International Journal of Astrophysics and Space Science

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A New General Perturbation Method for Determining the Long-Term Motion of Comets

Received: 14 October 2022    Accepted: 6 January 2023    Published: 21 February 2023
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Abstract

A number of authors have used special perturbation methods to propagate Comet Halley back before its oldest observation in 239 BC. Unfortunately, results from these studies vary drastically because it is so difficult to accurately model nongraviatational forces acting on comets. In contrast, general perturbation methods do not need to model any forces and can be more accurate over long periods of time. Regrettably, the most recent general perturbation method used for Comet Halley introduced a lot of subjectivity. A new general perturbation method integrating Halley’s Comet back in time is presented here. This new method uses least squares, based solely on math. Therefore, it does not introduce any subjectivity. It also permits statistical analysis of the model’s accuracy. Using this model, Halley’s Comet is propagated back to 2317 BC, and with the derived equations it can easily be integrated back much further in time. Results are very similar to two previous studies by other authors, varying by less than five years when propagated back over 2,200 years. This same new general perturbation method is also applied to Comet Swift-Tuttle. Results with Swift-Tuttle compare reasonably well with the only other known research that integrated this comet back in time.

DOI 10.11648/j.ijass.20231101.11
Published in International Journal of Astrophysics and Space Science (Volume 11, Issue 1, March 2023)
Page(s) 1-6
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Comet, Halley, Swift-Tuttle, Orbit Determination, Perturbations

References
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[2] Halley, E. (1705). A Synopsis of the Astronomy of Comets... Translated from the original, printed at Oxford. John Senex, 22.
[3] Pingré, A. G. (1783- 1974). Cométographie ou traité historique et théorique des comètes.
[4] Biot, E. C. (1843). Conn. des temps pour l'an 1846.
[5] Hind, J. R. (1850). History of comet of Halley. Monthly Notices of the Royal Astronomical Society, 10, 51.
[6] Yeomans, D. K., & Kiang, T. (1981). The long-term motion of comet Halley. Monthly Notices of the Royal Astronomical Society, 197 (3), 633-646.
[7] Vallado, D. A. (2001). Fundamentals of astrodynamics and applications (Vol. 12). Springer Science & Business Media.
[8] Chang, Y. C. (1979). Halley's comet: Tendencies in its orbital evolution and its ancient history. Chinese astronomy, 3 (1), 120-131.
[9] Yeomans, D. K., Chodas, P. W., Sitarski, G., Szutowicz, S., & Królikowska, M. (2004). Cometary orbit determination and nongravitational forces. Comets II, 1, 137-151.
[10] Whipple, F. L. (1950). A comet model. I. The acceleration of Comet Encke. The Astrophysical Journal, 111, 375-394.
[11] Marsden, B. G., Sekanina, Z., & Yeomans, D. K. (1973). Comets and nongravitational forces. V. The Astronomical Journal, 78, 211.
[12] Yeomans, D. K. (1977). Comet Halley-the orbital motion. The Astronomical Journal, 82, 435-440.
[13] Rickman, H., Froeschlé, C., & Gombosi, T. I. (1982). Cometary Exploration. Hungarian Acad. Sci, 109.
[14] Landgraf, W. (1984). On the motion of comet Halley. Werner Landgraf.
[15] Landgraf, W. (1986). On the motion of comet Halley. Astronomy and Astrophysics, 163, 246-260.
[16] Sitarski, G. (1988). On the nongravitational motion of Comet P/Halley. Acta astronomica, 38, 253-268.
[17] Sitarski, G., & Ziolkowski, K. (1986, December). Investigations of the long-term motion of Comet Halley: What is a cause of the discordance of results obtained by different authors?. In ESLAB Symposium on the Exploration of Halley's Comet (Vol. 250).
[18] Sitarski, G., & Ziolkowski, K. (1987). A new approach to investigations of the long-term motion of comet P/Halley. Astronomy and Astrophysics, 187, 896-898.
[19] Ziolkowski K. (1988). Investigations of the Comet Halley's Motion: Three Centuries in a Triumph of Newtonian Mechanics. Issac Newton's" Philosophiae Naturalis Principia Mathematica", 84.
[20] Battin, R. H. (1999). An introduction to the mathematics and methods of astrodynamics. AIAA. 471-472.
[21] Kamieński, M. (1961). Orientational Chronological Table of Modern and Ancient Perihelion Passages of Halley's Comet 1910 AD-9541 BC. Acta Astronomica, 11, 223.
[22] Kamieński, M. (1957). Researches on the Periodicity of Halley's Comet. Part III: Revised List of Ancient Perihelion Passages of the Comet. Acta Astronomica, 7, 111.
[23] Yau, K., Yeomans, D., & Weissman, P. (1994). The past and future motion of Comet P/Swift–Tuttle. Monthly Notices of the Royal Astronomical Society, 266 (2), 305-316.
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    Robert Bayne Brown. (2023). A New General Perturbation Method for Determining the Long-Term Motion of Comets. International Journal of Astrophysics and Space Science, 11(1), 1-6. https://doi.org/10.11648/j.ijass.20231101.11

