How does a satellite stay in orbit?

[SSerenity]

I've solved a bunch of these problems, but never really thought about it.

To find the speed required for a satellite to remain in orbit, we simply set our Force of Gravity: GmM/r^2 term = mv^2/r

Force of Gravity = Centripetal Force.

So it seems like these two forces must equally oppose each other to prevent it from crashing down.

But The force of gravity wants to pull our satellite toward the core of the earth.
Our centripetal Force also points toward the core of the earth.

These are both pointed in the same direction! How does this work?

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[phys2med]

Satellites are basically falling towards the earth at all times. They have enough speed to just keep falling in orbit.

 

[ashtonjam]

I like to think about the centripetal force as not being a 'real' force. It's a more general umbrella term for forces that point towards the center of a circular path of motion. By this, I mean that lots of forces can be considered the centripetal force. For example, a swinging ball from a string going in circles has tension as the centripetal force. A roller coaster going through a loop has the normal force as its centripetal force.

And in your case, a satellite only has one real force working on it: gravity. Since the gravitational force points towards the center of the circle no matter where the satellite is, it's considered the same as the centripetal force.

It's like saying GMm/r^2 = ma. That's a valid equation to write, since the net force on the satellite is the gravitational force. If you change the 'a' on the right to 'v^2/r', then the expression is still saying that the gravitational force is the net force, but you've modified it a tiny bit to include velocity and radius.

 

[phys2med]

http://en.m.wikipedia.org/wiki/File:Newton_Cannon.svg

Look at this picture to help conceptualize it. Give an object enough velocity and it can "outrun: thebforce of gravity pulling it down.

 

[mehc012]

I've solved a bunch of these problems, but never really thought about it.

To find the speed required for a satellite to remain in orbit, we simply set our Force of Gravity: GmM/r^2 term = mv^2/r

Force of Gravity = Centripetal Force.

So it seems like these two forces must equally oppose each other to prevent it from crashing down.

But The force of gravity wants to pull our satellite toward the core of the earth.
Our centripetal Force also points toward the core of the earth.

These are both pointed in the same direction! How does this work?

When you are solving for 'centripetal force' you are REALLY solving the question "what force is needed to provide enough inward acceleration to keep this object turning"? That force could be provided by tension (a string), friction (car tires in a turn), gravity (orbit) or 80 bajillion other things.

In order to maintain a stable orbit, you need to be travelling at exactly the right speed and altitude so that the inward pull of gravity exactly balances your tangential momentum...too fast/too high and you will shoot off into space; too slow/too low and you will eventually fall to Earth. So, yes...gravity and 'centripetal force' are both pointing the same direction. But that's because what you call 'centripetal force' is just a generic label for 'inward force allowing this circular motion to occur', while gravity is the more specific name of the centripetal force in this particular example.