CAPTURE OF A PASSIVELY STABILIZED SATELLITE BY EARTH'S GRAVITY FIELD

Abstract

I is currently high in passive stabilization of spacecraft, particularly satellites of the earth. Of the several techniques of passive stabilization, use of earth's gravity field is receiving perhaps most attention. In this technique, the satellite's configuration is so arranged that torques are produced on the satellite by the gradient of earth's gravity field, restoring the satellite toward one of its equilibrium positions if displaced from equilibrium. Under the action of these torques, the satellite librates or oscillates about one of the equilibrium positions. If the satellite also contains some damping mechanism, the oscillations will decay until they fall within a small steady-state deadband about one of the equilibrium positions. The satellite is so configured that in its equilibrium position an antenna, for instance, is directed to earth. The classic configuration that is torqued by earth's gravity gradient is a dumbbell. The dumbbell is oriented in pitch and roll but not yaw, where the yaw axis is the local vertical. Another configuration, one now being widely studied and developed, consists of a central body from which long thinwalled tubes uncoil once the satellite is in orbit. Because of their great length (hundreds of feet for some applications), the tubes endow the satellite with the necessary inertia to develop from the gravity field high restoring torques. If the tubes extend from the central body to form a cross having its two members at right angles and of unequal length, restoring torques in yaw, as well as pitch and roll, are developed. Yaw restoring torques are also developed if the rods extend to form an X, that is, with two members of equal length intersecting at an angle different from 90°. A typical mission profile of such a gravity oriented satellite consists of the following: 1) Injection into orbit from a final propulsion stage either spin-stabilized such as Scout or containing its own attitude stabilization such as Agena. In the former instance the satellite, after separation from the propulsion stage, is itself spinning. In the latter instance the satellite is slowly tumbling after separation. 2) Conversion of the spinning or tumbling of the satellite to oscillation about the local vertical. Oscillation about the local vertical, when seen from inertial space, is a steady rotation of the satellite plus a superimposed oscillation. The rotation is about an axis normal to the orbital plane. The rotation is at a rate eaual to the satellite's orbital rate, wnich is much slower than the rate at injection. As seen from inertial space, then, the spinning or random tumbling at injection must be converted to a much slower rotation about an axis having a particular direction in space. 3) Decay of the satellite's oscillation. The oscillation decays to a small deadband whose width is determined by the