So I understand the concept of gravity, in that it's not actually a force, but more of a displacement in the spacetime grid. An object with a big enough mass will bend the spacetime, causing smaller objects to "attract" to it (not really, but good enough for what I am trying to figure out)

Ok so that makes sense, but what I am not understanding is, how come planets don't just get engulfed by the Sun? There must be something acting against the gravity for the planet to be a certain distance away from the sun. Am I not understanding this concept correctly?

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  • $\begingroup$ Related: physics.stackexchange.com/q/9049/2451 and links therein. $\endgroup$ – Qmechanic Dec 25 '14 at 19:32
  • $\begingroup$ Treating gravity as a force was always wrong, even in Newton's time. Gravity is an acceleration, unless we are willing to define $m_{inertial}\neq m_{gravitational}$, but one can't have it both ways, pretend that gravity is a force AND implicitly accept the equivalence principle. $\endgroup$ – CuriousOne Dec 25 '14 at 21:52
  • $\begingroup$ In a nutshell, we are being constantly engulfed by the sun. It's just that our speed means that we always miss hitting the sun. This phenomenon is orbit. If I were stationary relative to the sun, then given time yes, I would be engulfed and burn. But given Earth's speed, the gravitational 'pull' of the sun merely pulls us into orbit. $\endgroup$ – Joshua Lin Dec 25 '14 at 22:37
  • $\begingroup$ Ok, I really appreciate your answer. $\endgroup$ – user68428 Dec 26 '14 at 2:54

Objects not being affected by forces move on straight lines in euclidean space.

If space is curved, there will not be straight lines, and particles follow trajectories that are the next best thing to straight, eg. paths whose length is the shortest. Knowing curvature, these can be calculated, for example by using variational principles (you can calculate length for curves, so you take a function that maps curves to their length and then differentiate this function to find extremal points).

These shortest-length curves are called geodesics. Now, in classical mechanics, trajectories are not only determined by position, but also by velocity, and the same goes for general relativity.

Celestial bodies in orbits move in such ways, because their geodesics are closed curves. They do not have forces acting on them, but instead they follow the locally "straight" path in space(time), which is, for their case, a closed loop (closed in space, that is).

I hope this answers your question.

  • $\begingroup$ So, as there is no gravitation, there is no centrifugal force? $\endgroup$ – Sofia Dec 25 '14 at 20:33
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    $\begingroup$ I'm sorry, I don't really understand you. There IS gravitation, but in the context of GR, we do not view gravity as a force, but rather, as an internal geometry of spacetime. Centrifugal forces only exist in noninertial frames anyways, even in Newtonian mechanics. The primary difference is, in Newtonian mechanics, we view gravity as a force that keeps the planet in orbit, while in GR, we view gravity as an intrinsic curvature of space time, and the orbital trajectory is the "straigth" trajectory the planet follows. $\endgroup$ – Bence Racskó Dec 25 '14 at 20:37
  • $\begingroup$ I see, this makes sense. I really appreciate your well thought-out answer. $\endgroup$ – user68428 Dec 26 '14 at 2:55
  • $\begingroup$ @Uldreth, curvature without force/acceleration cannot make things move. $\endgroup$ – bright magus Feb 8 '15 at 8:47
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    $\begingroup$ @brightmagus, actually it can. A stationary particle is "moving" in the time direction $\endgroup$ – S. McGrew Feb 22 '19 at 1:20

On a practical level (baseball, soccer, tennis, ...) Newton's account of gravity as a force with particular behaviors is entirely satisfactory. It is even used for launching satellites (well most of them), and predicting artillery impact points. It was this last application that made warfare even more horrendous than it had been (and safer for the artillerists, too). See Benjamin Robins, who was the most important early mover in the ballistic prediction business.

But, if something finds itself in a strong gravitational field (in Newtonian terms, Earth is not quite enough) or moving pretty fast (nothing in or around the Earth is fast enough**), Newton's account of his force is wrong. Mercury's orbit was famously intractable in Newtonian terms being just a bit off of Newtonian predictions no matter which brilliant calculator did the analysis. It turns out the the gravity is a force business is subtly wrong. In fact, gravity is intimately tied to the structure and geometry of space time, and is quite different near a mass than at some position well away from any mass. We will finesse the question of most of the mass in the Universe (dark matter, and probably dark energy) for these purposes just now. There are some ideas of what dark matter is (exotic particles usually) and some of these may be testable now that the LHC will be running at full design power for the first time.

Einstein's General Relativity (of 1915) made these connections tight enough for experimental test, the most famous of which as Eddington's eclipse expeditions in WWI. But Mercury's orbit matched GR predictions to well within observational error, and quite a few other GR predictions have also panned out. It's our best account at present.

So the obvious next question is why (how) does gravity affect the geometry of spacetime in the manner observed? Neither Newton nor Einstein were able to contribute much on this point. But a Universe pervading field (think ether, if you dare!? though the details are very different) for which a predicted particle would serve as the "force transmission" particle, was suggested by quite a few folks in the late 1960s. Higgs published first and so the field is named the Higgs field and the particle the Higgs particle. It has been quite hard to find. Fermilab should have had enough energy in its beam to find it -- but they didn't, and trawling through all that data they collected hasn't shown that they observed it but didn't notice. At least so far.

The LHC, being the most powerful ever built by a good factor, and after some teething problems, found something which is almost certainly the Higgs particle (though there may be perhaps 3 more in the family, as yet un glimpsed) in its first year of operation.

So, it appears that gravity is rather like the other fundamental particle forces (electromagnetic, strong, weak, and unified variants) in that the "force" is actually the exchange of particles which "carry" the force. There is much odd about gravity as these forces go, and much more work is needed to make sense of it. Perhaps Cavorite will be possible if we understand more?

The Higgs is popularly known as the "God particle" which is an egregious example of journalistic foolishness. One of the leaders in the search for the Higgs, for decades, was frustrated one day by its elusiveness (if it seixted at all) and was in the presence of some journalists, when he referred to it as that "Goddamned particle". The journalists (or one of them, stories vary), always on the alert for color in theoretical physics reporting, and knowing that they wouldn't get the entire phrase in their papers, just shortened it to "God particle". The physicist was not then and remained unhappy.

An exception to the necessity of taking into account GR on or near the Earth is the GPS satellite network. The timing requirements between the various satellites and a ground receiver are so exacting that the effects of GR on the orbits of those satellites is significant enough that a correction factor must be used in order to make the results accurate enough to use.

  • $\begingroup$ The Higgs field is responsible for giving some particles (some of) their mass. But apart from that, it has nothing to do with gravity. $\endgroup$ – PM 2Ring Feb 27 '19 at 1:18
  1. If we talk about the Newton's concept then there is gravitational force as centripetal force and its reaction as centrifugal force. And centrifugal force will save it to fall at the center.

  2. But if we talk about Einstein's concept of geodesics then there is no gravitational force or centrifugal force. Then falling bodies have to follow geodesics (shortest distance in curved space). The curvature in space-time fabric is due to the presence of the earth. And earth produces such changes in space-time due to large amount of extra energy packing in a unit of space-time. The space-time remains undistorted only if a unit of space-time has least energy density. So at once we use single concept newton's or Einstein's. Newton's concept is weaker but not wrong and Einstein's concept is stronger but not last.