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Year 2022, Volume: 43 Issue: 1, 116 - 122, 30.03.2022

Murat Kaplan

https://doi.org/10.17776/csj.963120

Abstract

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.
  • [11] Muñoz-Gutiérrez M., Reyes-Ruiz M., Pichardo B., Chaotic dynamics of comet 1P/Halley: Lyapunov exponent and survival time expectancy, Monthly Notices of the Royal Astronomical Society, 447 (2015) 3775-3784.
  • [12] Boekholt T. C., Pelupessy F., Heggie D. C., Portegies Zwart S., The origin of chaos in the orbit of comet 1P/Halley, Monthly Notices of the Royal Astronomical Society, 461 (2016) 3576-3584.
  • [13] Pérez-Hernández J. A., Benet L., On the dynamics of comet 1P/Halley: Lyapunov and power spectra, Monthly Notices of the Royal Astronomical Society, 487 (2019) 296-303.
  • [14] Rein H., Liu S.-F., Rebound: An open-source multi-purpose n-body code for collisional dynamics, Astronomy & Astrophysics, 537 (2012) A128.
  • [15] Rein H., Spiegel D. S., IAS15: A fast, adaptive, high-order integrator for gravitational dynamics, accurate to machine precision over a billion orbits, Monthly Notices of the Royal Astronomical Society, 446 (2014) 1424-1437.
  • [16] Giorgini J., Yeomans D.K., Chamberlin A.B., Chodas P.W., Jacobson R.A., Keesey M.S., Lieske J.H., Ostro S.J., Standish E.M., Wimberly R.N., JPL's On-line Solar System Data Service, In Bulletin of the American Astronomical Society, 28 (1996) 1158.
  • [17] Standish E., JPL Planetary and Lunar Ephemerides, de405/le405, interoffice memo. Memorandum 312. F-98-048, Jet Propulsion Laboratory, Pasadena, California (1998).
  • [18] Giorgini J., Yeomans D., On-line system provides accurate ephemeris and related data. NASA TECH BRIEFS, NPO-20416 48 (1999).
  • [19] Bordovitsyna T., Avdyushev V., Chernitsov A., New trends in numerical simulation of the motion of small bodies of the solar system, Celestial Mechanics and Dynamical Astronomy, 80 (2001) 227-247.
  • [20]Avdyushev V., Banschikova M., Regions of possible motions for new jovian satellites, Solar System Research, 41 (2007) 413-419.
  • [21] de la Fuente Marcos C., de la Fuente Marcos R., Asteroid 2015 DB216: A recurring co-orbital companion to Uranus, Monthly Notices of the Royal Astronomical Society, 453 (2015) 1288-1296.
  • [22] Cincotta P. M., Simó C., Simple tools to study global dynamics in non-axisymmetric galactic potentials-I, Astronomy and Astrophysics Supplement Series, 147 (2000) 205-228.
  • [23]Cincotta P. M., Giordano C. M., Simó C., Phase space structure of multi-dimensional systems by means of the mean exponential growth factor of nearby orbits, Physica D: Nonlinear Phenomena, 182 (2003) 151-178.
  • [24]Hinse T. C., Christou A. A., Alvarellos J. L., Goździewski K., Application of the megno technique to the dynamics of jovian irregular satellites, Monthly Notices of the Royal Astronomical Society, 404 (2010) 837-857.
  • [25]Compere A., Lemaître A., Delsate N., Detection by megno of the gravitational resonances between a rotating ellipsoid and a point mass satellite, Celestial Mechanics and Dynamical Astronomy, 112 (2012) 75-98.
  • [26]Compère A., Farrelly D., Lemaitre A., Hestroffer D., A possible mechanism to explain the lack of binary asteroids among the plutinos, Astronomy & Astrophysics, 558 (2013) A4.
  • [27] Goździewski K., Bois E., Maciejewski A., Kiseleva-Eggleton, L., Global dynamics of planetary systems with the megno criterion, Astronomy & Astrophysics, 378 (2001) 569-586.
  • [28]Goździewski K., Stability of the 47 uma planetary system, Astronomy & Astrophysics, 393 (2002) 997-1013.
  • [29]Satyal S., Quarles B., Hinse T., Application of chaos indicators in the study of dynamics of s-type extrasolar planets in stellar binaries, Monthly Notices of the Royal Astronomical Society, 433 (2013) 2215-2225.
  • [30]Maffione N. P., Darriba L. A., Cincotta P. M., Giordano C. M., Chaos detection tools: application to a self-consistent triaxial model, Monthly Notices of the Royal Astronomical Society, 429 (2013) 2700-2717.
  • [31] Maffione N. P., Giordano C. M., Cincotta P. M., Testing a fast dynamical indicator: The MEGNO, International Journal of Non-Linear Mechanics, 46 (2011) 23-34.
  • [32]Hinse T., Michelsen R., Jørgensen U., Goździewski K., Mikkola S., Dynamics and stability of telluric planets within the habitable zone of extrasolar planetary systems-numerical simulations of test particles within the hd 4208 and hd 70642 systems, Astronomy & Astrophysics, 488 (2008) 1133-1147.

On the Lyapunov Time Estimations For Comet 1/P Halley

Year 2022, Volume: 43 Issue: 1, 116 - 122, 30.03.2022

Murat Kaplan

https://doi.org/10.17776/csj.963120

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.

