Asteroid follow-up and precovery problem: Partial banana mapping solution

Precovery of asteroids, that is, finding older observations of already discovered asteroids, allows us to refine our knowledge of their orbits, glean information about close encounters and the probability of collisions with Earth, and to determine some dynamical and physical properties, such as the Yarkovsky acceleration. Existing approaches generally look for an observation next to the predicted position from the nominal orbit, and often do not take into account the whole uncertainty distribution of coordinates We aim to develop a computationally fast technique for predicting the possible spherical coordinates of near-Earth asteroids in order to find observations in existing catalogs or archived observations (plates, CCDs, etc.). We modified the partial banana mapping method, and used it to estimate impact probabilities of asteroids with the Earth. For a near-Earth asteroid, a Gaussian law for the equinoctial orbital elements well approximates the uncertainty region of the object at the epoch of the observation. We sample virtual asteroids on the main line of the curved uncertainty region at the epoch of observation project all of them with their small uncertainty vicinity onto the celestial sphere, and evaluate the brightness of the asteroids. We also estimate the probability of finding the asteroids on the image, and the length of the uncertainty region (which shows the quality of the orbit) in order to establish a priority list among the images. The higher the probability and the poorer the quality of the orbit, the more interesting it is to find the object for further improvement of its orbit and to refined its impact probability computation. We demonstrate the applicability of the developed method. We tested it on the case of precovery observations of asteroid (506074) Svarog (provisional designation 2015 UM$_ $) as if it had recently been discovered, meaning the orbit is obtained with only 3 months of observations. In this case, we estimated a probability of precovery of about 10, predicted the possible positions, and actually found the object close to the constructed uncertainty region. The nominal position is outside of the image's field of view, meaning that conventional methods would fail . The uncertainty region is curved and asymmetric, which shows that using only the covariance matrix of celestial coordinates for the nominal orbit would poorly approximate the actual uncertainty region in the place of the sky, preventing the asteroid from being found. The developed method selects interesting images and guides us in our search for asteroids on them, even if the position predicted for the nominal orbit is out of the image window.