Precise Distances for Main-Belt Asteroids in Only Two Nights

TL;DR

This paper introduces a novel two-night observational method to accurately determine asteroid distances using Earth's rotational reflex, significantly improving efficiency for main-belt asteroid surveys.

Contribution

The paper develops and demonstrates a new mathematical method leveraging Earth's rotation to measure asteroid distances from minimal data, enhancing survey efficiency.

Findings

Achieved 1.6% mean fractional error in distance estimates for known asteroids.

Demonstrated method works with any detection technique, not just digital tracking.

Enables rapid size and magnitude estimation for small main-belt asteroids.

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.