对火星轨道变化问题的最后解释

anetary orbital energy (which is directly related to the semimajor axis a) might be much less affected by perturbing planets than is the angular momentum exchange (which relates to e). Hence， the eccentricities of Venus and Earth can be disturbed easily by Jupiter and Saturn， which results in a positive correlation in the angular momentum exchange. On the other hand， the semimajor axes of Venus and Earth are less likely to be disturbed by the jovian planets. Thus the energy exchange may be limited only within the Venus–Earth pair， which results in a negative correlation in the exchange of orbital energy in the pair.

As for the outer jovian planetary subsystem， Jupiter–Saturn and Uranus–Neptune seem to make dynamical pairs. However， the strength of their coupling is not as strong compared with that of the Venus–Earth pair.

5 ± 5 × 1010-yr integrations of outer planetary orbits

Since the jovian planetary masses are much larger than the terrestrial planetary masses， we treat the jovian planetary system as an independent planetary system in terms of the study of its dynamical stability. Hence， we added a couple of trial integrations that span ± 5 × 1010 yr， including only the outer five planets (the four jovian planets plus Pluto). The results exhibit the rigorous stability of the outer planetary system over this long time-span. Orbital configurations (Fig. 12)， and variation of eccentricities and inclinations (Fig. 13) show this very long-term stability of the outer five planets in both the time and the frequency domains. Although we do not show maps here， the typical frequency of the orbital oscillation of Pluto and the other outer planets is almost constant during these very long-term integration periods， which is demonstrated in the time–frequency maps on our webpage.

In these two integrations， the relative numerical error in the total energy was ～10?6 and that of the total angular momentum was ～10?10.

5.1 Resonances in the Neptune–Pluto system

Kinoshita &