Thermal Analysis on a Satellite Box during Launch Stage by Analytical Solution

Simple methods are developed to predict temperatures of a satellite box during launch stage. The box is mounted on outer surface of satellite and directly exposed to space thermal environment for the time period from fairing jettison to separation. These simple methods are to solve a 1st order ordinary differential equation (ODE) which is simplified from the governing equation after applying several assumptions. The existence of analytical solution for the 1st order ODE is determined depending on treatment of time-dependent molecular heating term. Even for the case that the analytical solution is not available due to the time dependent term, the 1st order ODE can be solved by relatively simple numerical techniques. The temperature difference between two different approaches (analytical and numerical solutions) is relatively small (Jess than $1^{\circ}C$ along the time line) when they are applied to STSAT-I launch scenario. The present methods can be generally used as tools to quickly check whether a satellite box is safe against space environment during the launch stage for the case that the detailed thermal analysis is not available.