4 Navigation

Due to the alt-azimuthal mounting of the SVST, non-uniform image rotation required navigation prior to measurements of absolute directions. The light sensitivity of the optical setup and imaging system was such that no field stars were recorded in the field of view, thus precluding straightforward calculation of the local coordinate frame based on field star motion and orientation. Unstable tracking of the instrument prevented use of the line of motion of the comet photo-centre across the field for orientation. Absolute navigation was therefore based on measurements of physical features of the planet Mars, which was imaged with the same optical setup.

The relative image rotation of the alt-azimuthal system relative to the equatorial system occurring between two objects located at different positions on the celestial sphere is obtained from spherical trigonometry. After determination of the absolute orientation of the CCD frame pixel system to the equatorial system at one time, the image rotation is resolved, assuming a fixed optical setup. Features on the disk of Mars were used as an absolute orientation reference.

The sky-projected direction of the rotation axis of Mars was calculated from high-quality closely temporally spaced images from April 24 obtained with the $\lambda~550\ \rm nm$ filter at a mean central meridian longitude $\omega=359.5\hbox{$^\circ$}$. A valid assumption was that the CCD orientation remained fixed to the optical table throughout the observing period (no adjustments of the components of the optical setup were performed during this time span). As the two points defining the orientation of the disk on the sky, the photo-centre of north polar ice cap and the geometric centre of the illuminated disk were chosen.

It was assumed that the Martian north polar cap, whose perimeter was wholly inside the visible disk at the observations, was centrally positioned on the geographic pole to the order of the resolution of the data set. The validity of this assumption is confirmed by images obtained by the Hubble Space Telescope WFPC2 in March 1997 (James et al. 1997). At the central meridian of the navigational images of Mars, cap outliers were on the extreme disk edge and did not interfere with the determination of the centre of the main cap deposit. The centre of the main cap was estimated, from HST images, to be located at $0\pm15^\circ$ W, $88\pm1^\circ$ N. The error estimates equals an apparent angle of $0\hbox{$.\!\!^{\prime\prime}$}05$ from an Earth-based perspective, or a factor five smaller than the pixel angular size. The error in the position of the centre of the cap was determined from the navigational set to $0\hbox{$.\!\!^{\prime\prime}$}09$ or 0.4 pixel.

The centre of the illuminated disk was calculated from isophote contours along the limb, at intensity levels lower than those of the non-geometric limb defects caused by disk albedo variegation. The coordinates of isophote contours were measured to within a fraction of 0.002 of the disk diameter, corresponding to a $0\hbox{$.\!\!^{\prime\prime}$}03$ or 0.1 pixel position error.

Correction was then applied for the phase defect by the position angle and size of the maximum defect of illumination, to yield the centre of the geometric disk. In this step, a tabulated value (Blumberg & Boksenberg 1996) was used for the size of the defect of illumination in combination with the calculated pixel scale and its position angle taken from the images, obtained from the position angle of the line through the cap and illuminated disk centre. The maximum error in the directional angle of the axis of rotation of Mars is, from the above figures, $1.0\hbox{$^\circ$}$.

Thus two points on the disk defining the Martian axis of rotation were known, establishing the orientation of the CCD frame. This measurement was then used to navigate all comet images by the amount of relative image rotation between the times of Mars and comet exposures. In Fig. 1, navigated images of Hale-Bopp reduced with flat- and dark-frame only are shown for three dates during the observing period.

  

Figure 1: Examples of navigated images from (left to right) April 21 (21:24.6 UT, filter $\lambda$ 830 nm), 24 (20:45.5 UT, $\lambda$ 830 nm) and 25 (20:42.9 UT, $\lambda$ 550 nm). The April 24 image is the result of adding five images (see Table  2), where the central region of the coma in each image was deliberately saturated at exposure in order to register outer coma structure. Images are flat- and dark-corrected and cleaned by interactive pixel editing, and displayed deliberately saturated near the photo-centre to increase contrast in the fainter coma and shells. A linear gray-scale colour table has been applied. The image field size is 512$\times$512 pixels (123$''\times$123'') or $146\,000$ km at the geocentric distance of the comet, centered on the photo-centre. South is up, west is to the right