A fast method for quantifying observational selection effects in asteroid surveys

We present a fast method to calculate an asteroid survey's 'bias' - essentially a correction factor from the observed number of objects to the actual number in the population. The method builds upon the work of Jedicke and Metcalfe (Jedicke, R., Metcalfe, T.S. [1998]. Icaurs 131, 245-260) and Granvik et al. (Granvik, M., Vaubaillon, J., Jedicke, R. [2012]. Icarus 218, 262-277) and essentially efficiently maps out the phase space of orbit elements that can appear in a field-of-view. It does so by 'integrating' outwards in geocentric distance along a field's boresite from the topocentric location of the survey and calculating the allowable angular elements for each desired combination of semi-major axis, eccentricity and inclination. We then use a contour algorithm to map out the orbit elements that place an object at the edge of the field-of-view. We illustrate the method's application to calculate the bias correction for near Earth Objects detected with the Catalina Sky Survey (Christensen, E. et al. [2012]. AAS/Division for Planetary Sciences Meeting s, vol. 44, p. 210.13; Larson, S. et al. [1998]. Bulletin of the American Astronomical Society, vol. 30, p. 1037).