The Complex Spin State of 103P-Hartley 2: Kinematics and Orientation in Space
We derive the spin state of the nucleus of Comet 103P/Hartley 2, its orientation in space, and its short-term temporal evolution from a mixture of observations taken from the DIXI (Deep Impact Extended Investigation) spacecraft and radar observations. The nucleus is found to spin in an excited long-axis mode (LAM) with its rotational angular momentum per unit mass, M, and rotational energy per unit mass, E, slowly decreasing while the degree of excitation in the spin increases through perihelion passage. M is directed toward (RA, Dec; J2000) = 8+/-+/- 4 deg., 54 +/- 1 deg. (obliquity = 48 +/- 1 deg.). This direction is likely changing, but the change is probably <6 deg. on the sky over the approx. 81.6 days of the DIXI encounter. The magnitudes of M and E at closest approach (JD 2455505.0831866 2011-11-04 13:59:47.310) are 30.0 +/- 0.2 sq. m/s and (1.56 +/- 0.02) X 10(exp -3) sq. m /sq. s respectively. The period of rotation about the instantaneous spin vector, which points in the direction (RA, Dec; J2000) = 300 +/- 3.2deg., 67 +/- 1.3 deg. at the time of closest approach, was 14.1 +/- 0.3 h. The instantaneous spin vector circulates around M, inclined at an average angle of 33.2 +/- 1.3 deg. with an average period of 18.40 +/- 0.13 h at the time of closest approach. The period of roll around the principal axis of minimum inertia (''long'' axis) at that time is 26.72 +/- 0.06 h. The long axis is inclined to M by approx. 81.2 +/- 0.6 deg. on average, slowly decreasing through encounter. We infer that there is a periodic nodding motion of the long axis with half the roll period, i.e., 13.36+/- 0.03 h, with amplitude of 1 again decreasing through encounter. The periodic variability in the circulation and roll rates during a cycle was at the 2% and 10-14% level respectively. During the encounter there was a secular lengthening of the circulation period of the long axis by 1.3 +/- 0.2 min/d, in agreement with ground-based estimates, while the period of roll around the long axis changed by approx. -4.4 min/d at perihelion. M decreased at a rate of 0.038 (sq m/s) per day in a roughly linear fashion. Assuming a bulk density between 230-300 kg/m3 and a total volume for the nucleus of 8.09 X 10(exp 8) cubic m, the net torque acting on the nucleus was in the range 0.8-1.1 X 10(exp 5) kg m(exp 2) /s(exp 2). In order to bring the spacecraft photometric and imaging data into alignment on the direction of M, the directions of the intermediate and short principal axes of inertia had to be adjusted by 33 deg (on the sky) from the values indicated by the shape model with an assumed homogeneous interior. The adjusted direction of the intermediate axis is RA, Dec = 302 deg., -16.5 deg.. The morning and evening terminators in the images are identified, and the variation of the insolation at three regions on the nucleus associated with active areas calculated. The plume of water vapor observed in the inner coma is found to be directed close to the direction of local gravity over the sub-solar region for a range of reasonable bulk densities. The plume does not follow the projected normal to the surface at the sub-solar point.