The initial velocity required to give the satellite a circular orbit can be found from,

    
where   g = 32.2 ft/s²
            R_E = 3.960 mi = 20.9 x 10⁶ ft
            r_o = 10,000 mi = 52.8 x 10⁶ ft

          = 16,300 ft/s

The minimum initial velocity required to escape the earth's gravitational pull can be found from:

           = 23.1 x 10³ ft/s

Elliptical Orbit, 0 < ε < 1

To find the maximum radius, the eccentricity of the orbit must be determined when the initial velocity of the satellite is 20,000 ft/sec.

       = 0.500

Because 0 < ε < 1, the orbit must be elliptical, and thus the maximum radius occurs at apogee.

           = 158 x 10⁶ ft = 29,900 miles