Everything currently assumes a circular orbit, so the period comes straight from Kepler and the eclipse geometry uses a single altitude. Real orbital data centre proposals include eccentric parking and transfer orbits. This means accepting semi-major axis and eccentricity instead of altitude, integrating eclipse over true anomaly rather than assuming a constant shadow fraction, and stating clearly where the closed-form result stops being exact.
Everything currently assumes a circular orbit, so the period comes straight from Kepler and the eclipse geometry uses a single altitude. Real orbital data centre proposals include eccentric parking and transfer orbits. This means accepting semi-major axis and eccentricity instead of altitude, integrating eclipse over true anomaly rather than assuming a constant shadow fraction, and stating clearly where the closed-form result stops being exact.