How Far is the Satellite from Earth's Surface?

[Rbethell16]

Homework Statement

The radius of the Earth is 6.86 e6 m and the mass of the Earth is 5.98 e24kg. There is a satellite floating in space at a point where the Earth's gravitational acceleration is 3.2 m/s^2.

How far above the Earth's surface is the satellite?

Homework Equations

Fg = Gmm/r^2

The Attempt at a Solution

I know I need to find Fg - at least I think. But I don't know how to start...

 

[rock.freak667]

Homework Equations

Fg = Gmm/r^2

The Attempt at a Solution

I know I need to find Fg - at least I think. But I don't know how to start...

The gravitational force of attraction provides the centripetal force. So you need to equate F_g and F_centripetal (which you can just write as ma for this case).

 

[Rbethell16]

The gravitational force of attraction provides the centripetal force. So you need to equate F_g and F_centripetal (which you can just write as ma for this case).

ma - ok, I have the acceleration, but I get confused as to which "m" i am using. My problem is the intuition with formulas

 

[Rbethell16]

Wow I reread the problem and I am extra confused. How do I figure out the mass of the shuttle?

 

[rock.freak667]

Wow I reread the problem and I am extra confused. How do I figure out the mass of the shuttle?

You don't need it! if you have

ma= GMm/r²

an 'm' (the mass of the shuttle) cancels out

 

[Rbethell16]

Ahhh so 3.2 = G(5.98e24)/R^2. Then solve for R?

 

[rock.freak667]

Ahhh so 3.2 = G(5.98e24)/R^2. Then solve for R?

Yes, but be aware of what that R is.