Circular motion and space shuttles?

Question

Hi, I'm stuck on this problem:

A space shuttle orbits earth in a near-circular orbit at a constant speed approximately 100 miles above the Earth's surface.
If we assume that the centripetal acceleration is equal to the acceleration due to gravity at sea level (9.8 m/s^2) and the orbital radius is equal to the radius of the Earth (6380 km):

a) what is the average speed of the shuttle?
b) How long does it take the shuttle to make one orbit around earth?

I'm specifically having problems w/ the wording on the first sentence, is 100m the speed of the shuttle or is it the distance above earth?
is it:
...at a constant speed 100 miles, above the earth's surface...
or
...at a constant speed, 100 miles above the earth's surface.

- in any case how would i go about solving it?

I know that for circular motion:

Acceleration = (Velocity^2)/ Radius

Answer 1

100 miles is the distance from the Earth's surface. Essentially you have a situation where the centripetal acceleration of the shuttle is equal to the shuttles acceleration due to gravity at sea level. Set these values equal to each other and solve for velocity.

m g = m v^2 / r => g r = v^2 so v = sqrt(g * r) to get velocity of shuttle

To find time to get one orbit, take the circumference of the orbit and divide by the shuttle's velocity. Also, make sure to convert that 100 miles into meters before doing any calculations or your answers will be very screwed up.

Answer 2

The 100 miles is the distance above the ground, so you want the radius of the orbit, which will be that added to the earth's radius. The vehicle will be moving at a constant speed, in a circle with that radius. If you crank the numbers, you should get that the speed is about 17,500 mph, and the orbital period is about 90 minutes. Heat up that calculator and get to work.

Answer 3

In the first "is it" statement, you place the coma after the word "miles." Note that the statement does not specify, "mile per hour" hence the reference is to miles above the earths surface. I hope this helps clarify the question which I can't help you solve. I have more of a forte for grammar and its abuse.