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Orbital velocities and periods can be calculated by a more accurate formula than that used in the text. The velocity at orbital altitude is a function of the altitudes of apogee and perigee, with the subscripts ap and per, as measured from the center of the earth. That is why the altitudes from the surface have added to them the radius of the Earth. The velocity one needs for the scanner calculations is the linear velocity on the surface of the Earth; it is different from that at altitude. The angular velocity is constant, so the two velocities are related by the ratio of radii. Notice that for a 200 km altitude, the velocity is about 7.6 km/s, very close to the approximation made in the main part of the text.
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