According to the last night’s NOVA show on black holes, the Earth warps the space around it and this is why satellites are in orbit around it. The satellites are not turning, they are following the curve of space warped by the Earth.
I get this perfectly because this is what Einstein said about gravity. In another way this makes no sense because a beam of light would also follow the same path as the satellite. I don’t think that a light shone parallel to the surface of the Earth would follow a path around the Earth.
Explain.
The light is moving a lot faster. If you increased the satellite’s speed, it would also not follow the same path anymore. If you increased its speed enough, the satellite would head off to deep space in a not-quite-straight line, as with the light.
Sufficiently massive gravity sources WILL bend light rays around them. This is predicted by relativity and has been seen visually. But the only things massive enough to actually trap light into an orbit are black holes, which is why things within the event horizon aren’t visible.
Earth’s gravity does bend light, it just doesn’t bend it very much. But we’ve seen light bent enough by galaxies, for example. See Gravitational lens for details.
Every object with mass warps space. A grain of sand warps space in the same way as the Sun or the Earth does-- but on a much smaller scale. The deflection of light by the sun was measured in 1919 during a solar eclipse. But the light doesn’t follow the same path as a satellite, since it’s traveling much, much faster than any large object with mass, like a satellite.
I generally dislike the “indentation in a rubber sheet” analogy, but to illustrate the relationship between orbit and speed, i.e. the amount of bending that a moving object experiences as it moves through curved space, the analogy works quite intuitively.
Imagine rolling a marble toward the curved depression, off-center from earth. I think you get better intuition if you imagine a shallow depression and fairly slow speed. A slowly rolled marble will get bent sharply and just turn and crash into the earth. As you increase the speed of the marble it will bend less, and a fast enough marble will get deflected a little but make it back out of the depression to continue out the other side on a new trajectory. In between, there is a “sweet spot” where the ball is deflected to curve in a perfect circle around the earth momentarily. Of course, there’s a lot friction here, so the momentary circular path will quickly decay as it slows, and it will spiral into the earth. But absent friction, it would continue to orbit in a circle. [Technically, this is not quite correct, something approaching in a straight line from afar would go into an elliptical orbit if anything, but let that slide.] The important point is that although the curvature is the same for every object, the amount of deflection that results from that curvature depends on the object’s speed. That’s why light is only deflected a tiny amount. It’s also why, at a given distance from earth, there’s a unique speed for an orbit. Orbital speed is where the object constantly “falls in” just the right amount to make a circle.
You’ve actually picked up on an important point:
gravity cannot be described by the curvature of space as the trajectory of a (test) particle depends on its speed
If gravity where the curvature of space we would expect a particle to follow the curvature of space independently of its speed. However Einstein did not model gravity as the curvature of space, he modelled it as the curvature of spacetime. In spacetime the speed of particle affects its wordline (its path in spacetime) and gravity can be modelled as particles following the curvature of spacetime.
The key is that objects don’t follow “straight lines” (more technically, geodesics, or shortest paths) through space. They follow geodesics through spacetime.
Take, for instance, the path of the Earth around the Sun. The shortest path from right here, right now, to the opposite side of the Sun, six months from now, is around a half-(nearly)-circle, and so that’s the path the Earth takes from here-and-now to there-and-then. On the other hand, the shortest path from here-and-now to the opposite side of Earth’s orbit, sixteen minutes from now, is what looks to us like a straight line, and that’s the path that light takes (or would take, if that pesky Sun weren’t in the way blocking it-- So say instead that it’s the path a neutrino would take).
Reading this thread made it seem like there would have to be a maximal speed that a given object can orbit the earth (or any other body). For if an orbiting object speeds up, its orbit will grow larger, but then the gravitational force decreases and eventually a speed will be reached at which point it escapes the body. That doesn’t mean that it no longer feels the gravity, but its path ceases to close.
Yep. That’s basically what “escape velocity” means (“escape velocity” is a misnomer, since really it should be “escape speed” (anything moving at greater than escape speed will escape, regardless of the direction of its velocity (unless that direction actually intercepts the body)).
Syntax error: Missing closing ‘)’
Thank you. Do you have experience with Lots of Irritating Silly Parentheses?
Uh oh … mischief with the AI … random statement to follow …
There’s no sense crying
over every mistake.
You just keep on trying
till you run out of cake.
… the machines have taken over …
I always thought it was lots of idiotic senseless parentheses.
On a related theme - getting one’s head around the implications of frame dragging. I guess if we stick with the rubber sheet, in addition to the sheet taking on a curve, it has a slight rotational shear in it as well. So there is a near infinitesimal change of angle of the geodesic as you move radially to the Earth. And I would guess a very tiny difference in the path taken by an object depending upon its direction relative to the Earth’s rotation - something that could be modelled as the Earth’s rotation dragging on the object.
I liked that.
On the one hand explanations of why the trajectory of small objects changes in the proximity of large objects tend to ignore speed and force while focusing on how the large objects wrap the spacetime fabric.
On the other hand the trajectory of a particle depends on its speed.
If particles don’t rip through spacetime, then there is something about this proces of spacetime wrapping that needs more explaining.
I’m back to clarify my befuddlement. I really miss Isaac Asimov and his ability to explain complex concepts in simple statements.
In Newton’s model, space is distinct from body and time passes uniformly, where space and time are flat dimensions.
In Einstein’s model, space and time become intertwined, and spacetime gets pushed, pulled, stretched and warped by matter: “matter tells spacetime how to curve, and curved spacetime tells matter how to move.”
Visual explanations in nowadays mass media do not use the idea of gravitational force but that of ‘tracks’ in spacetime caused by large objects: light seems to bend near the sun due to the curbs and twists in the fabric of spacetime.
Of course these visual representations only show the space. How does time change things? When we use Minkowski’s diagram, a satellite’s trajectory around Earth turns from an ellipse into an elliptical spiral.
But when Earth wraps the spacetime frame around it, this spacetime wrapping is constant in time no matter how minute. Either the ‘tracks’ one can see in visual explanations of nowadays mass media are real and light has to follow them when passing by our planet or these ‘tracks’ is just a way of putting things and in fact the force of gravity and the speed of light are all that matters.
Ok, I get that.
I cannot get how light can move against the fabric of space. If the road is curved, the car can only follow the road no matter how fast it is going. There is no “off road” in space.
Some have tried to explain this in other posts but I think my brain is too small to understand.