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Solar radiation induced perturbations and control of satellite trajectories Van Der Ha, Jozef Cyrillus

Abstract

The long-term orbital perturbations due to solar radiation forces as well as ways to utilize these effects for corrections in the orbit are investigated. In order to obtain familiarity with relative merits of the formulations and methods relevant to the present objective, the special case of an orbit in the ecliptic plane and a force along the radiation is considered first. The long-term valid analysis is based upon the two-variable expansion method and incorporates the apparent motion of the sun by treating the sun's position as a quasi-orbital element. Analytical representations for orbital elements are derived and the perturbations are conveniently summarized in the form of polar plots showing the long-term evolution of the eccentricity vector. While the eccentricity is periodic with period close to one year, the argument of the perigee contains secular terms. The total energy and thus major axis remain conserved in the long run. However, in the course of one year, the effect of the earth's shadow may lead to small secular changes in the major axis thereby modifying the satellite's period. Next, the analysis is extended to orbits of an arbitrary inclination with closed-form analytical solutions established in some special cases. An interesting relation between the long-term behavior of the orbital inclination and the in-plane perturbations is discovered. Also, more general satellite configurations are studied: e.g., spacecrafts modelled as a plate in an arbitrary fixed orientation with respect to the earth or solar radiation as well as platforms kept fixed to the inertia! space. In all applications a realistic solar radiation force allowing for diffuse and/or specular reflection as well as for re-emission of absorbed radiation is considered. In a few cases, the analysis is extended to include arbitrarily shaped satellite bodies modelled by a number of surface components of homogeneous material characteristics. After establishing a comprehensive spectrum of the qualitative and quantitative aspects of solar radiation induced orbital perturbations, the attention is focused on the development of control strategies involving the rotation of solar panels attached to the satellite to manipulate both the direction and magnitude of the resulting force. A few on-off switching strategies are explored and the most effective switching locations for several specific objectives, e.g. maximization of the major axis, are determined. The switching strategies explored here constitute an attractive possibility for orbital corrections. The concept is particularly of interest to modern communications satellite technology since it allows their normal operation to remain unaffected over approximately half the time. Although on-off switching may lead to substantial changes in the major axis, it is not necessarily the best policy when time-varying orientations are also taken into consideration. The optimal control strategy for maximization of the major axis over one revolution is determined by means of the numerical steepest-ascent iteration procedure, and its effectiveness is compared with that of the switching programs. The solution should prove to be of interest in several future missions including the launching of a solar sail from a geocentric orbit into a heliocentric or escape trajectory. Subsequently, solar radiation effects upon a satellite (usually a solar sail) in a heliocentric orbit are explored. First, the sail is taken in a fixed but arbitrary orientation to the local frame. Using specific initial conditions, exact solutions in the form of conic sections and three-dimensional logarithmic spirals are established. For an arbitrary initial orbit, long-term approximate representations of the orbital elements are derived. An effective out-of-plane spiral transfer trajectory is obtained by reversing the force component normal to the orbit at specified positions. By choosing the appropriate control angles, any point in space can eventually be reached. Finally, time-varying optimal control strategies are explored for increasing the total energy (and angular momentum) during one revolution. While analytical approximate results can be established for near-circular orbits, in the general case a numerical steepest-ascent technique is employed. The results are compared with those from the constant sail setting indicating that the latter is a near-optimal strategy for low eccentricity starting orbits.

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