Simulating the Movement of Planets in the Solar System Using a Linear System
DOI:
https://doi.org/10.63876/ijtm.v2i1.95Keywords:
Solar System Simulation, Planetary Motion, Linear System, Gravitational DynamicsAbstract
This article discusses the simulation of planetary movements in the solar system using a linear system-based approach. Mathematical models of solar systems often involve non-linear differential equations, which include the complexity of gravitational interactions between planets and other celestial bodies. However, to simplify the calculation and analysis process, a linear approach can be used with certain assumptions. In this study, the motion of the planets is modeled using Newtonian mechanical principles adapted into a linear equation system. The simulation is carried out by utilizing numerical computing software to calculate the position and speed of the planet in a certain time span. The simulation results show that the linear system approach is able to represent the basic motion of the planet with an adequate degree of accuracy on short time scales, but it shows limitations in predicting complex dynamics, such as orbital resonance or the gravitational influence of small bodies. This approach is suitable for educational applications, where visualization of planetary movements can help understand the basic principles of orbital dynamics. These findings emphasize the importance of choosing the right simulation method according to the purpose, both for scientific and educational purposes. The study suggests the development of a hybrid model that combines a linear approach with non-linear elements to improve accuracy without losing computational efficiency.
Downloads
References
T. S. Kruijer, T. Kleine, and L. E. Borg, “The great isotopic dichotomy of the early Solar System,” Nat Astron, vol. 4, no. 1, pp. 32–40, Dec. 2019, doi: https://doi.org/10.1038/s41550-019-0959-9.
S. Sadiq and A. Alias, “Gravity and Solar System Evolution,” American Academic Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS), vol. 90, no. 1, pp. 214–237, 2022.
P. Cui and D. Qiao, “The present status and prospects in the research of orbital dynamics and control near small celestial bodies*,” Theoretical and Applied Mechanics Letters, vol. 4, no. 1, p. 013013, 2014, doi: https://doi.org/10.1063/2.1401313.
M. Abdel-Basset, R. Mohamed, S. A. A. Azeem, M. Jameel, and M. Abouhawwash, “Kepler optimization algorithm: A new metaheuristic algorithm inspired by Kepler’s laws of planetary motion,” Knowledge-Based Systems, vol. 268, p. 110454, May 2023, doi: https://doi.org/10.1016/j.knosys.2023.110454.
X. Han et al., “Effect of celestial body gravity on Taiji mission range and range acceleration noise,” Phys. Rev. D, vol. 106, no. 10, p. 102005, Nov. 2022, doi: https://doi.org/10.1103/PhysRevD.106.102005.
Q. Khan, A. Suen, and H. Khan, “Application of an efficient analytical technique based on Aboodh transformation to solve linear and non-linear dynamical systems of integro-differential equations,” Partial Differential Equations in Applied Mathematics, vol. 11, p. 100848, Sep. 2024, doi: https://doi.org/10.1016/j.padiff.2024.100848.
H. Nobahari, M. Alizad, and S. Nasrollahi, “A nonlinear model predictive controller based on the gravitational search algorithm,” Optim Control Appl Methods, vol. 42, no. 6, pp. 1734–1761, Nov. 2021, doi: https://doi.org/10.1002/oca.2757.
D. A. Bolatti and A. H. J. De Ruiter, “Quantification of attitude effects on orbital dynamics near asteroids,” Acta Astronautica, vol. 167, pp. 467–482, Feb. 2020, doi: https://doi.org/10.1016/j.actaastro.2019.10.044.
A. R. McDonald, R. Roberts, J. R. Koeppe, and B. L. Hall, “Undergraduate structural biology education: A shift from users to developers of computation and simulation tools,” Current Opinion in Structural Biology, vol. 72, pp. 39–45, Feb. 2022, doi: https://doi.org/10.1016/j.sbi.2021.07.012.
I. Setiawan, R. Sugihakim, and B. E. Gunara, “Bound States of Central Force System in Special Relativity,” 2022, doi: https://doi.org/10.48550/ARXIV.2208.06505.
D. E. Smith et al., “Summary of the results from the lunar orbiter laser altimeter after seven years in lunar orbit,” Icarus, vol. 283, pp. 70–91, Feb. 2017, doi: https://doi.org/10.1016/j.icarus.2016.06.006.
Md. Golam Robbani, Md. Asadujjaman, and Md. Mehedi Hassan, “A Proposed New Non-Linear Programming Technique for Solving a Mixed Strategy Problem in Game Theory,” IJSSAM, Jul. 2023, doi: https://doi.org/10.11648/j.ijssam.20230802.11.
H. Hasanuddin, “Simulasi Orbit Planet Eksentrisitas Tinggi dengan Metode Leapfrog,” jf, vol. 12, no. 1, pp. 1–8, May 2022, doi: https://doi.org/10.15294/jf.v12i1.33744.
C. D. Murray and S. F. Dermott, Solar System Dynamics. Cambridge: Cambridge University Press, 1999.
B. Gladman, “The Near-Earth Object Population,” Icarus, vol. 146, no. 1, pp. 176–189, Jul. 2000, doi: https://doi.org/10.1006/icar.2000.6391.
C. Migaszewski, K. Gozdziewski, and M. Slonina, “A linear distribution of orbits in compact planetary systems?,” 2013, doi: https://doi.org/10.48550/ARXIV.1306.3523.
C. L. Jones, J. D. Jensen, C. L. Scherr, N. R. Brown, K. Christy, and J. Weaver, “The Health Belief Model as an Explanatory Framework in Communication Research: Exploring Parallel, Serial, and Moderated Mediation,” Health Communication, vol. 30, no. 6, pp. 566–576, Jun. 2015, doi: https://doi.org/10.1080/10410236.2013.873363.
Muhamad Taufiq and Ida Kaniawati, “Mekanika Newtonian dan Signifikansi Filosofisnya,” JFI, vol. 6, no. 2, pp. 246–257, Jun. 2023, doi: https://doi.org/10.23887/jfi.v6i2.53649.
A. A. Ibrahem, H. M. Hendy, A. A. Ali, and A. M. Kamel, “Design and Assessment of Satellite Orbit Simulator and Predictor,” in 2023 International Telecommunications Conference (ITC-Egypt), Alexandria, Egypt: IEEE, Jul. 2023, pp. 737–741. doi: https://doi.org/10.1109/ITC-Egypt58155.2023.10206165.
F. Yoshida et al., “A deep analysis for New Horizons’ KBO search images,” Publications of the Astronomical Society of Japan, vol. 76, no. 4, pp. 720–732, Aug. 2024, doi: https://doi.org/10.1093/pasj/psae043.
D. F. Fernandes, M. C. Santos, A. C. Silva, and A. M. M. Lima, “Comparative study of CUDA-based parallel programming in C and Python for GPU acceleration of the 4th order Runge-Kutta method,” Nuclear Engineering and Design, vol. 421, p. 113050, May 2024, doi: https://doi.org/10.1016/j.nucengdes.2024.113050.
E. J. O. Schrama and P. N. A. M. Visser, “Choices for temporal gravity field modeling for precision orbit determination of CryoSat-2,” Advances in Space Research, vol. 73, no. 1, pp. 31–41, Jan. 2024, doi: https://doi.org/10.1016/j.asr.2023.11.034.