Keywords

N-body Integrations Lyapunov time Cornets

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.
  • [11] Muñoz-Gutiérrez M., Reyes-Ruiz M., Pichardo B., Chaotic dynamics of comet 1P/Halley: Lyapunov exponent and survival time expectancy, Monthly Notices of the Royal Astronomical Society, 447 (2015) 3775-3784.
  • [12] Boekholt T. C., Pelupessy F., Heggie D. C., Portegies Zwart S., The origin of chaos in the orbit of comet 1P/Halley, Monthly Notices of the Royal Astronomical Society, 461 (2016) 3576-3584.
  • [13] Pérez-Hernández J. A., Benet L., On the dynamics of comet 1P/Halley: Lyapunov and power spectra, Monthly Notices of the Royal Astronomical Society, 487 (2019) 296-303.
  • [14] Rein H., Liu S.-F., Rebound: An open-source multi-purpose n-body code for collisional dynamics, Astronomy & Astrophysics, 537 (2012) A128.
  • [15] Rein H., Spiegel D. S., IAS15: A fast, adaptive, high-order integrator for gravitational dynamics, accurate to machine precision over a billion orbits, Monthly Notices of the Royal Astronomical Society, 446 (2014) 1424-1437.
  • [16] Giorgini J., Yeomans D.K., Chamberlin A.B., Chodas P.W., Jacobson R.A., Keesey M.S., Lieske J.H., Ostro S.J., Standish E.M., Wimberly R.N., JPL's On-line Solar System Data Service, In Bulletin of the American Astronomical Society, 28 (1996) 1158.
  • [17] Standish E., JPL Planetary and Lunar Ephemerides, de405/le405, interoffice memo. Memorandum 312. F-98-048, Jet Propulsion Laboratory, Pasadena, California (1998).
  • [18] Giorgini J., Yeomans D., On-line system provides accurate ephemeris and related data. NASA TECH BRIEFS, NPO-20416 48 (1999).
  • [19] Bordovitsyna T., Avdyushev V., Chernitsov A., New trends in numerical simulation of the motion of small bodies of the solar system, Celestial Mechanics and Dynamical Astronomy, 80 (2001) 227-247.
  • [20]Avdyushev V., Banschikova M., Regions of possible motions for new jovian satellites, Solar System Research, 41 (2007) 413-419.
  • [21] de la Fuente Marcos C., de la Fuente Marcos R., Asteroid 2015 DB216: A recurring co-orbital companion to Uranus, Monthly Notices of the Royal Astronomical Society, 453 (2015) 1288-1296.
  • [22] Cincotta P. M., Simó C., Simple tools to study global dynamics in non-axisymmetric galactic potentials-I, Astronomy and Astrophysics Supplement Series, 147 (2000) 205-228.
  • [23]Cincotta P. M., Giordano C. M., Simó C., Phase space structure of multi-dimensional systems by means of the mean exponential growth factor of nearby orbits, Physica D: Nonlinear Phenomena, 182 (2003) 151-178.
  • [24]Hinse T. C., Christou A. A., Alvarellos J. L., Goździewski K., Application of the megno technique to the dynamics of jovian irregular satellites, Monthly Notices of the Royal Astronomical Society, 404 (2010) 837-857.
  • [25]Compere A., Lemaître A., Delsate N., Detection by megno of the gravitational resonances between a rotating ellipsoid and a point mass satellite, Celestial Mechanics and Dynamical Astronomy, 112 (2012) 75-98.
  • [26]Compère A., Farrelly D., Lemaitre A., Hestroffer D., A possible mechanism to explain the lack of binary asteroids among the plutinos, Astronomy & Astrophysics, 558 (2013) A4.
  • [27] Goździewski K., Bois E., Maciejewski A., Kiseleva-Eggleton, L., Global dynamics of planetary systems with the megno criterion, Astronomy & Astrophysics, 378 (2001) 569-586.
  • [28]Goździewski K., Stability of the 47 uma planetary system, Astronomy & Astrophysics, 393 (2002) 997-1013.
  • [29]Satyal S., Quarles B., Hinse T., Application of chaos indicators in the study of dynamics of s-type extrasolar planets in stellar binaries, Monthly Notices of the Royal Astronomical Society, 433 (2013) 2215-2225.
  • [30]Maffione N. P., Darriba L. A., Cincotta P. M., Giordano C. M., Chaos detection tools: application to a self-consistent triaxial model, Monthly Notices of the Royal Astronomical Society, 429 (2013) 2700-2717.
  • [31] Maffione N. P., Giordano C. M., Cincotta P. M., Testing a fast dynamical indicator: The MEGNO, International Journal of Non-Linear Mechanics, 46 (2011) 23-34.
  • [32]Hinse T., Michelsen R., Jørgensen U., Goździewski K., Mikkola S., Dynamics and stability of telluric planets within the habitable zone of extrasolar planetary systems-numerical simulations of test particles within the hd 4208 and hd 70642 systems, Astronomy & Astrophysics, 488 (2008) 1133-1147.
There are 32 citations in total.

Details

Primary Language English
Subjects Classical Physics (Other)
Journal Section Natural Sciences
Authors

Murat Kaplan 0000-0003-2595-5463

Publication Date March 30, 2022
Submission Date July 6, 2021
Acceptance Date December 28, 2021
Published in Issue Year 2022Volume: 43 Issue: 1

Cite

APA Kaplan, M. (2022). On the Lyapunov Time Estimations For Comet 1/P Halley. Cumhuriyet Science Journal, 43(1), 116-122. https://doi.org/10.17776/csj.963120
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