Really stuck on this question about gravitational fields

[smiley1121]

Homework Statement

The gravitational field strength experianced by a satellite orbiting Earth is 4.5 N kg^-1. Calculate how high above the Earths surface the satellite is in orbit.

other info:

the gravitational constant is 6.67x10^-11
the mass of the Earth is: 6.0x10^24 kg
the radius of the Earth is: 6.38x10^6 m

Homework Equations

I think you have to use

g= GM / r^2

but the problem is i know to find distance you have to add it to the radius but I am really unsure on how to rearrange this to find distance when i already have g.

The Attempt at a Solution

really not sure :l

 

[Delphi51]

Welcome to PF, Smiley. I don't want to spoil your adventure with this problem, but I'll give you a terrific hint. In all these orbit problems that you'll meet this year, a circular orbit is implied. So you have circular motion. That means something is providing a centripetal force pulling the satellite toward the center of the circle. It is the force of gravity. Begin all these problems by writing
centripetal force = force of gravity
Fill in the detailed formulas and solve for the quantity you want!

 

[smiley1121]

thankyou for your reply!
I think what you're trying to tell me is that i use gravity in my answer (as in 9.8?). Except i don't really understand where gravity fits in because aren't i supposed to be finding the distance?

I really appreaciate the help! :)

 

[Delphi51]

Sorry, I now see that your question is not really an orbit problem. It s simpler than I wrote earlier!

Don't use g = 9.8; that is only true at the surface of the Earth. Out where this satellite is, you are given g = 4.5 N kg^-1. Just put that into your formula
g= GM / r^2
and solve for r. You will have to adjust that answer a bit to get the one the question asks for.

 

[rwisz]

You are on the right track by using the equation g=GM/r^2. To find the distance above the Earth's surface, you can rearrange the equation to solve for r. It would look like this: r=√(GM/g). Plugging in the given values, the equation becomes r=√[(6.67x10^-11 N m^2/kg^2)(6.0x10^24 kg)/4.5 N kg^-1]. This gives a distance of approximately 2.68x10^7 meters, which is the height above the Earth's surface that the satellite is orbiting.