Abstract
Analytical formulas are derived for orbit-averaged behavior of magnetic control laws for unloading the excess angular momentum of a spacecraft reaction wheel control system in the presence of secular environmental torques. The specific example of an axially symmetric spacecraft with an inertially fixed attitude for which the dominant environmental torque is the gravity-gradient torque is treated in detail, but extensions of the general approach to other inertially fixed and earth-pointing spacecraft are discussed. The analytical formulas are compared to detailed simulations performed for the Solar Maximum Mission spacecraft, and agreement to within 10% is found. The analytical formulas can be used in place of detailed simulations for preliminary studies, and can be used to find selected cases giving the most stringent tests of momentum unloading capability for which detailed simulations may be performed.
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