A Comparative Study of Resonances in the Dynamics of the Mimas-Tethys System
- 1 Department of Mathematics, Chatra College, Chatra, India
- 2 Department of Mathematics, Vinoba Bhave University, Hazaribag, India
- 3 Department of Mathematics, K. B. Women’s College, Hazaribag, India
Abstract
The probability of capture of Mimas-Tethys in 2:4 resonance was found to be 0.76 by Champenois when they considered the orbit of Tethys to be elliptical (that is eccentricity of Tethys to be 0.0008) and chaos was taken into account. It means probability of capture in i<sup>2</sup><sub style="margin-left:-6px;">1</sub> or i<sup>2</sup><sub style="margin-left:-6px;">3</sub> resonance is 0.24 ( i.e. probability of non capture in i 1 i 3 resonance). Here we have done the comparative study of the dynamics of Mimas-Tethys system at i 1 i 3 , i 1 i 3 e 3 , i<sup>2</sup><sub style="margin-left:-6px;">1</sub> e 3 , i<sup>2</sup><sub style="margin-left:-6px;">3</sub> e 3 and i<sup>2</sup><sub style="margin-left:-6px;">1</sub> , i 1 i 3 e 3 , i<sup>2</sup><sub style="margin-left:-6px;">1</sub> e 3 , i<sup>2</sup><sub style="margin-left:-6px;">3</sub> e 3 resonances along with secular resonance of Saturn’s six inner satellites and Saturn’s oblateness. We have drawn Poincare surface of sections and Time series graphs to compare their effect.
- Allan, R.R. (1969) Evolution of Mimas-Tethys Commensurabilities. Astronomical Journal, 74, 997-506. https://doi.org/10.1086/110827
- Sinclair, A.T. (1972) On the Origin of the Commensurabilities amongst the Satellites of Saturn. Monthly Notices of the Royal Astronomical Society, 160, 169-187. https://doi.org/10.1093/mnras/160.2.169
- Vienne, A. and Duriez, L. (1992) A General Theory of Motion for the Eight Major Satellites of Saturn. III. Long-Period Perturbations. Astronomy and Astrophysics, 257, 331-352.
- Laskar, J. (1990) The Chaotic Motion of the Solar System: A Numerical Estimate of the Size of the Chaotic Zones. Icarus, 88, 266-291.
- Vienne, A. and Duriez, L. (1995) TASS1.6: Ephimerides of the Major Saturnian Satellites. Astronomy and Astrophysics, 297, 588-605.
- Champenois, S. and Vienne, A. (1999) The Role of Secondary Resonances in the Evolution of the Mimas-Tethys System. Icarus, 140, 106-121.
- Champenois, S. and Vienne, A. (1999) Chaos and Secondary Resonances in the Mi-mas-Tethys System. Celestial Mechanics and Dynamical Astronomy, 74, 111-146. https://doi.org/10.1023/A:1008314007365
- Greenberg, R. (1973) The Inclination-Type Resonance of Mimas and Tethys. Monthly Notices of the Royal Astronomical Society, 165, 305-311. https://doi.org/10.1093/mnras/165.3.305
- Jha, S. and Agrawal, S.K. (2014) Effect of Second and Third Order Resonances on Mimas-Tethys System. IJAMM, 3, 9-21.
- Jha, S. and Agrawal, S.K. (2014) Chaotic Dynamics of Mimas-Tethys System Due to Secular Resonance of Enceladus. GJDSA, 4, 1-11.
- Jha, G.K. and Jha, S. (2015) Comparative Study of Secular Resonance Effect of Ence-ladus and Dione on Mimas-Tethys System. IJAMM, 4, 27-31.
- Jha, G.K. and Jha, S. (2016) Combined Effect of Oblateness of Saturn and Secular Resonance of Rhea on Mimas-Tethys System. M0, 3. (Accepted)
- Jha, G.K. and Jha, S. (2016) Role of Saturn’s Oblateness and Secular Resonance of Va-rious Combination of Inner Satellites with Titan on Mimas-Tethys System. IJST. (Accepted)
- Jha, G.K. and Jha, S. (2017) Comparative Study of the Dynamics of Mimas-Tethys System at Different Resonances. International Journal of Advance Astronomy, 5, 44-49. (Accepted) https://doi.org/10.14419/ijaa.v5i1.7095
- Thomas, P.C., et al. (2007) Shapes of the Saturninan Icy Satellites and Their Significance. Icarus, 190, 573-584.