Understanding space-time curvature

[rez]

Edit to Add: I probably should of titled this "Understanding gravitational curvature".

Two-dimensional analogy of space-time distortion. The presence of matter changes the geometry of spacetime, this (curved) geometry being interpreted as gravity. Note that the white lines do not represent the curvature of space, but instead represent the coordinate system imposed on the curved spacetime which would be rectilinear in a flat spacetime.

I feel as though I understand this explanation, however, I am uneasy about a little detail.

I would like to have seen another planet in that picture to represent how a planet revolves around another planet.

if I were to dig a hole in a sand box place a ball in the center of the hole and then place another ball outside of the center of the hole I would think the ball would roll down into the other ball. I don't see how the outside ball would maintain a certain distance and then spin around the other ball solely because of the idea of gravity being curved...

How far off base am I?

[rez]

haha, I found the answer! Now the question becomes why does matter take the path of least resistance, or how does it even know that path.

Imagine that you're standing halfway down the steep slope of a crater. You want to get to the halfway point of the slope on the other side of the crater. You could walk down the slope to the bottom of the crater, then up the other side until you got halfway up. But that would take a lot of effort.

It would take less effort if you stayed on a ledge at the same level (not moving up or down the crater) and walked around to the other side. Sure, it would be a longer walk, but you would be exerting less energy. You'd be taking the path of least resistance.

[Athena]

First, I love your thinking game. I know virtually nothing about the helpful science, but would like to play.

I don't buy that explanation of least resistance/ effort, because going down would require no effort and the movement would push the moving object at least part way up. Visualize a car going down hill with no brakes and at least part way up the next hill. If this is a loop, the moving object must be going very fast to make it around the loop, instead of dropping, and want would power that motion on the way up?

I have puzzled such matters for years, there can not be just garvity. There must be a force that pushes things away as well, or the whole universe would become a black hole, won't it? What is the force that causes anything to spin? Why is there any motion at all? Now this talking God stuff in my book.

[gallo]

Imagine a planet traveling through space, all alone, in a straight line. Now imagine that it encounters a star. That matter in the star would cause curvature of the space around it. So as the planet was passing by the star, it would still travel in a straight line, only that line would be in curved space. The result would be an eliptical path around the star.

[Captain Chaos]

I do not buy the straight path through curved space explanation - it is unclear.


No matter how fast an object moves, if it is moving in a straight line (in uncurved space) it follows the same path.


However, if you have two objects moving next to a large gravity well, the faster-moving of the two objects will be less affected by the gravity well - it will travel what appears to be a straighter course.

If it were a straight path, the speed of the object would not affect its course, just how fast it goes through its course.


This is a pretty simple objection, and thus I am sure there is just something in the explanation that is confusing, rather than incorrect.

[rez]

I do not buy the straight path through curved space explanation - it is unclear.

No matter how fast an object moves, if it is moving in a straight line (in uncurved space) it follows the same path.

However, if you have two objects moving next to a large gravity well, the faster-moving of the two objects will be less affected by the gravity well - it will travel what appears to be a straighter course.

If it were a straight path, the speed of the object would not affect its course, just how fast it goes through its course.

This is a pretty simple objection, and thus I am sure there is just something in the explanation that is confusing, rather than incorrect.

I don't see how this is an objection. You basically just described why planets have different orbits...unless I am mistaken...

[Captain Chaos]

I don't see how this is an objection. You basically just described why planets have different orbits...unless I am mistaken...

Not all moving objects get caught into an orbit.

If you move fast enough past a gravity well, your path will be perturbed, but you will not wind up in orbit.

Your speed will affect the degree to which your path will be perturbed.

This would not be the case if your were moving in a straight line through curved space.

[gallo]

Not all moving objects get caught into an orbit.

If you move fast enough past a gravity well, your path will be perturbed, but you will not wind up in orbit.

Your speed will affect the degree to which your path will be perturbed.

That's true, but my explanation was not a comprehensive discussion of the relativistic theory of gravitation. Objects moving fast enough would not be caught in orbit. On the other hand, objects moving too slowly would spiral pretty quickly into the star. But that isn't all that relevant to the question and I was trying to keep it simple.

Of course, we could explain it the old way, by Newtonian gravity. A planet near a star is drawn towards the star. At the same time the planet moves sideways so that as it falls it misses the star. Thus it continues to fall around the object in an elipctical path.

[Fonceai]

If you move fast enough past a gravity well, your path will be perturbed, but you will not wind up in orbit.

Because each gravity well around a planet has a very narrow velocity variance for its orbital speed.

I don't need to explain centripetal and centrifugal force, but if the velocity is just right, depending on the distance from the celestial body, orbit is accomplished.

[gallo]

I don't need to explain centripetal and centrifugal force, but if the velocity is just right, depending on the distance from the celestial body, orbit is accomplished.

You don't? But why don't you just go ahead and do it anyway, in case some of us don't understand.

Thanks.

[Fonceai]

I'd hate to sound like a condescending prick and presume someone doesn't know something.

I've decided not to play the "let me teach you something" card.

Instead, if someone isn't sure how centripetal or centrifugal force is relevant and wants to ask, I'll explain how it relates to orbital mechanics.

[gallo]

I'd hate to be a condescending prick and presume someone doesn't know something.

I made no such assumption. You claimed knowledge and I asked you to explain. Either do so or shut up.

Instead, if someone isn't sure how centripetal or centrifugal force is relevant and wants to ask, I'll explain how it relates to orbital mechanics.

I did ask. What is it that you think I was saying? But you seem to find it necessary to insult instead of explain. I guess that means that you don't actually know.