Possible collisions of P/Halley and P/Machholz 1 with Jupiter and the terrestrial planets

Abstract

The perturbed motion of comet Halley and comet Machholz 1 1986 VIII was investigated within a time interval of about 20 millennia. The minimal distance of 0.043 AU between P/Halley and Venus may occur on April 4, 4868 AD. The distance of 0.036 AU between P/Halley and Jupiter will take place on April 1, 6616 AD. The orbit of P/Machholz 1 crosses the orbits of Mercury and Venus eight times, that of the Earth six or eight times, and the orbit of Mars four times per a period of advance of the argument of perihelion. A distance of about 0.06 AU between P/Machholz 1 and the Earth may take place in August 2576 AD and 5751 AD and in February 4770 AD. The minimal comet-Earth distance of 0.035 AU occurs on September 14, 5971 AD. The closest encounter between P/Machholz 1 and Jupiter at the distance of 0.098 AU may be in May 4499 AD. These results may be considered as a forecast of possible collisions.