Finding Asteroids Down the Back of the Couch: A Novel Approach to the Minor Planet Linking Problem

We present a novel approach to the minor planet linking problem. Our heliocentric transformation-and-propagation algorithm clusters tracklets at common epochs, allowing for the efficient identification of tracklets that represent the same minor planet. This algorithm scales as $O(N log N)$, with the number of tracklets $N$, a significant advance over standard methods, which scale as $O(N^3)$. This overcomes one of the primary computational bottlenecks faced by current and future asteroid surveys. We apply our algorithm to the Minor Planet Center's Isolated Tracklet File, establishing orbits for $\sim41,000$ new minor planets.