Precise Distances for Main-Belt Asteroids in Only Two Nights

Abstract

We present a method for calculating precise distances to asteroids using only two nights of data from a single location -far too little for an orbit -by exploiting the angular reflex motion of the asteroids due to Earth's axial rotation. We refer to this as the rotational reflex velocity method. While the concept is simple and well-known, it has not been previously exploited for surveys of main-belt asteroids. We offer a mathematical development, estimates of the errors of the approximation, and a demonstration using a sample of 197 asteroids observed for two nights with a small, 0.9-meter telescope. This demonstration used digital tracking to enhance detection sensitivity for faint asteroids, but our distance determination works with any detection method. Forty-eight asteroids in our sample had known orbits prior to our observations, and for these we demonstrate a mean fractional error of only 1.6% between the distances we calculate and those given in ephemerides from the Minor Planet Center. In contrast to our two-night results, distance determination by fitting approximate orbits requires observations spanning 7-10 nights. Once an asteroid's distance is known, its absolute magnitude and size (given a statistically-estimated albedo) may immediately be calculated. Our method will therefore greatly enhance the efficiency with which 4-meter and larger telescopes can probe the size distribution of small (e.g. 100 meter) main belt asteroids. This distribution remains poorly known, yet encodes information about the collisional evolution of the asteroid belt -and hence the history of the Solar System.

Digital Tracking Observations Can Discover Asteroids 10 Times Fainter Than Conventional Searches

“…Among our 215 detected asteroids, 197 were measured on both April 19 and April 20 with sufficient precision that we could derive meaningful distances for them using Earth rotational reflex velocities as described in Heinze & Metchev (2015). The resulting precise distances allow us to calculate absolute magnitudes and hence approximate diameters for our newly discovered asteroids.…”

“…The measured tracks of our asteroids relative to the background starfield are shown in Figure 9, and the measured drift rates are plotted and compared to known objects in Figure 2. These precisely measured angular velocities allow us to calculate the geocentric distance of each two-night object using Earth rotational velocity reflex as we describe in Heinze & Metchev (2015). The mean error of our distance determinations is only 1.5% for known objects.…”

“…The RMS error of these distances is 0.3 AU. This crude distance estimation should not be confused with the far more accurate method of Heinze & Metchev (2015), but the latter cannot be used at this stage because it requires that measurements of the asteroid have already been linked across two subsequent nights.…”

“…The fact that we have reached a comparable regime using only an 0.9-meter telescope shows the power of digital tracking. A digital tracking survey on a 4-8 meter telescope would easily probe fainter asteroids than have ever previously been detected, and would open up a new regime for statistical studies of the main belt -especially when combined with the distance determination method we describe in Heinze & Metchev (2015). To compare the sensitivity of our digital tracking analysis to that of conventional asteroid surveys, we use only the set of asteroids we have confirmed as genuine.…”

“…Another significant advantage is that with digital tracking, every detection comes with a precise measurement of the asteroid's motion, which can aid in determining distances (Heinze & Metchev 2015) and orbital information even for extremely faint objects unlikely to be recovered over longer timescales of weeks to years.…”