## Orbit Maintenance

Once in their mission orbits, many satellites need no additional orbital adjustments. On the other hand, mission requirements may demand that we maneuver the satellite to correct the oibital elements when perturbing forces.have changed them. Two particular cases of note are satellites with repeating ground tracks and geosynchronous equatorial satellites, placed at an assigned longitude.

Using two-body equations of motion, we can show that a satellite will have a repeating ground track if it has exactly an integer number of revolutions per integer number of days. Its period, therefore, must be:

where m and k are integers, and 1 sidereal day = 1,436.068 167 min. For example, a satellite orbiting the Earth exactly 16 times per day has a period of 89.75 min and a semimajor axis of6,640 km.

Next we would modify the period of the satellite to account for the drift in the orbital plane caused by the Earth's oblateness (J2). We can calculate the change in the right ascension of the ascending node, AQ, because of J2 from the two-body orbital elements. In this case the new period is:

Because we base the nodal drift on the two-body orbital elements, we must iterate to find the new orbital period and semimajor axis. Continuing with the previous example, assume a perigee altitude of 120 km and an inclination of 45 deg. In this case, we find that the compensated period is 88.20 min and the new semimajor axis is 6,563 km.

Several examples of spacecraft placed in orbits with repeating ground tracks are shown in Table 6-7.

TABLE 6-7. Examples of Repeating Ground Tracks.

Satellite

Inclination (deg)

Sem[major Axis (km) Revs

Days

SEASAT LANDSAT 4/5 GEOSAT

0 0