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    ACS Style

    Robert Bayne Brown. A New General Perturbation Method for Determining the Long-Term Motion of Comets. Int. J. Astrophys. Space Sci. 2023, 11(1), 1-6. doi: 10.11648/j.ijass.20231101.11

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    AMA Style

    Robert Bayne Brown. A New General Perturbation Method for Determining the Long-Term Motion of Comets. Int J Astrophys Space Sci. 2023;11(1):1-6. doi: 10.11648/j.ijass.20231101.11

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  • @article{10.11648/j.ijass.20231101.11,
      author = {Robert Bayne Brown},
      title = {A New General Perturbation Method for Determining the Long-Term Motion of Comets},
      journal = {International Journal of Astrophysics and Space Science},
      volume = {11},
      number = {1},
      pages = {1-6},
      doi = {10.11648/j.ijass.20231101.11},
      url = {https://doi.org/10.11648/j.ijass.20231101.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijass.20231101.11},
      abstract = {A number of authors have used special perturbation methods to propagate Comet Halley back before its oldest observation in 239 BC. Unfortunately, results from these studies vary drastically because it is so difficult to accurately model nongraviatational forces acting on comets. In contrast, general perturbation methods do not need to model any forces and can be more accurate over long periods of time. Regrettably, the most recent general perturbation method used for Comet Halley introduced a lot of subjectivity. A new general perturbation method integrating Halley’s Comet back in time is presented here. This new method uses least squares, based solely on math. Therefore, it does not introduce any subjectivity. It also permits statistical analysis of the model’s accuracy. Using this model, Halley’s Comet is propagated back to 2317 BC, and with the derived equations it can easily be integrated back much further in time. Results are very similar to two previous studies by other authors, varying by less than five years when propagated back over 2,200 years. This same new general perturbation method is also applied to Comet Swift-Tuttle. Results with Swift-Tuttle compare reasonably well with the only other known research that integrated this comet back in time.},
     year = {2023}
    }
    

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    Y1  - 2023/02/21
    PY  - 2023
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    DO  - 10.11648/j.ijass.20231101.11
    T2  - International Journal of Astrophysics and Space Science
    JF  - International Journal of Astrophysics and Space Science
    JO  - International Journal of Astrophysics and Space Science
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    AB  - A number of authors have used special perturbation methods to propagate Comet Halley back before its oldest observation in 239 BC. Unfortunately, results from these studies vary drastically because it is so difficult to accurately model nongraviatational forces acting on comets. In contrast, general perturbation methods do not need to model any forces and can be more accurate over long periods of time. Regrettably, the most recent general perturbation method used for Comet Halley introduced a lot of subjectivity. A new general perturbation method integrating Halley’s Comet back in time is presented here. This new method uses least squares, based solely on math. Therefore, it does not introduce any subjectivity. It also permits statistical analysis of the model’s accuracy. Using this model, Halley’s Comet is propagated back to 2317 BC, and with the derived equations it can easily be integrated back much further in time. Results are very similar to two previous studies by other authors, varying by less than five years when propagated back over 2,200 years. This same new general perturbation method is also applied to Comet Swift-Tuttle. Results with Swift-Tuttle compare reasonably well with the only other known research that integrated this comet back in time.
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Author Information
  • United States Air Force Academy, Department of Astronautics, United States Air Force Academy, Colorado, USA

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