Intrinsic distributions of cometary perihelia and magnitudes

Distributions of perihelia q and of absolute magnitude H0 are formed for a group of 256 long-period comets. These are considered to be representative of a much larger group of comets, many of which were not discovered because of unfavorable position or faintness. From the statistics of comet discovery conditions a discovery probability function is derived, which depends on q and H0 but is otherwise averaged over orbital elements. Using this it is possible to unfold the measured distributions and obtain the underlying intrinsic distributions. Thus the intrinsic distribution in q is found to increase from a relative value of 0.4 for to unity at .0. At large q values the curve is less certain: The data are fitted almost equally well by either a constant distribution or by one with a slow linear rise. The intrinsic distribution in H5 almost quadruples for each unit increase in H0 when H0 is between the second and fifth magnitude, but increases much less rapidly for fainter comets. Using these intrinsic distributions and allowing for selection effects, calculations are made which explain the Holetschek effect and an observed nonuniform distribution with respect to argument of perihelion w. It is shown, further, that observed distributions of comets with respect to longi- tude of ascending node and with respect to inclination i are not appreciably affected by observational selection.