Centripetal Acceleration of space shuttle

[E.M.S]

Homework Statement

"The Space shuttle is located in a low orbit at a distance of 1.6 x 10^5 m above the surface of the earth. If gravity is the only force acting on the shuttle, what is the shuttle's speed while in this orbit?"

Variables:
Shuttle Velocity = ?
r = 1.6e5 + 6.38e6 (radius of the earth) = 6.54e6

Homework Equations

Ac = v² / r

The Attempt at a Solution

I'm having issues because of the lack of information. The only givens in the problem are the distance of the shuttle and the radius of the earth. My idea was that if Ac = v² / r, then the velocity would be the sqroot of Ac x r. Since the mass of the shuttle is not given, i can't calculate the actual value of gravity, so I assume they want me to use 9.8 m/s². Multiplying 9.8 x 6.54e6 (The value of the Earth radius plus shuttle distance) = 6.41e7, the sq root of this is 8006 m/s. The actual answer to the problem is 7810 - which makes sense in the context of a gravity value of 9.3 m/s², but because this information was not given in the problem and the mass of the shuttle was not given so that the actual gravity could be derived, I am still at a loss for how I'm supposed to come up with this answer.

 

[E.M.S]

Okay nevermind on this, I just realized that I was also given the equation for the radius of a circular orbit (r = G (mass Earth / v ₂)), and everything fits when I plug it into that equation.

 

[raging11]

i think the equation for circular orbit would be
radius=gravity(mass of earth/velocity^2)
Try plugging in your knowns