Where is the centre of a comet?

In discussing the orbits of comets it has been assumed more or less of necessity that a comet may be regarded as a simple gravitating particle in order that its motion relative to the sun may be describable by means of a point tracing out a curve. The assumption must contain some element of truth because of the degree of agreement with dynamical theory exhibited by the observed paths, but even so when we come to consider the internal structure of comets this assumption appears to be far from closely satisfied. If for the moment we pause to consider the motion round the sun of a large planet like Jupiter, it can be rigorously demonstrated as a matter of dynamics that there exists a certain point of the body—its centre of mass—whose motion round the sun is the same as if all the mass of the planet were concentrated at this point and all the external forces acted on it, exactly as if it were a particle of negligible size. The idea of centre of mass produces a remarkable simplification where the motion of the planet is concerned because Jupiter is effectively a rigid body despite its diameter of nearly 140,000 miles. The centre of mass remains fixed in it because it is rigid, and so the motion of this point adequately represents the general motion about the sun of the planet as a whole. (The rotatory motion of the planet about its centre is a secondary problem.) But where a comet is concerned there is no prior reason whatever for supposing that the line from the observer through the brightest point, or through the central point of the visible area, which varies with the means of observation, passes through the centre of mass of the comet as a whole. As will be explained later, the outline boundary of a comet is not always well defined, and the comet's position at any time is usually settled by the simple expedient of guiding on its brightest part, which does in fact sometimes appear as a definite point within the head.