Roche’s fundamental idea can be extended in many directions and admits of varied applications. There must, for instance, be a danger-zone, marked off by a Roche’s limit, surrounding the sun. The distance of this danger-zone from the sun depends on the density of the body for which it is dangerous (p. 249). For a body having the low density of a comet the distance will be very great indeed. Whatever the distances of their danger-zones, comets must occasionally pass through them and become broken up in so doing. Two comets, Biela’s comet (1846) and Taylor’s comet (1916), were observed actually to break in two while at about the earth’s distance from the sun, and in 1882 a comet was seen to divide into four parts. Biela’s comet returned in due course (1852) in the form of two distinct comets a million and a half miles apart, since which time neither part of the original comet has been seen again. The orbit of this comet was identical with that of the Andromedid meteors, which make a display of shooting-stars in the earth’s atmosphere on favourable 27ths of November, so that it is likely that these shooting-stars are the broken remains of Biela’s comet. Other conspicuous swarms of shooting-stars also move in the tracks of comets—the Leonids which used to make a magnificent show every 33 years move in the track of Comet 1866 I, the Perseids in the track of another Comet (1862 II), and the Aquarids in the track of Halley’s famous comet. In each case, there can be little doubt that the shooting-stars are scattered fragments of the comets. Besides this there are several families of comets whose members follow one another round and round in the same orbit, as though they had originally formed a single mass.

In the same way a Roche’s limit must surround the planet Jupiter, so that comets and other bodies may be broken up through getting inside the danger-zone marked off by this limit. Jupiter’s innermost satellite is already perilously near it. But the greatest interest of this particular danger-zone is that it probably accounts for the existence of the asteroids. In the early days of the solar system, when the orbits of the planets were less nearly circular than they now are, a primaeval planet between Mars and Jupiter may well have described an orbit so elongated as to take it repeatedly within the danger-zone of Jupiter. If so, we need look no further for the origin of the asteroids. It is significant that the average orbit of all the asteroids agrees almost exactly with that of the planet which Bode’s law (p. 19) would require to exist between Mars and Jupiter.