not work (the very thought of AG that works in an accelerating reference frame tells one something about what a technical challenge it will be to develop it - somehow that would seem even more magical than someone levitating in "normal" gravity!  Grin )

Anyway, over to our physics experts, who will hopefully find a way to explain their ideas without reams of incomprehensible formulae. :-)
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Rigil Kent
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« Reply #1 on: November 17, 2013, 07:09:45 AM »

Speculative preamble by non physicist: I think real gravity is indeed quite different to artificial gravity, as the author says. Real gravity is an attractive force. But the artificial gravity experienced by an observing body inside of a spinning wheel is a symptom of inertia, the resistance of the body to accelerate. The body wants to travel at a constant velocity in a straight line, but the inner wall at the perimeter of the giant wheel keeps scooping it back towards center. The force that the wall exerts on the observer's body is then misinterpreted as gravity.

If the anti-gravitational device works by disrupting the attractive forces associated with real gravity, then it will not necessarily also affect a body's inertia.

ETA: It might be possible to manipulate a pebble in such a way that it floats inside the space between the perimeter and hub walls of the giant spinning wheel (although it may require construction of the wheel around the stationary pebble in space!). If this is indeed possible, it will serve as a clear demonstration of the difference between the effects of the two gravities.


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« Last Edit: November 17, 2013, 08:18:47 AM by Rigil Kent » Logged
Mefiante
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« Reply #2 on: November 17, 2013, 10:11:07 AM »

Einstein’s General Relativity (GR), which contemplates gravity and accelerated motion, is founded on a deceptively simple principle, namely the Equivalence Principle.  It states that gravitational mass is exactly equal to inertial mass.  That is, the force of gravity you feel on Earth’s surface (due to your gravitational mass) is exactly equal to the force that would be required to accelerate you rectilinearly at 9.8 m/s² in gravity-free space (due to your inertial mass).  The upshot is that if you were in a closed container and couldn’t see outside, there is no experiment you could do to determine whether you are in a gravitational field or being accelerated along a straight trajectory.  To the best of my knowledge, gravitational mass and inertial mass are currently known to be equal to an accuracy of better than one part in 10 quadrillion (short scale).

However, Banks’ “orbital” is different.  You can easily establish that you’re in one of those simply by throwing a ball in the direction that appears to you as vertically upwards.  The ball will visibly follow a curved path due to the Coriolis effect.

In Rigil’s diagram, it’s not possible to get an object to float as long as the orbital is spinning around any hub that is situated away from the object.  The reason for this is that such an object would need to follow a curved path in order to stay afloat as it were.  But Newton’s first law tells us that an object needs an unbalanced external force exerted on it to change its velocity — and remember that velocity is a vector, having both magnitude and direction.  An object rotating at a constant rate is the classic case where the speed is constant but the velocity changes.  (All of the aforesaid is quite beside the fact that without any external help, the orbital will automatically spin around its own centre of mass.)

If anti-gravity (other than rocket engines) were easily achievable, say as a shield, and it uses little if any energy, you could use it to generate essentially free power.  In one of the simplest demonstrations of this, just shield off one half of a heavy cylinder that is mounted on a horizontal spindle, the shield being parallel to the spindle.  The unshielded half of the cylinder will be attracted downward by gravity while the other half is not, resulting in a nett torque being exerted on the cylinder around the spindle, causing the cylinder to spin ever faster.

The laws of thermodynamics forbid free energy, and hence you can be sure that any gravity defeating device will consume more energy than the energy imbalance it creates at any given moment.  So if you have an anti-gravity gadget and you want to use it lift your piano to your second-storey apartment, the energy the gadget will consume will be more than the gravitational potential energy you will have added to the piano by lifting it through the requisite height.

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brianvds
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« Reply #3 on: November 17, 2013, 11:26:36 AM »

 An object rotating at a constant rate is the classic case where the speed is constant but the velocity changes.

I was under the impression that such a rotational movement is in effect a form of acceleration, precisely because the direction changes all the time.

Anyway, look like Mr. Banks is off the hook. :-)

On another forum, there was once a long discussion about a similar situation, namely the one encountered in one of Arthur C. Clarke's "Rama" books, in which a giant cylindrical spaceship is rotated to create artificial gravity. In one scene, a person in a pedal-powered aircraft sets off from one side to other. He sets off right on the spin axis, where he feels no gravitational attraction, on his way to the other "pole" of the ship. But whenever he veers a bit off course, he has to pedal quite a bit to get himself back onto the spin axis, because he begins to experience gravity.

That bit never made sense to me, though someone convinced me eventually that it would work that way.

Similarly, in another scene a person jumps from a cliff in the giant spaceship to fall in a body of water below him; in the book he experiences acceleration. Once again I couldn't understand that, though lots of explanations and diagrams later, it did begin to make sense.

Man, am I glad I did not get it into my head to become a physicist - I can't wrap my head around even the most elementary stuff; how would I ever master relativity or quantum mechanics?  Grin
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« Reply #4 on: November 17, 2013, 11:59:00 AM »

I was under the impression that such a rotational movement is in effect a form of acceleration, precisely because the direction changes all the time.
Yes, that is exactly right, but the point I was getting at is to illustrate the difference between speed (a scalar quantity) and velocity (a vector) by means of a familiar example.  The speed of an object rotating at a constant rate remains constant but its velocity changes, and a change in velocity is acceleration, as per Newton’s second law.

Anyway, look like Mr. Banks is off the hook. :-)
Actually, he isn’t.  It strikes me now that I never actually answered your original question, which was whether a hypothetical anti-gravity mechanism would also work in a Banksian orbit.  The answer is yes, provided Einstein’s Equivalence Principle is in fact valid (and, as said, we know it to be valid to a very high degree of certainty).  The reason it must work is that changes in an object’s gravitational behaviour must be equivalent to, and indistinguishable from changes in its inertial behaviour.  The Banksian orbit uses the object’s inertial behaviour to bring about the effects of gravity. 

The Clarkian situation was misrepresented to you.  A small spaceship travelling along the axis of a rotating cylinder would travel in a straight line as seen by someone in an inertial (i.e. non-accelerating) frame of reference.  While the small spaceship is in flight, the presence of the large cylinder is largely irrelevant (except for the gravitational field its mass produces).  For the small spaceship to feel any artificial gravity from the cylinder’s rotation would require it to travel in a corkscrew trajectory as seen by our external inertial observer.  However, an observer inside the large cylinder would describe the small spacecraft’s motion as a corkscrew trajectory.

Similarly, a “freefalling” object in such an environment feels no acceleration the same way that you don’t feel acceleration when jumping off a cliff here on Earth.  Instead, what you feel in both cases is weightlessness while falling — physically, you are in a proper inertial frame.  In both cases, however, the surroundings accelerate relative to your frame of reference, giving the impression of falling.  In the gravitational scenario, the acceleration is due to mass attraction and in the second one it is due to non-linear (i.e. accelerated) motion.

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