THE SPIN STATE OF 9P/TEMPEL 1. M. J. S. Belton1, P. C. Thomas2, B. Carcich2, C. J. Crockett3 and the Deep Impact Science Team. 1Belton Space Exploration Initiatives, LLC, michaelbelton@beltonspace.com, 430 S. Randolph Way, Tucson AZ 85716; 2Center for Radiophysics and Space Research, Space Sciences Building, Cornell University, Ithaca, NY 14853. 3Dept. of Astronomy, Univ. of Maryland, College park, MD.

Introduction: Efforts to determine an accurate spin state for 9P/Tempel in connection with the Deep Impact Mission prior to its launch in January, 2005 began in 1997 and involved a wide variety of observations from the ground and from the Hubble and Spitzer Space telescopes [1]. The results yielded a preliminary estimate of the diurnal period , two possible pole positions, and no evidence for excited spin [2]. These results served their purpose in support of the mission but 63 days of well sampled visible, unresolved, photometry on approach to encounter plus resolved imaging of the nucleus’ shape and rotation now lead to a precise estimate of the spin state. Establishment of a high precision spin ephemeris is of considerable interest for this comet: a) in order to tie many remote observations that are well separated in time to specific locations on the surface, and b) to predict the space orientation of the artificial Deep Impact crater and other significant features on the surface when planning future attempts to return to the comet. Approach photometry: Two sources of clear filter aperture photometry (navigation and science) taken with the MRI instrument are combined to provide 63 days of time-series data.. The sampling and signal-tonoise ratio of this data improves as encounter nears. Over the time span of the observations the solar phase angle (α) changes from 25.5 to 63 deg; the spacecraft range (d) changes from 0.38 AU to 0.0004 AU; and the heliocentric distance (R) from 1.64 AU to 1.51 AU. Several digital apertures were used to evaluate the data. In the figures we show results for a 5x5 pixel aperture. The variations of R, d, α, Hapke parameters for Borrelly [3], plus the application of a simple physical model of reflection from the nucleus allow a clean separation of the nucleus lightcurve (Fig. 1) from the signal of the inner coma. The light-curve was analysed using the Window- Clean algorithm [2] and other harmonic analysis software. In this way a synodic period near 1.7 days was determined. A power spectrum of the latent periodicities is shown in Fig. 2. The results show the above period with two harmonics and no sign of any other periodicities. This is consistant with fully relaxed spin. By modeling the Deep Impact lightcurve and tying to earlier observation by the Hubble and Spitzer Space Telescopes with software (MODELSIM) that takes into account the changing aspects of the sun, target and observer a precise estimate of the diurnal period of the nucleus is obtained at 1.6976 ± 0.00006 days Imaging: Images taken by all three of Deep Impact cameras (Deconvolved HRI, MRI and ITS) both on approach and look-back were used to estimate the shape and spin orientation of the nucleus. In doing this the body center was placed at the center of mass (assuming a homogeneous internal distribution) and the spin axis aligned to the axis of maximum moment of inertia. The position of the pole was found to be RA, Dec (J2000) = 293.8, +72.6 with an absolute pointing uncertainty of about 5 deg. The sense of the spin is direct. The prime meridian is proposed to pass through a 350 m crater 500 m NNW of the impact site. The direction of the N pole is illustrated in Fig. 3. To ensure consistency between the shape model and the observed approach light curves model light-curves were computed using Hapke photometric parameters and the shape model adjusted until a satisfactory comparison was obtained both for the images and the light-curve. Light-curve pole determination: In addition to the approach light-curve, others are available from various sources (HST, Spitzer, ground-based telescopes) that are taken under different geometric situations [2]. The information from these can be combined to deduce two possible directions in which the spin pole might lie on the sky. Basically, for a given shape, the amplitude of each light-curve and its observing geometry allows a small circle to be drawn on the sky which represents a locus of possible pole positions. For fully relaxed spin, where these small circles intersect on the sky is the direction of the spin pole. This is illustrated for 9P/Tempel 1 in Fig. 4 . The derived pole position that is closest to the pole determined from the images is RA, Dec (J2000) = 317, +81 with an absolute point uncertainty of ± 8 deg. The “imaging “ and “light-curve” estimates are separated by 9.8 deg and are consistent within their uncertainities [their uncertainty ranges overlap]. Further work. The shape model continues to be refined and will be combined with the lightcurve data to refine the position of the pole still further. The diural period will be tested for long-term stability using light-curve data widely separated in time (years). It is possible that changes could occur due to reaction forces due to mass loss (non-gravitational forces) as was seen in comet 10P/Tempel 2 by Mueller and Ferrin [4]. References: [1] Meech, K. J. et al. (2005) Space Sci. Rev. 117, 297 - 334. [2] Belton, M.J.S. et al. (2005) Space Sci. Rev. 117, 137 – 160. [3] Buratti, B.J. et al. (2004) Icarus 167, 16., 1344–1345. [4] Mueller, B. E. A. and Ferrin, I. (1996) Icarus 123, 463 – 477. Figure 1. 10 days of the approach light-curve of 9P/Tempel 1 extracted from 5x5 pixel aperture photometery through the MRI Clear filter. The two narrow features near 1.88 and 3.63 days are outbursts. Zero on the time axis is the time of impact. Figure 2. Power spectrum of the approach light-curve. The three peaks correspond to periodicities at 1.692, 0.851 and 0.567 days. I.e. they are harmonically related in the ratio 1: 1/2: 1/3. There are no other significant peaks. Figure 3. 9P/Tempel 1 as seen by the ITS camera with the N pole, spin direction, and prime meridian marked. Latitude and Longitude lines are spaced by 10 deg. Figure 4. North pole plot showing the pole solution derived from the shape model (Black square) and five light-curve observations including the Deep Impact approach light-curve. Declination lines are every 10 degrees. 0 deg. RA is at the top and RA increases clockwise in steps of 30 degrees. The small circles that are not declination lines each correspond to a different lightcurve observation and are loci of possible pole positions for an ellipsoidal model shape with a/b=1.8.