On the analysis of multistep-out-of-grid method for celestial mechanics tasks

• Autorzy: Olifer L. , Choliy V.

Identyfikatory

DOI

10.1515/arsa-2016-0009

• Języki publikacji: EN

Abstrakty

EN

Occasionally, there is a necessity in high-accurate prediction of celestial body trajectory. The most common way to do that is to solve Kepler’s equation analytically or to use Runge-Kutta or Adams integrators to solve equation of motion numerically. For low-orbit satellites, there is a critical need in accounting geopotential and another forces which influence motion. As the result, the right side of equation of motion becomes much bigger, and classical integrators will not be quite effective. On the other hand, there is a multistep-out-of-grid (MOG) method which combines Runge-Kutta and Adams methods. The MOG method is based on using m on-grid values of the solution and n × m off-grid derivative estimations. Such method could provide stable integrators of maximum possible order, O (h^m+mn+n−1). The main subject of this research was to implement and analyze the MOG method for solving satellite equation of motion with taking into account Earth geopotential model (ex. EGM2008 (Pavlis at al., 2008)) and with possibility to add other perturbations such as atmospheric drag or solar radiation pressure. Simulations were made for satellites on low orbit and with various eccentricities (from 0.1 to 0.9). Results of the MOG integrator were compared with results of Runge-Kutta and Adams integrators. It was shown that the MOG method has better accuracy than classical ones of the same order and less righthand value estimations when is working on high orders. That gives it some advantage over ”classical” methods.

Słowa kluczowe

EN

out-of-grid methods; numerical integrators

• Wydawca: Centrum Badań Kosmicznych PAN ; De Gruyter
• Czasopismo: Artificial Satellites : Journal of Planetary Geodesy
• Rocznik: 2016
• Tom: Vol. 51, No. 3
• Strony: 99--105
• Opis fizyczny: Bibliogr. 5 poz., rys., tab.

Twórcy

autor

Olifer L.

• National University “Kyiv Polytechnic Institute”, Peremohy ave., 37, 03056, Kyiv, Ukraine
• Space Research Institute National Academy of Sciences of Ukraine and State Space Agency of Ukraine, Glushkov Ave 40, 4/1, 03680, Kyiv 187, Ukraine

autor

Choliy V.

• Taras Shevchenko National University of Kyiv, Glushkova ave., 4, 03127, Kyiv, Ukraine
• Main Astronomical Observatory National Academy of Sciences of Ukraine, Zabolotnogo str., 27, 03680, Kyiv

Bibliografia

• Beaudet P. (1972) Multi-off-grid methods in multi-step integration of ordinary differential equations, in Proc. of the Conference on the Numerical Solutions of ODE, 1972, Texas Univ., USA, 498 p.
• Dahlquist G. (1956) Convergence and stability in the numerical integration of ODE, Math.Scand., Vol. 4, 33-53.
• Pavlis N., Holmes S., Kenyon S., Factor J. (2008) An Earth Gravitational Model to Degree 2160: EGM2008, Presented at the 2008 General Assembly of the European Geosciences Union, Vienna, Austria, April 13-18, 2008.
• Press W., Teukolsky S., Vetterling W., Flannery B. (1992) Numerical recipes in C, Cambridge.: Cambridge University Press, 1992.
• Taradiy V., Tsesis M. (1984) Computation of the Earth’ satellites trajectories. Implementing of the Adams algorithm and program of variable step and order. Preprint / AS UkrSSR. Institute of theoretical physics N ITF-84-92P,- in Russian., Kyiv, 1984.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).