Propagation of the trajectories for reentry spherical debris including rotation, melting fragmentation and voxel method

It is estimated that more than 22.000 objects are in orbit around the Earth, with a total mass of 8.400.000 kg. These numbers consider only objects with dimensions above 10 cm and some non-operational, but still orbiting satellites without control (debris). The debris represent a hazard to operational satellites and aerospace operations due to the high probability of collisions. Due to the interaction of the debris with the atmosphere of the Earth and the solar activity, they began to lose energy and finally decay. During the de-orbit process, the debris fall into the Earth's atmosphere at hypersonic speeds and these objects can break-up and/or be fragmented due to the aerodynamics, thermal and structural loads. It is important to obtain the trajectory and attitude of any fragment to determine the possible survival mass, impact area, hazard conditions and risks to the population, the air traffic control, and infrastructure. In this case, it is implemented a computational code to integrate the equations of motion to propagate the dynamics and kinematics of spherical debris or propellant tanks. It is also analyzed the results of trajectories with six degrees of freedom, atmospheric winds, and Magnus effect. A voxel method is implemented to analyze the tanks heat transfer, surface temperature and structures stress. To determine and observe the influence of the rotation and the Magnus force in six reentry spherical bodies, three materials are selected; aluminum alloy, due to its application in many aerospace structures; titanium and graphite epoxy I, due to their highest melting point and specific heat. Generally, these materials are used in tanks and rocket motors. More than 62 trajectories were simulated. The mathematical model and computational code were validated in three degrees of freedom. Results are compared with data from other computational tools available in the scientific literature. The results show a good approximation with reported cases of study. New results are generated in the simulations of rotational bodies, due to the influence of aerodynamic forces in the trajectory and the changes in the stagnation regions. Due to the implementation of wind and rotation of the debris, the fragments increased the survivability and the dispersion area.