A satellite of mass m, originally on the surface of the Earth, is placed into Earth orbit at an altitude h. (a) Assuming a circular orbit, how long does the satellite take to complete one orbit

 T = 5.45 10⁻¹⁰  

Explanation:

Let's use Newton's second law

          F = ma

force is the universal force of attraction and acceleration is centripetal

          G m M / r² = m v² / r

          G M / r = v²

as the orbit is circular, the speed of the satellite is constant, so we can use the kinematic relations of uniform motion

          v = d / T

the length of a circle is

          d = 2π r

we substitute

        G M / r = 4π² r² / T²

        T² =

the distance r is measured from the center of the Earth (Re), therefore

        r = Re + h

where h is the height from the planet's surface

let's calculate

         T² =   (Re + h) ³

         T =

         T = 5.45 10⁻¹⁰  

neither accurate nor precise.