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orbital velocity: v = 2πr / T
where r is the radius and T the period.
For orbit, centripetal acceleration = gravitational acceleration
v²/r = GM/r²
r = GM / v² = GM / (2πr/T)² = GMT² / 4π²r²
r = ³√(GMT² / 4π²) →→ for geosynch, T = 24*3600s
r = ³√(6.674e−11N·m²/kg²*5.98e24kg*(24*3600s)² / 4π²)
r = 4.23e7 m
To get the altitude, subtract 1 Earth radius:
h = r - Re = 4.23e7m - 6.371e6m = 3.6e7 m