The complex spin state of 103P/Hartley 2: Kinematics and orientation in space

Abstract

We derive the spin state of the nucleus of Comet 103P/Hartley 2, its orientation in space, and its shortterm 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°, 54 ± 1°(obliquity = 48 ± 1°). This direction is likely changing, but the change is probably <6°on the sky over the $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 m 2 /s and (1.56 ± 0.02) Â 10 À3 m 2 /s 2 respectively. The period of rotation about the instantaneous spin vector, which points in the direction (RA, Dec; J2000) = 300 ± 3.2°, 67 ± 1.3°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°, 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 $81.2 ± 0.6°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 $À4.4 min/d at perihelion. M decreased at a rate of À0.038 (m 2 /s) per day in a roughly linear fashion. Assuming a bulk density between 230-300 kg/m 3 and a total volume for the nucleus of 8.09 Â 10 8 m 3 , the net torque acting on the nucleus was in the range 0.8-1.1 Â 10 5 kg m 2 /s 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°(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°, À16.5°. 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.

Jet Morphology and Coma Analysis of Comet 103P/Hartley 2

“…Belton et al (2012) performed extensive studies on these images to precisely determine rotational modes and periods. A total of 24,799 nucleus images were used as data in their analysis.…”

“…Additionally, they examined period ratios to determine that the nucleus rotates in a long-axis mode (LAM). Lastly, they calculated the direction of the rotational angular momentum vector, M. The findings from Belton et al (2012) are a critical component in this research since they provide all the necessary information to understand the dynamics of the nucleus rotation. The values and spin characteristics listed in the following sections are directly from their publication.…”

“…The periods of rotation for each Euler angle were reported by Belton et al (2012) at the time of closest approach of the EPOXI spacecraft to the Hartley 2 nucleus. Closest approach occurred on 4 November 2010 at 13:59:47 UT, which is designated t = 0 for all calculations hereafter.…”

“…Angle η0 acts as the initial phase of nutation at the time of closest approach. Belton et al (2012) determined that θ(0) = 81.60°, which can be used with θAvg to compute this initial phase. Unfortunately, the derived imprecision for θAvg means η0 ≈ sin -1 (−0.4 ± 0.6), which yields a wide range of possibilities for η0.…”

“…The rates of period change dP/dt were converted to dimensionless quantities. The uncertainty for dPψ/dt was not listed by Belton et al (2012), so it was approximated to about ± 0.5 min/day and converted. Angles ϕ0 and ψ0 were arbitrarily set to zero.…”