Why Curved Space Affects Satellite Orbit: The Role of Newtonian Force

[devang2]

If the space around the Earth is curved according to general theory of relativity no lateral force is required to put the satellite in orbit because when the rocket carrying satellite has reached the certain height the satellite should spontaneously start sliding along the curved path traced for it but it does not happen so .Newtonian force is needed to put the satellite in desired orbit. Why is it so ?

 

[my_wan]

If you put put it at a certain height the curved space will merely make it fall straight to the ground. Like rolling straight down hill. If you push it to the side fast enough it'll still fall toward the Earth, but because it's also moving sideways it keep missing.

To visualize this here is a video using a trampoline.

 

[phinds]

If the space around the Earth is curved according to general theory of relativity no lateral force is required to put the satellite in orbit because when the rocket carrying satellite has reached the certain height the satellite should spontaneously start sliding along the curved path traced for it but it does not happen so .Newtonian force is needed to put the satellite in desired orbit. Why is it so ?

Why do you think the "curved path" points anywhere but towards the center of the earth?

 

[bahamagreen]

I'm sure he's trying to figure out what is curved, and where and how...

A static point away from the Earth can be connected to the center of the Earth by a radial straight line that points to the center of the Earth, but it points "stronger" as you approach... does that count as a kind of curvature?
A point with a lateral component of movement will not make a straight path, but now neither will its path point to the center of the Earth...whether it orbits will depend on the radius of the Earth (whether it misses or hits the surface).

There are a lot of analogies for getting insight into various principles; there must be one better than the balls on a stretchy fabric surface... that demonstration is interesting, but most will notice that it only works in an existing gravitational field or equivalent acceleration of the demonstration, so it is kind of using "gravity to explain gravity". Also, the curve of the fabric is not the right topology for curved space, is it? It seems "off" by 90 degrees?

Is there a more correct analogy?

 

[jcsd]

This is a good question: if space were curved you would expect the trajectory of an object moving through a gravitational field to be independent of the magnitude of its velocity. However that isn't the case.

General relativity can only really be understood as the curvature of four dimensional spacetime and not of space. There are some situations when it is useful to talk about the curvature of space (e.g. cosmology), but otherwise thinking of general relativity in terms of curved space isn't helpful.

 

[my_wan]

Agreed that the trampoline analogy is limited in a multitude of ways, and the dimensionality is no small part of it. At best it's a conceptual springboard to get past certain conceptual blocks, but by no means the only hurdle to overcome.

 

[A.T.]

Is there a more correct analogy?

For a purely radial fall, yes:

https://www.youtube.com/watch?v=DdC0QN6f3G4

But that doesn't help you with orbits, because they require 2 spatial dimensions. However you also require the time dimension, which is why rolling on that trampoline has nothing to do with curved-space-time in General Relativity.