Question

I have some doubts about gravitational motion.
1. Why do the objects have to revolve around a body? Why dont they get attracted and just stick to it?
Secondly, how are the conditions for the velocity required for the orbits determined? And the paths ( hyperbolic, elliptical..) determined?
Thanks. :)

Answer 1

So basically the earth is falling towards the sun in this picture, but at the same time it's on a straight course. Just like you would throw a ball straight or a bullet is shot straight, it slowly falls as it moves forward. The difference is that the object in orbit is going forward faster than it's falling so it's always in a continual state of falling and never does because it misses the object. That make sense?

Answer 2

I hate to sound negative, but did you seriously just answer a question like this with General Relativity? The premise of the question suggests that the asker is having their first exposure to gravitation, which further suggests that they are in their first physics course (or at least one of introductory level). It's as though somebody asked about the derivative of x^2 and your answer referenced the fact that R is a one-dimensional Riemannian manifold.

Answer 3

In response to the question -- if we assume that Newton's Law of Gravitation is valid, i.e.
\[F = -G\frac{Mm}{r^2} \]
it can be shown via calculus that the orbits are either elliptic (if they are bounded) or hyperbolic (if not). If you do not have considerable skill with differential equations I'm afraid all we can say is "it can be shown", though if you do happen to possess more knowledge of the subject the solution is not terribly difficult.

@Kainui answered your question about orbits rather well, I think.

Answer 4

@Kainui. That makes sense. Thank you.
Jemurray3 thanks. :)

Answer 5

@matt101 That explanation helped the most. Thank you. I did read it. And don't delete it :)

Answer 6

Yeah, I mean we all know that classical physics isn't exactly right but when it comes down to it, we sent a man into space by using only classical mechanics. Physics as we know it will only ever be mathematical models that closely match reality and not describe reality itself. I'm afraid that's just the nature of the beast.

Answer 7

@matt101 and just to clarify, your explanation was excellent, and it wasn't wrong. I just didn't think it matched the level of subtlety of the question, that's all.

Answer 8

I'm glad it was able to help. Here's the answer one more time, in case anyone else was interested:

First of all, I'd recommend you look into Einstein's theory of General Relativity (GR). That will probably answer all of your questions.

Simply put, GR suggests that gravity isn't a conventional force, that is a push or a pull. Instead, gravity is a force that arises due to the physical geometry of space and time. Assume the universe an infinitely large "rubber sheet". In the absence of matter, space is completely flat in all directions. However, once matter is added, it deforms the space around it in proportion to its mass. Think of putting a ping pong ball and a bowling ball on the rubber sheet: the ping pong ball is light and will not sink much into the rubber sheet, whereas the heavier bowling ball will. Mass deforms space-time in much the same way.

From Newton's laws of motion, you know an object in motion continues to travel in a straight line unless acted on by some force. Therefore, since planets orbiting stars, for example, move in ellipses, there must be some force acting on them to cause them to change their direction of motion. This force is gravity. However, what if the apparent elliptical path of orbit really is a straight line of motion with respect to that planet?

This is where GR comes in. Consider a straight line through space. A star is extremely mass and therefore greatly deforms the space around it. If that 2D straight line goes through the area of deformity, it appears curved to an outside viewer who can see in 3D. However, the line is STILL STRAIGHT from a 2D perspective - this sort of line is called a geodesic. Planets follow their geodesics through space. In other words, they ARE moving in a straight line, but this does not appear to be the case to us, who live in a 3D world.

An everyday example of a geodesic: Suppose you want to fly from New York to Paris. The shortest distance would be a straight line, but that would involve going THROUGH the Earth! Instead, airplanes follow a geodesic path - they fly over the surface of the Earth. Of course, to you on the plane, you feel like you're going in a straight line the entire time. Since the Earth is so much bigger than you, it is "flat" from your vantage point and you are effectively moving in two dimensions. However, an astronaut in space watching your plane has a true 3D perspective and would observe it curving around the Earth as it travels to its destination.

I could go on, but I hope that answers your question. I think I almost scratched the surface... :)