Distance between two Keplerian orbits

• Autorzy: Mohamed Ayman Homda , Dwidar Hany Ramdan , Adham Inal , Bakry Abd-Elazaz , El-Raffie Ahmed

Identyfikatory

DOI

10.2478/arsa-2021-0006

• Języki publikacji: EN

Abstrakty

EN

In this paper, constrained minimization for the point of closest approach of two conic sections is developed. For this development, we considered the nine cases of possible conics, namely, (elliptic-elliptic), (elliptic-parabolic), (elliptic–hyperbolic), (paraboli-elliptic), (paraboli-parabolic), (parabolic–hyperbolic), (hyperbolic-elliptic), (hyperbolic-parabolic), and (hyperbolic–hyperbolic). The developments are considered from two points of view, namely, analytical and computational. For the analytical developments, the literal expression of the minimum distance equation (S) and the constraint equation (G), including the first and second derivatives for each case, are established. For the computational developments, we construct an efficient algorithm for calculating the minimum distance by using the Lagrange multiplier method under the constraint on time. Finally, we compute the closest distance S between two conics for some orbits. The accuracy of the solutions was checked under the conditions that L|_solution ≤ε₁G||_solution ≤ε₂, where ε_1,2 < 10 ^-10. For the cases of (paraboli-parabolic), (paraboli-hyperbolic), and (hyperbolic-hyperbolic), we studied thousands of comets, but the condition of the closest approach was not met.

Słowa kluczowe

EN

distance function; Lagrange multiplier; objective function; Hessian matrix; minimum distance

• Wydawca: Centrum Badań Kosmicznych PAN ; De Gruyter
• Czasopismo: Artificial Satellites : Journal of Planetary Geodesy
• Rocznik: 2021
• Tom: Vol. 56, No. 3
• Strony: 57--77
• Opis fizyczny: Bibliogr. 13 poz., rys., tab.

Twórcy

autor

Mohamed Ayman Homda

• Egyptian Space Agency, Cairo, Egypt

autor

Dwidar Hany Ramdan

• Department of Astronomy, Space Science, and Meteorology, Faculty of Science, Cairo University, Cairo, Egypt

autor

Adham Inal

• Astronomy and Meteorology Department, Faculty of Science, Al-Azhar University, Cairo, Egypt

autor

Bakry Abd-Elazaz

• Astronomy and Meteorology Department, Faculty of Science, Al-Azhar University, Cairo, Egypt

autor

El-Raffie Ahmed

• Egyptian Space Agency, Cairo, Egypt

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).