Relationship between centripetal force and gravitational force of satelite

[Tommy1995]

In order for a satelite to achieve an orbit around the Earth the centripetal force of it needs to be exactly the same as the force of gravitation which is acting upon the satelite. Why is this so?

 

[CWatters]

The question is slightly badly worded.

An acceleration occurs when there is a change of velocity. Velocity has components speed and direction and to change either component you need an acceleration. Centripetal acceleration is the name given to an acceleration that causes an object to move in a curved path.

In the case of a satelite gravity provids the centripetal acceleration. So gravity is allways "the same" as the centripetal acceleration (except perhaps when thrusters are being fired but let's ignore that).

So what I think you are really asking is this... What centripetal acceleration is required for a stable circular orbit and what happens if it's more or less than that value?

The centripetal acceleration required for uniform circular motion is given by v²/r. That equation is derived here..

http://www.gb.nrao.edu/~rmaddale/Education/Wvsta'98/Centripetal.html
or
http://dev.physicslab.org/Document....me=CircularMotion_CentripetalAcceleration.xml

So for a stable circular orbit gravity must provide exactly that acceleration. If it was more or less than that value the path wouldn't be circular.

Imagine you have got your satelite into a nice stable circular orbit, what happens if gravity were to suddenly increase dramatically or dissapear?

 

[Tommy1995]

Centripetal acceleration is the name given to an acceleration that causes an object to move in a curved path.

In the case of a satelite gravity provids the centripetal acceleration. So gravity is allways "the same" as the centripetal acceleration (except perhaps when thrusters are being fired but let's ignore that).

So for a stable circular orbit gravity must provide exactly that acceleration. If it was more or less than that value the path wouldn't be circular.

I can nicely see where your getting at CWatters! I was wondering if this might mean mean that the centripetal acceleration of a satelite traveling in its orbit would be the same as the gravitational acceleration provided by the planet it is orbiting?

 

[HallsofIvy]

Where else do you think it could come from? Gravity is the only force acting on the satellite, isn't it?

 

[Tommy1995]

Thanks so much guys ! I finally understand this ! :d