Astronomy
A satellite through day and night
Keep a satellite powered through sunlight and eclipse. Deploy solar wings, change their pointing and decide when the scientific payload can stay on.
The model and its limits
Circular orbit of adjustable altitude and cylindrical Earth shadow: the eclipse half-width asin(R/(R+h)) and the period follow from the altitude. Panel power uses incidence and deployment; the battery integrates energy with a finite capacity. Orbit time runs 60 times faster; battery degradation is omitted. The orbit inset is schematic.
Equations used in the module
Equations P_solar = S A eta d max(0, cos(theta)); dE/dt = P_solar - P_load; 0 <= E <= E_max
