The large asteroid/comet 5145 Pholus in the outer Solar system has an orbit which currently crosses Saturn, Uranus and Neptune. We numerically integrate 27 test particles with initial orbits similar to but distinct from the present orbit of Pholus forward over 800 000 yr. Many particles remain in the outer Solar system with slow orbital evolution, and another group is accelerated into long-period orbits with perihelia still in the outer planetary region, exceedingly slow evolution then following. However, a significant fraction (5 out of 27) attain orbits crossing Jupiter's path, or at least approaching that planet (i.e. q < 6 au), and much swifter evolution then occurs. Time-scales for substantial alterations are of the order of 10(6) yr if long-period orbits are reached, 10(5) yr if the objects remain in intermediate-period orbits in the outer Solar system, and less than 10(4) yr once Jupiter-approaching orbits are entered. Four of the particles are eventually ejected from the Solar system: two by Jupiter, and two by Saturn before they ever become Jupiter-approaching. Two of the particles enter Mars- and even Earth-crossing orbits for a few tens of thousands of years, and our results imply a 5-10 per cent chance that an object with an orbit like Pholus may attain an Earth-approaching orbit within 1 Myr. It is well documented that comets often fragment, due to thermal stresses or other factors, when on orbits bringing them that close to the Sun. Thus, if Pholus is basically cometary in nature, as expected, then there is a significant probability that it will eventually decay in such a fragmentation episode, leaving many macroscopic bodies on Earth-crossing orbits. Assuming that Pholus is just one of the more massive bodies in a large population of planet-crossing objects in the outer Solar system, this implies that such orbital and physical evolution on the part of these bodies is likely to be a major source of Apollo-type asteroids.
