Acceleration Required to Maneuver One Satellite Around Another at Close Range.
Equations are derived for computing the components of acceleration required either to maintain two earth satellites in a fixed relative position or to move one satellite relative to another in a prescribed manner. These equations are applied to determine the total instantaneous acceleration required for several different fixed relative positions and motions of two satellites at close range. Then, for some cases, the required acceleration is related to the propulsive energy required by computing the ratio of propellant weight to initial weight for missions of up to 100-day duration using specific impulses of 300, 1,000, and 10,000 seconds. In general, the total acceleration required for a specified maneuver of one satellite around another changes with the relative direction of motion and the inclination of the plane of motion of the maneuvering satellite around the reference satellite. Specifically, the required acceleration tends to be minimum if the angular motion of the maneuvering satellite around the reference satellite is opposite to the angular motion of the reference satellite around the earth. The ratio of propellant weight to initial weight becomes excessive for mission durations of more than 20 days if the satellites are separated by 100 feet or more and the specific impulse is 1,000 seconds or less. 51 pp. Ref.