<abstract xmlns="http://www.w3.org/1999/xhtml">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 <italic>n × m</italic> off-grid derivative estimations. Such method could provide stable integrators of maximum possible order, <italic>O</italic> (<italic>hm</italic>+<italic>mn</italic>+<italic>n−</italic>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 right-hand value estimations when is working on high orders. That gives it some advantage over ”classical” methods.</abstract>

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 (hm+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 right-hand value estimations when is working on high orders. That gives it some advantage over ”classical” methods.

On the Analysis of Multistep-Out-of-Grid Method for Celestial Mechanics Tasks

National University “Kyiv Polytechnic Institute”, Peremohy ave., 37, 03056, Kyiv,

Space Research Institute National Academy of Sciences of Ukraine and State Space Agency of Ukraine, Glushkov Ave 40, 4/1, 03680, Kyiv 187,

Taras Shevchenko National University of Kyiv, Glushkova ave., 4, 03127, Kyiv,

Main Astronomical Observatory National Academy of Sciences of Ukraine, Zabolotnogo str., 27, 03680, Kyiv,

Artificial Satellites

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"On the Analysis of Multistep-Out-of-Grid Method for Celestial Mechanics Tasks"}

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...

On the Analysis of Multistep-Out-of-Grid Method for Celestial Mechanics Tasks

Published Online: Sep 29, 2016

Page range: 99 - 105

Received: May 31, 2016

Accepted: Sep 05, 2016

DOI: https://doi.org/10.1515/arsa-2016-0009

Keywords
Out-of-grid methods, numerical integrators

© 2016 Artificial Satellites

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On the Analysis of Multistep-Out-of-Grid Method for Celestial Mechanics Tasks

Published Online: Sep 29, 2016

Page range: 99 - 105

Received: May 31, 2016

Accepted: Sep 05, 2016

DOI: https://doi.org/10.1515/arsa-2016-0009

KeywordsOut-of-grid methods, numerical integrators

© 2016 Artificial Satellites

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Out-of-grid methods, numerical integrators