Analytical technique for satellite projected cross-sectional area calculation

Calculating the projected cross-sectional area (PCSA) of a satellite along a given direction is essential for implementing attitude control modes such as Sun pointing or minimum-drag. The PCSA may also be required for estimating the forces and torques induced by atmospheric drag and solar radiation pressure. This paper develops a new analytical method for calculating the PCSA, the concomitant torques and the satellite exposed surface area, based on the theory of convex polygons. A scheme for approximating the outer surface of any satellite by polygons is developed. Then, a methodology for calculating the projections of the polygons along a given vector is employed. The methodology also accounts for overlaps among projections, and is capable of providing the true PCSA in a computationally-efficient manner. Using the Space Autonomous Mission for Swarming and Geo-locating Nanosatellites mechanical model, it is shown that the new analytical method yields accurate results, which are similar to results obtained from alternative numerical tools.