Subtract the surface after finding the orbit

An ideal spherical model planet has radius 5.0×10⁵ m, gravitational parameter μ = 4π²×10¹⁰ m³/s² and rotation period 10,000 s. A satellite is placed in a circular equatorial prograde orbit that stays above one longitude.

What is its altitude above the surface?

Organize the givens & assumptions

R_planet = 5.0×10⁵ m
μ = 4π²×10¹⁰ m³/s²
T_rot = 1.0×10⁴ s

Dominant spherical primary; circular equatorial prograde orbit; no perturbations; the rotation period is relative to inertial space.

A $1000\ \mathrm{km}$
B $500\ \mathrm{km}$
C $1500\ \mathrm{km}$
D $0\ \mathrm{km}$

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