The theory of the preceding chapter has shown how, in agreement with general ideas already arrived at by astronomers, comets consist of very large numbers of widely separated particles. With this picture of the internal structure of a comet, we come now to a simple consequence of the theory that throws considerable light on the whole question of the formation of tails. The difficulty has always been to understand why comets should more or less suddenly begin to emit material for tail formation and how they are able to go on repeating the cycle at each perihelion return more or less indefinitely.

It has been seen that as a result of gravitational forces within the accretion stream the cometary segments form initially at great distance from the sun and so give rise in the first place to long-period comets. Also, since by equation (19) of Chapter III the mass md depends on, R3/2 comets of greatest mass will tend to form at the greatest distance. Now as such a comet falls towards the sun its self-gravitation will remain unchanged, at any rate in order of magnitude, whereas the differential force on it due to the sun will increase like R-3. Since R decreases from several hundred astronomical units down to a few solar radii as the comet moves inwards, the effect of the sun's action increases by a very large factor. For example, we might have initially R = 500 a.u. = 105 solar radii, and if the comet eventually passes within about 2 solar radii of the sun's centre, the differential force would be increased as compared with the comet's internal self-gravitation by a factor of about 1014. This completely reverses the relative importance of the two effects; at great distance the internal gravitation predominates, though probably only by a moderate factor, whereas when close to the sun the internal gravitation is utterly negligible.

The same result holds good even though the comet is not a sun-grazer (i.e. q ∼ radius of the sun), and the point is of such importance to our argument that it may be worth while examining it more generally.