Physics Question...(Uniform Circular Motion)?

Question

A satellite moves at constant speed in circular orbit about the center of Earth and near the surface of Earth. Assume that the magnitude of the acceleration is 9.8 m/s2. Also assume that the radius of the satellite's orbit is the radius of earth.

a) Determine the linear velocity of the satellite
b) computer the period of revolution

** radius of earth = 6,367,442.5 m**

I'm a little confused now that gravity is in the question...Please Help

Thank You

Answer 1

Very near the surface of Earth, force of attraction is the weight mg.

a )
Now, mg = mv^2 / r
=> v
= √(rg)
= √(6367442.5)*(9.8)
= 7899 m / s

b)
Period of revolution
= time for one revolution
= 2 π r / v
= 2 π (6367442.5 / 7899) s
= 5065 s
= 84.4 minutes

Answer 2

The cetrifugal force(the tendancy for the satellite to move in a strait line and not follow the earths surface) has to balance the gravitational force(the tendancy for the satellite to be pulled into the center of the earth). In other words, they have to be equal, or the NET force on the satellite relative to the center of the earth has to be 0. Otherwise the satellite would rise or fall(relative to the center of earth) and not stay in orbit.