On the Lyapunov Time Estimations For Comet 1/P Halley
Abstract
In three consecutive articles published in recent years, quite different estimates were made for the Lyapunov time of comet 1/P Halley, whose orbit is known to have high precision. In this work, we examined the Lyapunov time of the comet 1/P Halley using the MEGNO method and compared our results with previous studies. To investigate the effects of numerical overflows on the results that may have occurred during the calculations, we conducted tests with and without the renormalization procedure. We used various renormalization intervals to see their possible effects on the results and to avoid improper ones. We reached the maximum Lyapunov exponents at renormalization times for 2250 yr, 2265 yr, and 3000 yr. In both cases where renormalization is used and not used, the Lyapunov time is calculated as 119 yr and 190 yr, respectively. Besides, we performed orbital integrations for ∓ 10 kyr for comet 1/P Halley with the clone orbits produced by the MCCM method and compared the standard errors of the means of the orbital parameters with the Lyapunov times. We conclude that calculated different Lyapunov times correspond to different levels of the standard errors of the means.
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References
- [1] Hughes D. W., Green, D. W., Halley's first name: Edmond or Edmund, International Comet Quarterly 29 (2007) 7-14.
- [2] Yeomans D. K., Comet Halley-The orbital motion, The Astronomical Journal, 82 (1977) 435-440.
- [3] Yeomans D. K., Kiang T., The long-term motion of comet Halley, Monthly Notices of the Royal Astronomical Society, 197 (1981) 633-646.
- [4] Stelzried C., Efron L., Ellis J., Halley comet missions, Nature, 321 (1986) 240-242.
- [5] Giorgini J., Chodas P., Yeomans D., Orbit uncertainty and close-approach analysis capabilities of the horizons on-line ephemeris system, In Bulletin of the American Astronomical Society, 33 (2001) 1562.
- [6] Giorgini J., New challenges for reference systems and numerical standards in astronomy, Proceedings of the Journées 2010 "Systèmes de Référence Spatio-Temporels", N. Capitaine (ed.), Observatoire de Paris, 2011..
- [7] Giorgini J., IAU General Assembly, Meeting# 29, 22 (2015).
- [8] Chirikov R., Vecheslavov V., Chaotic dynamics of comet Halley, Astronomy and Astrophysics, 221 (1989) 146-154.
- [9] Bailey M., Emel'Yanenko V., Dynamical evolution of halley-type comets, Monthly Notices of the Royal Astronomical Society, 278 (1996) 1087-1110.
- [10] Shevchenko I. I., On the lyapunov exponents of the asteroidal motion subject to resonances and encounters, Proceedings of the International Astronomical Union, 2 (2006) 15-30.