Methods for the calculation of unsteady-state thermal conditions of isothermal space objects

A mathematical model is given, which describes unsteady-state thermal conditions of isothermal space objects (SO) of a convex shape. Calculations are performed of the surface-average temperature of SOs with a high thermal conductivity or of fast-rotating objects. Numerical results are obtained, as well as an approximate analytical solution which enables one to calculate the unsteady-state temperature of an SO having a sheath. The mathematical model has a general form for an SO of an arbitrary shape moving along a trajectory at a constant or variable distance from the Earth center. The first calculations are performed for an object of a spherical shape moving along a parabolic ballistic trajectory both at a preassigned angle of irradiation from the Sun and in the shadow of the Earth.