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Modelling Asteroid Trajectory in Earth’s Atmosphere
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Orientador(es)
Resumo(s)
Earth’s atmosphere is humanity’s last defence against the potential threat of asteroid impacts. To assess the impact risk and devise effective mitigation strategies, it is essential to understand the interaction between asteroids and the atmosphere. This paper presents a comprehensive study that employs a system of differential-algebraic equations (DAEs) to model the trajectory and associated physical processes involved in an atmospheric entry and the consequent impact of an asteroid. The Apophis asteroid is utilized as a case study to compare and evaluate the performance of two numerical methods for solving these equations. The findings from this research contribute to advancing our understanding of asteroid entry dynamics and provide valuable insights for enhancing asteroid impact mitigation strategies. The Apophis asteroid, represented as a 340 m diameter sphere with a density of 3190 kg.m−3, enters the atmosphere at a velocity of 30759 m.s−1 and a 45-degree angle from an altitude of 81 km. The first method employed is the 4th-order Runge-Kutta method (RK4) with a constant time-step, commonly used for solving highly non-linear problems like this. The second method is based on the Dormand-Prince method, which utilizes a dynamic time step and provides a 4th-order solution with error estimation using a 5th-order solution. Computational efficiency and the resulting solutions are compared between the two methods. The study finds that the Dormand-Prince method offers a more accurate numerical solution with less computational effort. However, both approaches demonstrate a correspondence of at least three significant digits, confirming their validity. Overall, during its traversal through the atmosphere, the Apophis asteroid experiences a decrease in initial velocity by 0.83%, a loss of 22% of its initial mass, and a variation in its angle with the horizontal by 1.5%.
Descrição
Palavras-chave
Asteroid Apophis Runge Kutta Dormand Prince
Contexto Educativo
Citação
Morais, R.H., Marques, L.F.F., da Silva, A.R.R., Melicio, R., Modelling Asteroid Trajectory in Earth’s Atmosphere, 34th Congress of the International Council of the Aeronautical Sciences, ICAS 2024, Florence, Italy, 9-13 September 2024