Frank and Sigwarth [2000, hereafter referred to as FS] object to the conclusions reached in Mutel and Fix [2000, hereafter referred to as MF] in which we report an upper limit to the number density of small comets with properties described by L. A. Frank and colleagues [e.g., Frank et al., 1986; Frank and Sigwarth, 1993, 1997, 1999]. The upper limit, which is considerably lower than the claimed number density (e.g., Frank and Sigwarth, 1993), results from an unsuccessful optical search for small comets. FS make three claims that they assert invalidate our conclusions. First, they claim that the expected number of detections has been severely overestimated because the effective sampling volume per image was not calculated correctly. Second, they argue that sample volume Vs scales with range r as Vs o• r 5, so that the detections claimed in previous optical searches (Yeates, 1989; Frank et al., 1990) are consistent with the lack of detections reported by MF. Third, using the number densities of claimed detections from previous Spacewatch searches, they estimate there should be -20-30 small comet trails with apparent magnitude near m -17.3 in the Iowa Robotic Observatory sample.In this paper we investigate these assertions and find that none are correct. First, we generalize the sample volume calculation of MF by considering a distribution in perihelia and inclination angles, which was not previously considered. We find that the mean sample volume averaged over a suitable range of perihelia is very nearly the same as the sample volume calculated by MF. Second, we examine the effect of nonzero inclination on the search volume. For both the IRO and Spacewatch searches, there is a narrow inclination acceptance range, as expected for any search using the "skeet shoot" technique, since there is no compensation for motion normal to the ecliptic plane. We recalculate the sample volume and resulting detection rate expected for both the IRO and Spacewatch searches, assuming a uniform inclination distribution for small comets. Finally, we estimate the number of detections expected for objects in the "window of opportunity" suggested by FS and find that it is far higher than their estimate. Sample Volume CalculationIn order to calculate the sample volume per image, FS arbiwarily select a maximum detectable comet trail length (66 pixels) and a fixed "tuning range" (55,000 kin). However,

No abstract

Citation: Mutel, R. L., and J. D. Fix, Comment on ''Detection of small comets with a ground-based telescope'' by L. A. Frank and

No abstract

Abstract. We have conducted an extensive optical search for small comets with the characteristics proposed by Frank et al. [1986] and Frank and Sigwarth [1993, 1997]. The observations were made using the 0.5-m reflector of the Iowa Robotic Observatory between September 1998 and June 1999. The search technique consisted of tracking a fixed point in the ecliptic plane at +9 ø geocentric solar phase angle. The telescope scan rate was chosen to track objects moving prograde at 10 km s -1 relative to the Earth at a distance of 55,000 km.The camera was multiply shuttered to discriminate against trails caused by cosmic rays and sensor imperfections. Of 6143 total images, we selected 2713 which were suitable for detection of objects with a magnitude 16.5 or brighter with 120 pixel trails. The sensitivity and reliability of the visual detection scheme were determined by extensive double-blind tests using synthetic trails added to over 500 search images. After careful visual inspection of all images, we found no trails consistent with small comets. This result strongly disagrees with previous optical searches of Yeares [1989] and Frank et al. [1990], whose detection rates and magnitudes, when converted to the present search, predict 65 + 22 detections. We conclude that at 99% confidence, the number density of any prograde objects in the ecliptic plane brighter than magnitude 16.5 with speeds near 10 km s -1 have a number density less than 5% of the small-comet density derived by Frank et al. [1990]. Any object fainter than this magnitude limit with a mass corresponding to the small-comet hypothesis (M > 20,000 kg) must have either an implausibly low geometric albedo (p < 0.01) or a density larger than that of water.