Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: lenadorap on 05/03/2010 12:37:45
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Hi
Can there be a tangential component of Gravity if a planet is rotating at a faster speed?
lenadorap
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With a perfectly spherical, uniform and rigid planet I think the answer is no. However, in practice there are a lot of imperfections that result in such a component. If a real body is in orbit the interactions can be quite complex and tidal effects do produce tangential components.
I do not know enough about the theory regarding relativistic "frame dragging" to know whether there are tangential components to gravity here. I don't think so, though there are many very subtle effects on other rotating bodies. Maybe someone else can comment on this. Much work is still ongoing in this area.
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Check out http://en.wikipedia.org/wiki/Gravitomagnetism and http://en.wikipedia.org/wiki/Gravity_Probe_B. It's all good stuff, but people find it tricky because they don't have a handle on magnetism. In magnetism we talk about curl or rot, the latter being short for rotor. See http://en.wikipedia.org/wiki/Curl_(mathematics) and http://online.cctt.org/physicslab/content/PhyAPB/review/summaries/Magnetism.asp.
The easiest way to get a handle on it is to think of a magnetic field as a "turn" field. Sounds naff I know, but look at what happens to an electron beam in a magnetic field:
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fic.upei.ca%2Fprojects%2Fcap%2Fsites%2Fic.upei.ca.projects.cap%2Ffiles%2Fimagecache%2F500x500s%2Fphoto%2Foriginal%2F2007-08-HS-Indiv-3rd.jpg&hash=0079c9785101f66b5656d6746791e93e)
A gravitomagnetic field is another "turn field" that makes gyroscopes precess in gravity probe B. They're "turning" because the earth is turning. See http://einstein.stanford.edu/ for the latest, which confirms the frame-dragging effect. I'm not sure of the status on the geodetic effect.
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Thanks for the references, farsight. I guess, from the analogy to Maxwell's equations, that the answer to lenadorap is that there is no tangential field component on a test body that is stationary with respect to a rotating spherical, uniform rigid mass, but that would be if the mass is moving as it would be subject to the gravitomagnetic force. Do you think this is right?
I have never studied this aspect of GR (maybe when I eventually retire) but it is interesting that the comparisons with Maxwell's equations shows such congruity. It really is surprising that both electromagnetism and gravity have such similar behaviour when the conventional view is that one is from field theory and the other from curving of space. I see that there are some tests being done to verify aspects of frame dragging (satellites with gyros). If this all gets verified, and it seems to be so far, then it should change some conceptual views we have of the world.
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Actually I'm not sure graham. There's a dynamical aspect to all of this, and the word "field" tends to describe one particular effect, such that another effect is called a different field. The best example of this is the electromagnetic field, which is really one field, not two.
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But the electromagnetic force and gravity are quite different. The force in the photo is at right angles to the line connecting the charge and the magnetic field. Gravity is a force Along the the line connecting the point and the source.
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Neither I nor Farsight are confusing gravity with electromagnetism in the way you think. The concept of gravitomagnetics has nothing to do with magnetism but it is just that the equations that govern electromagnetism (Maxwells equations) have an identical counterpart in gravity (according to this theory). This is not wholly verified yet (programmes are underway) but it is generally accepted. This means that a rotating object affect the motion of an object moving nearby in a way related to the relative motion of the object - the analogy being to how an electron might move near a current carrying coil. The main difference is in the sign because masses always attract. Look up gravitomagnetics in Google.
Farsight has some specific views on the relationship between electromagnetics and matter but he was expressing a general concensus view in his answer.
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Can there be a tangential component of Gravity if a planet is rotating at a faster speed?
There is, as other posters in this thread have mentioned.
It's called "Lense-Thirring effect" and it's a "frame-dragging" effect, that is, the very spacetime is dragged from the rotating massive object (it comes from general relativity theory and it seems it has recently been confirmed experimentally by the Gravity Probe B).
If you were in a spaceship near such a spinning object, it would drag you around, in the same direction of motion of the object.
http://en.wikipedia.org/wiki/Lense%E2%80%93Thirring_precession
As an example of the Lense-Thirring effect consider the following:
Think of a satellite rotating around the Earth. According to Newtonian Mechanics, if there are no external forces applied to the satellite but the gravitation force exerted by the Earth, it will keep rotating in the same plane forever (this will be the case whether the Earth rotates around its axis or not.) With General Relativity, we find that the rotation of the Earth exerts a force to the satellite, so that the rotation plane of the satellite rotates, by a very small amount, in the same direction as the rotation of the Earth.
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I looked this up a bit and all I found was references about objects in orbit being dragged about. If I were in a rocket that was firing its engines in an attempt to stay stationary (in the Newtonian picture) would frame dragging still make me start moving slowly around the earth?
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I think so, JP. But the effect is miniscule for the earth, see http://einstein.stanford.edu/. I was thinking it wasn't confirmed, but I'm not sure about that and now I have to go. By the by, I thought the toroidal mass with two degrees of rotation at http://en.wikipedia.org/wiki/Gravitomagnetism#Higher-order_effects was interesting.
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NASA have an ongoing experiment...
http://www.nasa.gov/vision/universe/solarsystem/19apr_gravitomagnetism.html
that is trying to verify the gravitomagnetic effect of the earths rotation on an orbiting gyroscope. I believe they are expecting to finish their data analysis quite soon. The effects are very small around the earth. I remember reading that the gravitomagnetic effect of the earth on the moon's orbit was of the order of a few metres only!
The gravitomagnetic analog to EM theory (Maxwell's equations) is only correct in low field, flat space approximations where Einstein's field equations can be linearised and give a mathematical solution. In the case of frame dragging I think that this can only be properly addressed by numerical analysis as it usually involves massive bodies.
Begin rant...
It would be nice to have access to some software that can model general relativistic effects. Modelling simple configurations can't be that hard (can it??) and even modest PCs have quite a bit of compute power nowadays. Programs that model Maxwell's equations abound but are expensive because of their commercial value. Cheap/free ones have very klunky data entry systems, are old fashioned and user hostile! But I would have thought that there was not so much commercial value in GR so the universities would be more liberal, like Stanford was originally with its electronic simulation tools. I guess they all want to protect their investments and protect their competitive research edge; a bit sad really. It's the same with trying to view papers; everyone wants to make a few pennies via Springerlink etc.
...End rant.