Are the analytical proper elements of asteroids still needed?

The asteroid proper elements computed from an analytical secular perturbation theory are thought to be of inferior accuracy with respect to the synthetic proper elements computed by means of a purely numerical procedure. To verify this, we carried out two different tests: one based on a plain comparison of the analytical and synthetic proper elements to check whether they differ by more than the corresponding errors of synthetic elements, and the other consisting in direct determination of instabilities of analytical elements themselves. In both tests, we used much larger samples than in the previous attempts. The results clearly confirm the superior quality of synthetic values. We also present a new synthetic method to determine the locations of secular resonances, based on a polynomial fit of the values of asteroid secular rates g, s, and subsequent computation of resonance frequencies on a grid in the phase space of proper elements. Plots showing the contour lines corresponding to selected small values of resonant divisors serve to visualize the resonance locations. We analyzed in detail the accuracy of the fit and of the secular resonance locations, comparing them with the previously available positions determined by means of the analytical theory; we found that the two methods give qualitatively the same results, but that the results of the new synthetic method appear to be more reliable. In view of the above results, we conclude that the regular maintenance of the catalog of analytical proper elements can be discontinued in the future.