Orbit determination and evolution of comet C/1995 O1 (Hale-Bopp)

The situation leading to the determination of the Hale-Bopp orbit is discus sed, largely in terms of a procedure that generates two sequences of parabo lic orbits. The comet is also considered in relation to the problem of the possibility of impact on the earth. The placement of its orbital nodes near the orbits of the earth and Jupiter is clearly an intriguing feature. The role of the prediscovery observation in 1993 is described, as it appeared b oth as a boon and a burden. Although evidence has been put forward that the Hale-Bopp nucleus is unusually large, it seems likely that nongravitationa l forces are noticeably affecting the comet's motion. While discussion of t he comet's future long-term motion may be amenable to the usual treatment a s a problem of diffusion, it is not entirely improbable that the present si tuation arose from a recent dramatic approach to Jupiter. It is shown that such a Jupiter encounter in June -2215 is not inconsistent with the non-exi stence of records at the comet's last perihelion passage, which could then have been the first to occur as close as 0.9 AU to the sun. Of course, the Jupiter encounter might also have given rise to the possible large satellit e to Hale-Bopp discussed by Sekanina.