Dynamics of Pluto
Abstract
We report the results of our investigation of the orbit of Pluto as obtained from the LONGSTOP 1B numerical integration of the outer planets spanning 100 Myr. We have analyzed all the critical arguments associated with the 3 : 2 resonance in mean motion with Neptune up to degree 2 in the eccentricities and inclinations. The longitude libration with a period of about 19,900 years is confirmed; the librating argument has a very large (84°) and remarkably constant maximum excursion. The 3.78Myr period libration of the argument of pericenter of Pluto is also confirmed. A third resonance belonging to an entirely new class of superresonances is discovered; it results from a 1:1 locking between a circulating and a librating secular argument and has a libration period of 34.5 Myr. The three resonance locking do not undergo any significant changes over the LONGSTOP 1B 100Myr time span or over the 845Myr span of the Digital Orrery numerical integration. Thus, the Orrery finding of a positive Lyapounov exponent for Pluto still calls for a plausible dynamical explanation. The distance between two initially nearby Plutos grows exponentially up to a saturation distance which simply reflects the maximum excursion of the longitude libration. Since chaos is known to be originated by small divisors, we have looked for possible resonances between the frequencies associated with the critical arguments. The only possible small divisor which is not of exceedingly high order is associated with a 3:1 super resonance; in the LONGSTOP 1B solution the corresponding argument circulates with a period of ≃246Myr. Small divisors are very sensitive to the values of the planetary masses, and it turns out that the Orrery value of this small divisor is essentially zero (mostly because of the different value they used for the mass of Neptune). We conjecture that the positive Lyapounov exponent might be due to the Orrery solution being locked in this further resonance. If this is so, then the value of the Lyapounov exponent could be very sensitive to the initial conditions and masses. Moreover, the macroscopic stability of the orbit of Pluto would be explained because highorder resonances are associated with small chaotic regions. A more challenging task is to explain how Pluto was locked in such a complicated system of three resonances.
 Publication:

Icarus
 Pub Date:
 November 1989
 DOI:
 10.1016/00191035(89)900316
 Bibcode:
 1989Icar...82..200M
 Keywords:

 Orbital Resonances (Celestial Mechanics);
 Pluto (Planet);
 Solar Orbits;
 Chaos;
 Liapunov Functions;
 Libration;
 Neptune (Planet);
 Lunar and Planetary Exploration