How does an object orbit something

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I am having a very hard time understanding this concept in physics. Why would something orbit an object? Why doesn't it leave the orbit and move straight?

Also when a satellite leaves Earth how does it go into orbit? Does it have to be launched at a specific angle.
 
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Things can orbit because they experience a force that it at right angles to the direction they are traveling in.

You can see this on paper - mark a fat dot for the center of mass and a small dot for the satellite. Give the satellite a small random direction to travel. Now for each time interval, the satellite moves a small distance in the last direction it was headed in, but it is also attracted a small distance towards the fat dot. Try drawing that.

When a spacecraft goes into orbit, it's radial velocity has to reach zero and it's tangential velocity has to be right for the orbit. There are lots of ways of doing this - one way, indeed, involves being careful about the angle the rocket is launched. But recall, rockets are under power - they can, in principle anyway, manouver, and they can accelerate and decelerate. This gives more options.
 
ASidd said:
Why would something orbit an object? Why doesn't it leave the orbit and move straight?
Wiki article:

http://en.wikipedia.org/wiki/Orbit

ASidd said:
Also when a satellite leaves Earth how does it go into orbit? Does it have to be launched at a specific angle.
To get a satellite into a circular orbit normally requires at least two impulses, or one very long continuous (relatively low thrust) impulse. Wiki article:

Hohmann_transfer_orbit.htm