To investigate the question of how neutral particles could travel from comet Halley to the ICE spacecraft, Kepler orbits are calculated that connect the positions of Halley and ICE, in space and time. From these orbits, the initial speed of the particle, relative to Halley, can be found as a function of departure time. It is found that there is a minimum relative speed of 7.5 km s-1, for particles leaving the comet on February 6, 1986, three days before perihelion. Particles emitted before this date actually require a higher relative speed. Lower speeds of about 5 km s-1 are again possible for departure dates in November, 1985, when the molecular production rate is considerably reduced. ¿American Geophysical Union 1987