The Past Orbit of Halley's Comet

Abstract

Perturbations of the orbit of Halley's Comet over the last 28 revolutions are calculated and a parallel re-examination of Chinese records on this object made. For the calculation, the method used by Cowell and Crommelin in 1907/8 is refined in several respects. Perturbing forces in three dimensions are considered and the average perturbation in Ω is found to be very nearly + 1°·0 per revolution, much larger than the value of +0°·15 adopted previously. The contributions by Mercury and Mars are found to be by no means negligible. The perturbations by Jupiter are calculated to the second order with respect to its mass. Secular changes in the planetary orbits, and the more important periodic ones in those of Jupiter and Saturn are taken into account. The calculated perturbations are given in Table A, and the orbital elements in Table V. The time of perihelion passage, T, at each return is generally determined from observations; this redundancy of data not only provides a gauge as to how well the various returns are linked by the calculation, but also leads to an assessment of the effect on the mean motion of non-gravitational forces over the last II periods. This effect amounts to an average lengthening of the period by 4·1 days after each return. All available records, mainly Chinese ones, are re-examined with the aim of improving on the catalogue values of T. The results are in Table IV. A synopsis of traditional Chinese astronomy is given in order that Chinese records may be discussed intelligibly. Some new identifications of Chinese stars are made, and the conversion of chĭ (‘foot’) to degrees is found to be |$1\,ch\breve{i}\,=\,{1}^{^{\circ} }\cdot50\pm{0}^{^{\circ} }\cdot24$| A set of remarkably precise data for the Return of + 837 are made use of for the first time, and the three recorded novae in the same year are shown to be not connected with Halley's Comet. Agreements between recorded positions and calculated ephemerides in different returns confirm that the so-called lunar mansions are nothing less than well-defined ranges in right ascension, and that, in particular, this coordinate was observed with an accuracy of 0°·5 in the + 9th century in China. In several instances the recorded position should be understood to refer to the tail of the comet. The apparent paths during Returns of the years + 1301, + 1222, + 1066, + 837, + 295, + 218 and – 11 are shown in Fig. 2 over a background of Chinese constellations.