Analysis of the orbital evolution of space debris using a solar sail and natural forces

Space Junk: The Risk of Space Missions and the Proposal of Solar Sail Technology to Mitigate the Problem

“…To perform numerical simulations, debris located in LEO with initial conditions and identification were used checked in Table 1 We take the re-entry of the debris at an altitude of perigee radius (r_p) less than the Earth radius altitude, approximately 6380 km from the center of the Earth to the surface, plus 120 km where the atmosphere is denser. So it is admitted that below 6500 km of altitude, where the friction with the atmosphere makes re-entry imminent, according to [3][4][5], taking this region as the re-entry zone, represented by the lines red in the r_p evolution graphs over 20 years, in the same way as it was admitted in [5]. All the initial conditions of the simulated debris, in Table 1, are substituted in the disturbing potential and in the equations of orbital motion.…”

“…The motion equations were integrated via Lagrange planetary equations, Equation 1, 2, 3 and 4, which are a system of nonlinear differential equations in Keplerian terms (orbital elements) that describe the motion of bodies orbiting a central body (in this case Earth). In [8], the Lagrange planetary equations restricted to the models are Where M is the average anomaly and R is the perturbing function given in [5], modeled to orbital parameters considering elliptical and inclined orbits, and with reduced degree of freedom, where is the sum of the main forces that perturb the orbital motion of the debris-sail system, represented as In Maple, line graph simulations lasted around 5 hours for plotting individually, using a single GPU capable of 2.3 GHz average processing time over four independent cores (AMD Ryzen 7 3700U). For numerical simulations, values such as mass, equatorial radius, zonal coefficients and mean radius of the Earth, made available by the online platform of NASA "Jet Propulsion Laboratory".…”

“…According to [2][3][4][5], another alarming problem with space debris is related to the duration of "life" in Earth orbit. In GEO (geostationary orbit), which is of utmost importance due to the amount of existing active satellites located in its surroundings, the altitude favorable and synchronization with Earth's rotation, space debris can remain in orbit for hundreds of years at risk of collision and overfilling of the orbit due to the almost non-existent evasion of this debris.…”

“…The use of solar sails in space is similar to the use of sails on terrestrial sailing vessels, however their motion is related to the increased effect of solar radiation pressure (SRP). According to [5,7,8], for the solar sail to maximize its functionality, it is taken into account that the reflectance will cause the SRP effect to be maximum on the surface of the sail and, therefore, the greater the area/mass coefficient in the system of the body attached to the sail, the greater the effectiveness of the acceleration that this system can provide, cleaning space debris in shorter measures of time. The solar sail, in addition to enhancing the ability of the SRP to increase the eccentricity of the orbit, as predicted [5], is also capable of acting as a drag sail by increasing the frictional contact with the atmosphere at lower altitudes, losing tangential velocity of rotation and re-entering more quickly.With the advancement of technology today, it is very common to send small satellites in low Earth orbit, the Cubesats.…”

Modeling Longitudinal Evolution of Decommissioned Geostationary Satellites using Neural Networks

“…By interpreting these relationships, we can make more accurate orbital predictions and enhance our overall understanding of satellite movements. [19,20].…”