Free precession of the comet Halley nucleus

Images^1-3 of the comet Halley nucleus by the Vega and Giotto spacecraft and a compilation⁴ of recurring events show a 'rotation' period of roughly 2.2 days. In contrast, molecular emission intensities⁵ (C₂ and CN) in the inner coma exhibit 7.4-day periodic variations. In this report the comet Halley nucleus is modelled dynamically as a rigid homogeneous ellipsoid with three unequal principal axes in torque-free rotation about its centre of mass. Two qualitatively-distinct, free-precessional modes are found, each exhibiting both 2.2-day and 7.4-day periodicities. As viewed from the nucleus, the two modes are distinguished by the closed path (called a polhode) that the end of the angular velocity vector traces with a period of 7.4 days (see Fig. 1). The long-axis mode has a polhode that encloses only the long principal axis of the nucleus. It reduces to a motion proposed by Sekanina^6,7 when the minor axes are equal. However, because the polhode encloses the long axis in a long-axis mode, the resulting motion with a 7.4-day period around that axis conflicts⁸ with the Vega and Giotto images of the nucleus. The short-axis mode occurs when the minor axes are unequal and the polhode encloses only the short principal axis of the nucleus. The resulting motion is around the short axis and does not conflict with the spacecraft images.