对火星轨道变化问题的最后解释

he innermost planet may be nearest to instability. This result appears to be in some agreement with Laskar's (1994， 1996) expectations that large and irregular variations appear in the eccentricities and inclinations of Mercury on a time-scale of several 109 yr. However， the effect of the possible instability of the orbit of Mercury may not fatally affect the global stability of the whole planetary system owing to the small mass of Mercury. We will mention briefly the long-term orbital evolution of Mercury later in Section 4 using low-pass filtered orbital elements.

The orbital motion of the outer five planets seems rigorously stable and quite regular over this time-span (see also Section 5).

3.2 Time–frequency maps

Although the planetary motion exhibits very long-term stability defined as the non-existence of close encounter events， the chaotic nature of planetary dynamics can change the oscillatory period and amplitude of planetary orbital motion gradually over such long time-spans. Even such slight fluctuations of orbital variation in the frequency domain， particularly in the case of Earth， can potentially have a significant effect on its surface climate system through solar insolation variation (cf. Berger 1988).

To give an overview of the long-term change in periodicity in planetary orbital motion， we performed many fast Fourier transformations (FFTs) along the time axis， and superposed the resulting periodgrams to draw two-dimensional time–frequency maps. The specific approach to drawing these time–frequency maps in this paper is very simple – much simpler than the wavelet analysis or Laskar's (1990， 1993) frequency analysis.

Divide the low-pass filtered orbital data into many fragments of the same length. The length of each data segment should be a multiple of 2 in order to apply the FFT.

Each fragment of the data has a large overlapping part: for example， when the ith data begins from t=ti and ends at t=ti+T， the next data segment ranges from ti+δT≤ti+