Detection of near earth asteroids based upon their rates of motion

Spacewatch has been successfully discovering Near Earth asteroids (NEAs) for five years based upon the difference in the ecliptic rates of motion of these asteroids compared to their distant Main Belt, Trojan and Centaur cousins. The search for NEAs is usually restricted to regions on the sky near the ecliptic and opposition in order to take advantage of their increased brightness, the good correlation between the rates of motion and orbital elements, and their increased numbers in this direction. The present study introduces an analytic determination of the best location on the sky to search for NEAs based on their rate of motion. Assuming a reasonable orbit and magnitude-frequency distribution for NEAs, Main Belt, Mars crossing, Hungaria and Trojan asteroids, it is possible to derive the probability that an object moving with a specified rate in each direction at a given ecliptic latitude and longitude with respect to opposition is a NEA. The discovery probabilities are studied as a function of ecliptic latitude and longitude with respect to opposition, absolute magnitude of the discoverable NEAs, confidence level on the NEA detection, and limiting magnitude of the detection system. The discovery probabilities are examined for each of the NEAs discovered by Spacewatch. Imposing a 90% confidence level on the requirement that a candidate is a large NEA for a detection system with a limiting magnitude of V=21, it was found that scanning at opposition offers the best opportunity for NEA discovery. Discoveries are symmetric in the east-west direction about opposition due to an interesting inter-relation in the solutions for orbital elements of objects which may appear at the specified location. Detection systems with a fainter magnitude limit may find it better to scan about 45 degrees from opposition in order to find the larger NEAs. (C) 1996 American Astronomical Society.