A comprehensive attitude formulation with spin for numerical model of irradiance for CubeSats and Picosats

•Analytical thermal-attitude model for transient irradiation flux on CubeSats is presented.•Numerical results are showed for incident radiation and temperature under diverse spins.•Each attitude is simulated for orbits with and without eclipse.•Occurrence of low temperature gradient in attitudes with high speed on three axis.•The temperature field may be managed by the attitude control. A comprehensive but simple formulation for the attitude of a nanosatellite is presented herein with a focus on problems associated with spin and heat transfer. Sequential matrices of rotation predict the position and orientation of the spacecraft, which govern the heat fluxes composed of solar, albedo and infrared radiation. These fluxes are boundary conditions for the energy equation and are implemented to solve the temperature field based on the finite volume method. Common spins are used as benchmark cases to study their effect on the temperature of CubeSats. The attitude of nadir, detumbling, high speed, arbitrary motion and maximum exposure to the Sun are simulated for orbits with and without eclipse, at an altitude of 650 km and inclination of 90°. Results for total heat influx and temperature of the external surfaces are shown for single full orbits. Low spins are associated with the largest temperature gradients, due to the unequal distribution of heat fluxes. High angular speed homogenizes the temperature, especially for a spin around three axes. In general, for high spin, temperatures are nearly constant and appropriate for regular operational temperatures. Data collect from CubeSats in orbit are compared with the numerical values and satisfactory agreement is observed, despite differences in the designs and geometries. The model presented is comprised of a formulation for the spin and for the thermal irradiation over a CubeSat and can be implemented in traditional programming languages to investigate different orbital parameters for CubeSats and Picosats.