Prospects for determining air shower characteristics through geosynchrotron emission arrival times

Using simulations of geosynchrotron radiation from extensive air showers, we present a relation between the shape of the geosynchrotron radiation front and the distance of the observer to the maximum of the air shower. By analyzing the relative arrival times of radio pulses at several radio antennas in an air shower array, this relation may be employed to estimate the depth of maximum of an extensive air shower if its impact position is known, allowing an estimate for the primary particle's species. Vice versa, the relation provides an estimate for the impact position of the shower's core if an external estimate of the depth of maximum is available. In realistic circumstances, the method delivers reconstruction uncertainties down to 30 g/cm^2 when the distance to the shower core does not exceed 7 km. The method requires that the arrival direction is known with high precision.