Physics & Cosmology: Questions about Gravity & Orbital Motion

[Nogueira]

I was reading Paralel worlds by Michio Kaku, due to its content I'm hoping to learn a little more about physics and cosmology, before i go to university, at one certain point, right in the beggining, while explaining Einstein's view on gravity, the author says that for Einstein, the Earth moves around the Sun because of the deformation caused by the Sun on space causing the idea of a gravitic force rather than an actual force. So, if gravity is a product of the space-time disturbances, how does the Earth's gravity appears? And if the sun disturbs space like a bowling ball on a matress how can there be several bodies orbiting the sun? And why don't these bodies fall to the sun is it because they deform space the same way the sun does reversing what the sun does? Also, why do comets have much more eliptical orbits than the planets if the sun disturbance on space is even?

Sorry for the long post, for the bad and confusing english, and feel free to correct the errors when you find them. Thank you in advance.

 

[PeterDonis]

Hi, Nogueira, and welcome to PF (since it looks like this is only your third post)!

the Earth moves around the Sun because of the deformation caused by the Sun on space causing the idea of a gravitic force rather than an actual force.

Yes, from the standpoint of General Relativity (GR), the Earth does not feel any "force of gravity" from the Sun, and it moves on the straightest possible path that it can through the spacetime around the Sun. The Earth's path looks curved to us because the spacetime itself is curved by the Sun's mass.

So, if gravity is a product of the space-time disturbances, how does the Earth's gravity appears?

The same way. A satellite orbiting the Earth moves on the straightest possible path that it can through the spacetime around the Earth, just as the Earth does around the Sun. The satellite's path looks curved because the spacetime around the Earth is curved by the Earth's mass.

And if the sun disturbs space like a bowling ball on a matress how can there be several bodies orbiting the sun?

I'm not sure why you would see a problem with this. The spacetime around the Sun has room for multiple bodies in it. If you're wondering how the deformations due to multiple bodies interact, see below.

And why don't these bodies fall to the sun

Because they have sideways motion as well, just as a satellite orbiting the Earth does. Objects that don't have enough sideways motion, like a rock dropped from a rooftop, do fall into the object at the center (the Earth, in the case of the rock). Put another way, these bodies have angular momentum, and that affects their trajectories.

is it because they deform space the same way the sun does

They do, but which deformations are significant enough to matter depends on the distance scale you are looking at. On the scale of the Solar System, the only significant curvature of spacetime is due to the Sun; the planets are all too small to make much difference. But on the scale of the Earth, the curvature of spacetime due to the Earth is the only one that's significant; the curvature due to the Sun, at the radius of the Earth's orbit, is much too small on the size scale of the Earth.

reversing what the sun does?

None of the deformations "reverse" any of the others; they all add up (but which ones are large enough to be significant depends on the distance scale, as above). It's worth noting, though, that the effects due to multiple objects do not, in general, add linearly; GR is a nonlinear theory. (In the Solar System, the nonlinearities are extremely small, so for virtually all purposes we can add effects from multiple bodies linearly and get a good enough approximation; but the exact theory is nonlinear.)

Also, why do comets have much more eliptical orbits than the planets if the sun disturbance on space is even?

Because their sideways motion is different than that of planets, relative to the size of their orbits. Put another way, their angular momentum relative to their orbital energy is very different from that of planets. The orbital parameters of a particular object don't just depend on the properties of the underlying spacetime; they also depend on the specific motion of the object itself.

 

[Nogueira]

Thank you very much for answering, I later recalled the ansewr to the question of why they don't fall, just one more question though, according to GR how does the spacetime deformation caused by the Earth makes the apple fall from the tree?

 

[PeterDonis]

Thank you very much for answering, I later recalled the ansewr to the question of why they don't fall, just one more question though, according to GR how does the spacetime deformation caused by the Earth makes the apple fall from the tree?

The apple doesn't have any sideways motion (at least, not enough to be significant), so the straightest possible path for it to follow, in the curved spacetime around the Earth, is the path that free-falls straight down. So as soon as the apple is no longer connected to the tree, it will follow that path. (While it's connected to the tree, the tree is keeping it from falling; and the tree itself is held up by its own structure and by the Earth.)

 

[Nogueira]

Ok, thank you very much.