The Outer Solar System for 210 Million Years

We used a special purpose computer to integrate the orbits of the outer five planets for 100 Myr into the future and 100 Myr into the past. The strongest features in the Fourier transforms of the orbital elements of the Jovian planets can be indentified with the frequencies predicted by linear secular theory. Many of the weaker features in the Fourier spectra are identified as linear combinations of the basic frequencies. We note serious differences between our measurements and the predictions of Bretagnon (1974). The amplitude of the 3.796 Myr period libration of Pluto's longitude of perihelion is modulated with a period of 34 Myr. Very long periods, on the order of 137 million years, are also seen.