Enhancing Stellar Orbit Accuracy through the Radius Power Law Time Step Function Model

Authors

  • Hasanuddin Hasanuddin Department of Physics, Faculty of Mathematics and Natural Sciences, University of Tanjungpura, Pontianak, 78124, Indonesia https://orcid.org/0000-0002-0604-929X
  • Agustinus Eusebius Department of Physics, Faculty of Mathematics and Natural Sciences, University of Tanjungpura, Pontianak, 78124, Indonesia
  • Yudha Arman Department of Physics, Faculty of Mathematics and Natural Sciences, University of Tanjungpura, Pontianak, 78124, Indonesia

DOI:

https://doi.org/10.25077/jif.18.1.35-44.2026

Keywords:

astrophysical systems, numerical integration, stellar orbits, symplectic integrator, time step function

Abstract

Accurately determining stellar orbits within astrophysical systems is paramount for understanding celestial mechanics. This study proposes a novel approach to enhance orbit accuracy by incorporating a radius power law time step function model. The methodology involves the numerical integration of the system's dynamics using a forward fourth-order symplectic integrator, combined with a time step function dependent on the distance of the test particle from the system's center. We conduct simulations on various astrophysical scenarios represented by conservative potentials, including point mass, Plummer, and Hernquist models. Our results demonstrate that employing a power-law time step function with an exponent of 1.5 significantly reduces phase-space error (measured by the ratio of radial to orbital periods) and improves orbit accuracy (measured by the gradient of the relative total energy drift). The method is easy to implement, computationally efficient, and adaptable to N-body and more general dynamical systems. Its solid theoretical basis and numerical reliability make it a practical tool for improving orbit accuracy in diverse astrophysical applications.

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References

Aarseth, S. J. (2003). Gravitational N-body simulations. In Gravitational N-Body Simulations, by Sverre J.~Aarseth, pp. 430. ISBN 0521432723.~Cambridge, UK: Cambridge University Press, November 2003. Cambridge University Press.

Aarseth, S. J., & Heggie, D. C. (1993). A 6000-body simulation with primordial binaries. In G. H. Smith & J. P. Brodie (Eds.), The Globular Cluster-Galaxy Connection (Vol. 48, p. 701).

Adams, F. C., & Bloch, A. M. (2005). Orbits in Extended Mass Distributions: General Results and the Spirographic Approximation. The Astrophysical Journal, 629(1), 204–218. https://doi.org/10.1086/431455

Baes, M., & Dejonghe, H. (2002). The Hernquist model revisited: Completely analytical anisotropic dynamical models. Astronomy and Astrophysics, 393(2), 485–497. https://doi.org/10.1051/0004-6361:20021064

Binney, J., & Tremaine, S. (2008). Galactic dynamics: Second edition. Princeton University Press.

Bovy, J. (2023). Dynamics and Astrophysics of Galaxies (in Preparation). Princeton University.

Chin, S. A., & Chen, C. R. (2005). Forward Symplectic Integrators for Solving Gravitational Few-Body Problems. Celestial Mechanics and Dynamical Astronomy, 91(3), 301–322. https://doi.org/10.1007/s10569-004-4622-z

Dehnen, W. (2017). Towards time symmetric N-body integration. Monthly Notices of the Royal Astronomical Society, 472(1), 1226–1238. https://doi.org/10.1093/MNRAS/STX1944

Dehnen, W., & Hernandez, D. M. (2017). Symplectic fourth-order maps for the collisional N-body problem. Monthly Notices of the Royal Astronomical Society, 465(1), 1201–1217. https://doi.org/10.1093/mnras/stw2758

Dehnen, W., & Read, J. I. (2011). N-body simulations of gravitational dynamics. European Physical Journal Plus, 126(5), 55. https://doi.org/10.1140/epjp/i2011-11055-3

Hands, T. O., Dehnen, W., Gration, A., Stadel, J., & Moore, B. (2019). The fate of planetesimal discs in young open clusters: implications for 1I/’Oumuamua, the Kuiper belt, the Oort cloud, and more. Monthly Notices of the Royal Astronomical Society, 490(1), 21–36. https://doi.org/10.1093/mnras/stz1069

Hasanuddin. (2020a). GitHub - hasanastro4/simpthon. Https://Github.Com/Hasanastro4/Simpthon.

Hasanuddin. (2022). Simulasi Orbit Planet Eksentrisitas Tinggi dengan Metode Leapfrog. Jurnal Fisika, 12(1), 1–8.

Hasanuddin, H. (2020b). Analisis Galat Energi dan Galat Fase Metode Forward 4th Order Symplectic Chin-Chen untuk Kasus Sistem Osilator Harmonik Sederhana. POSITRON, 10(2), 88–92. https://doi.org/10.26418/positron.v10i2.40023

Heggie, D., & Hut, P. (2003). The Gravitational Million-Body Problem: A Multidisciplinary Approach to Star Cluster Dynamics. In The Gravitational Million-Body Problem: A Multidisciplinary Approach to Star Cluster Dynamics, by Douglas Heggie and Piet Hut. Cambridge University Press, 2003, 372 pp.. Cambridge University Press.

Hernandez, D. M., & Dehnen, W. (2023). Switching integrators reversibly in the astrophysical N-body problem. Monthly Notices of the Royal Astronomical Society, 522(3), 4639–4648. https://doi.org/10.1093/mnras/stad657

Hernquist, L. (1990). An analytical model for spherical galaxies and bulges. Astrophysical Journal, 356, 359–364. https://doi.org/10.1086/168845

Leimkuhler, B., & Reich, S. (2005). Simulating Hamiltonian Dynamics (1st ed.). Cambridge University Press. https://doi.org/10.2277/0521772907

Pham, D., Rein, H., & Spiegel, D. S. (2024). A new timestep criterion for N-body simulations. The Open Journal of Astrophysics, 7, 1. https://doi.org/10.21105/astro.2401.02849

Plummer, H. ~C. (1911). On the problem of distribution in globular star clusters. Monthly Notices of the Royal Astronomical Society, 71, 460–470. https://doi.org/10.1093/mnras/71.5.460

Plummer, H. C. (1915). The Distribution of Stars in Globular Clusters. Monthly Notices of the Royal Astronomical Society, 76(2), 107–121. https://doi.org/10.1093/MNRAS/76.2.107

Zemp, M., Stadel, J., Moore, B., & Carollo, C. ~M. (2007). An optimum time-stepping scheme for N-body simulations. Monthly Notices of the Royal Astronomical Society, 376(1), 273–286. https://doi.org/10.1111/j.1365-2966.2007.11427.x

Published

2025-10-09

How to Cite

Hasanuddin, H., Eusebius, A., & Arman, Y. (2025). Enhancing Stellar Orbit Accuracy through the Radius Power Law Time Step Function Model . JURNAL ILMU FISIKA | UNIVERSITAS ANDALAS, 18(1), 35–44. https://doi.org/10.25077/jif.18.1.35-44.2026

Issue

Vol. 18 No. 1 (2026): March 2026 (Forthcoming Issue)

Section

Research Article

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