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How do relativity explain elliptical orbits of planets?
So relativity can't explain the elliptical orbits of the planets?
Didn't relativity replace Newtonian gravity?
How can you explain elliptical orbits without gravity?
I can see why you're having problems trying to think in terms of the 'marbles on a rubber sheet' model because, despite the fact that it's used so often, it's actually a very poor model of what's going on in general relativityI read D H's post, but I don't think it answered my question.
In my mind I find it easy to picture a circular orbit. If i think about the classic diagram with a 2d surface pressed down by the sun and the Earth following a line in this depression of spacetime, it seem to result in a circular orbit. But in reality its elliptical and i just wondered why.
I think you're likely to be disappointed. Going back to the Newtonian case, if it were possible to say 'there is an inverse square force therefore the orbits are obviously ellipses' then why did Halley have to pester Newton for a mathematical demonstration of this fact.I don't really care about the mathematics, but more about the physical cause, if that make any sense.
You are already aware of the explanation. GR explanation for gravitation is curved spacetime.I'm guessing that the cause is gravity and now i want to know how the relativity version of gravity explain elliptical orbits. Maybe, this is impossible for relativity or no one has though it up yet, but I would still like to know that.
I would say that planets move because reality (in particular gravity) actually behaves as described by those equations. The rest is just math. I understand that you want an easy-to-visualize geometric picture of what's going on, but I don't think that's possible. That doesn't mean that GR doesn't explain elliptical orbits. It does, in exactly the way that we described.Descriptive math is fine, but that was not what i was looking for. I'm sure you would agree that planets don't move because we have a few equations that are good at describing reality. There must be a physical cause. Right?
Thanks. I hope you would help me clarify some points.You are already aware of the explanation. GR explanation for gravitation is curved spacetime.
An orbiting body travels through the curved spacetime along a special kind of geometric path called a geodesic. Because spacetime is curved these geodesics are also curved. In fact, these geodesics are elipses in the classical limit.
True, but neither are they under Newton's laws. It looks pretty elliptical if one if the masses is negligible but in the general case two masses in orbit do not follow an elliptical path under Newton's laws.General relativity explains why orbits are NOT elliptical. See: precession of the perihelion of Mercury.
So would you say that a comets orbit which is very elongated ellipse (i think), is just at short as a circular one from...lets say a satellite?This means that elliptical orbits are just as 'short' and graceful as circular ones.
It's a fair question. A comet has a great deal more energy than an artificial satellite, but it is still effectively 'falling' around the earth.So would you say that a comets orbit which is very elongated ellipse (i think), is just as short as a circular one from...lets say a satellite?
... I'm sure you would agree that planets don't move because we have a few equations that are good at describing reality. There must be a physical cause. Right?
I'm guessing that the cause is gravity and now i want to know how the relativity version of gravity explain elliptical orbits. Maybe, this is impossible for relativity or no one has though it up yet, but I would still like to know that.
Yes. Same with any other object in freefall under the influence of gravitation alone.Thanks. I hope you would help me clarify some points.
So, would you say that the cause for orbits is that the planets follow geodesic?
Actually, in spacetime geodesics are the longest path between events. Remember, an event has four dimensions, 3 space and 1 time. So it is not just the longest distance between points A and B, but the longest distance between point A at t0 and point B at t1. This is a very important point to notice. One reason that the "rubber sheet" analogy is so poor is that it only demonstrates curvature in space. In GR it is not just space that is curved, it is spacetime that is curved. And since v<<c in typical scenarios the curvature in the time part is actually very important.which is the shortest path between points?
If you want an answer for that you need the math. That is just how the differential geometry works out.Why are the geodesics ellipses?
When you include the time dimension both circles (helixes) and ellipses (distorted helixes) are geodesics in the same spacetime depending on the initial or boundary conditions.When i try to picture it in my mind circles looks like a shorter path than ellipses, but maybe I'm wrong.
See post #2.I think someone should point out that relativity does NOT explain "elliptical orbits" because orbits are NOT elliptical!
While the difference is unmeasurable for most planets, it was precisely the calculation of Mercury's non-elliptical orbit that was the first real test of general relativity.
I think someone should point out that relativity does NOT explain "elliptical orbits" because orbits are NOT elliptical!
While the difference is unmeasurable for most planets, it was precisely the calculation of Mercury's non-elliptical orbit that was the first real test of general relativity.
True, but neither are they under Newton's laws. It looks pretty elliptical if one if the masses is negligible but in the general case two masses in orbit do not follow an elliptical path under Newton's laws.
So relativity can't explain the elliptical orbits of the planets?
Didn't relativity replace Newtonian gravity?
How can you explain elliptical orbits without gravity?
So relativity can't explain the elliptical orbits of the planets?
Didn't relativity replace Newtonian gravity?
How can you explain elliptical orbits without gravity?
Yes, this is correct, but my understanding is that the two statements are essentially equivalent. You could just as easily define them as the longest path and then derive the fact that they are "straight". The Euclidean analogy is "the shortest distance between two points is a straight line".1. Geodesics are defined as the straightest possible paths, not as the shortest (or longest).