Simulation of orbital dynamics of satellite communication spacecraft by linear interpolation

Space technologies are increasingly permeating our lives. Global positioning systems, communications, geology, hydrology, agriculture, and military affairs are just a few of the industries that rely on satellite data. The Russian Federation's satellite constellation is growing every year, and the satellite control system is correspondingly becoming more complex. The high speed of satellites requires constant recalculation of their coordinates with high accuracy. The SGP4 models for low-orbit satellites and the SDP4 models for high-orbit satellites are most commonly used for this purpose. These models provide sufficient calculation accuracy but require significant computing power. When controlling a large number of objects, the computational load can be excessive. This paper is devoted to assessing the error in interpolation calculations of spacecraft positions in low-Earth orbit. To simplify and accelerate calculations of low-orbit satellite dynamics, this paper proposes a linear interpolation method for accelerating satellite position calculations. The results from the SGP4 model were used as a benchmark. A comparative analysis of the accuracy of calculations using the linear interpolation method and the SGP4 model was conducted. It was determined that the acceptable time interval for interpolation should not exceed 60 seconds, ensuring correct interaction between ground stations and the spacecraft.

1. Savvina E.V. Inter-Orbital Spacecraft Transfer: Trajectory Design by Iterating Parameter Values within a Data Grid. Problemy Upravlenia. 2023;(2):65–74. (In Russ.). https://doi.org/10.25728/pu.2023.2.6

2. Aldokhina V.N., Kulikov S.V., Korolev V.O. Model of the Satellite Motion Predicting in Near-Earth Space. Modern High Technologies. 2021;(1):7–11. (In Russ.). https://doi.org/10.17513/snt.38463

3. Lysenko L.N., Betanov V.V. Printsipy i osnovnye napravleniya sovershenstvovaniya nazemnogo avtomatizirovannogo kompleksa upravleniya kosmicheskimi poletami. Herald of the Bauman MSTU. Series "Mechanical Engineering". 2011;(1):17–30. (In Russ.).

4. Vallado D.A., Crawford P. SGP4 Orbit Determination. In: AIAA/AAS Astrodynamics Specialist Conference and Exhibit, 18–21 August 2008, Honolulu, HI, USA. American Institute of Aeronautics and Astronautics; 2008. https://doi.org/10.2514/6.2008-6770

5. Chagina V.A., Grishko D.A., Maiorova V.I. Satellite's Trajectory Propagation at Near-Circular Orbits Using TLE Files in the Simplified SGP Model. Mashinostroenie i komp'yuternye tekhnologii. 2016;(1):52–66. (In Russ.).

6. Sokolov I.A., Tsekhanovich G.S. Analysis of the Movement Model of a Spacecraft in Earth Orbit. Siberian Aerospace Journal. 2025;26(1):107–125. https://doi.org/10.31772/2712-8970-2025-26-1-107-125

7. Karshakov E.V., Pavlov B.V., Tkhorenko M.Y., Papusha I.A. Promising Map-Aided Aircraft Navigation Systems. Gyroscopy and Navigation. 2021;12(1):38–49. https://doi.org/10.1134/S2075108721010077

8. Cilden-Guler D., Hajiyev Ch. SVD-Aided EKF for Nanosatellite Attitude Estimation Based on Kinematic and Dynamic Relations. Gyroscopy and Navigation. 2023;31(4):138–156. (In Russ.).

9. Titenko E.A., Sizov A.S., Schitov A.N., Shevtsov A.N., Schitova E.N., Skripkina E.V. Structural Diagram of the Module for Determining the Location of Small Space Vehicles. T-Comm. 2021;15(4):28–34. (In Russ.). https://doi.org/10.36724/2072-8735-2021-15-4-28-34

10. Anqi L. Analysis of Spacecraft Trajectories for the Space Mission Earth-Apophis-Earth and the Spacecraft Orbital Motion Around the Asteroid Apophis. Engineering Journal: Science and Innovation. 2017;(7). (In Russ.). https://doi.org/10.18698/2308-6033-2017-7-1635

11. Zhang L., Ge P. Trajectory Optimization and Orbit Design of Spacecraft in Hovering Mission. The Journal of the Astronautical Sciences. 2020;67(4):1344–1373. https://doi.org/10.1007/s40295-020-00226-z

12. O'Leary J., Barriot J.-P. An Application of Symplectic Integration for General Relativistic Planetary Orbitography Subject to Non-Gravitational Forces. Celestial Mechanics and Dynamical Astronomy. 2021;133(11-12). https://doi.org/10.1007/s10569-021-10051-7

13. Gorbunov A.V., Churkin A.L., Pavlov D.A. Kosmicheskii kompleks gidrometeorologicheskogo i okeanograficheskogo obespecheniya "Meteor-3M" s kosmicheskim apparatom "Meteor-M". Voprosy elektromekhaniki. Trudy VNIIEM. 2008;105:17–28. (In Russ.).

14. Lysenko L.N., Betanov V.V., Zvyagin F.V. Teoreticheskie osnovy ballistiko-navigatsionnogo obespecheniya kosmicheskikh poletov. Moscow: Izd-vo MGTU im. N.E. Baumana; 2014. 519 p. (In Russ.).