First, solar, lunar, and earth oblatness perturbations produce cyclic variations in the orbital inclination. For satellites at geosynchronous altitude, the period of the variations is 53 years. The maximum inclination depends on the initial inclination and the phasing of the ascending node. Frick^ shows that the inclination is approximately constant with respect to a reference plane whose orientation depends on orbital altitude. The cyclic variations of inclination with respect to the equator are caused by precession of the orbit with respect to reference plane. At geosynchronous altitude, the reference plane is inclined 7°20' with respect to the equator. Figure 2.4-4 shows the annual AV required to maintain orbital inclination with respect to the equatorial plane at or below a specified value. Inclination can be kept at 0° (long period affects only) at a cost of 46.3 m/sec/yr. On the other hand, no AV is required to maintain an inclination of 7°20' if the orbit is established in the reference plane. 1 Frick, R. H., Orbital Regression of Synchronous Satellites Due to the Combined Gravitational Effects of the Sun, the Moon, and the Oblate Earth. Rand Corp., R-454-NASA (Aug. 1967). Figure 2.4-4. Propulsion Requirement for Orbit Inclination Control
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