1. A computer-implemented method for scheduling beams of an antenna on board a satellite for receiving Automatic Dependent Surveillance Broadcast (ADS-B messages) during a defined time period comprising: for each beam of the antenna, calculating a beam score based, at least in part, on the expected gain of the beam during the defined time period; determining a number of beams of the antenna having non-zero beam scores during the defined time period; comparing the number of beams of the antenna having non-zero beam scores during the defined time period to a threshold value; determining, based on having compared the number of beams of the antenna having non-zero beam scores during the defined time period to the threshold value, that the number of beams of the antenna having non-zero beam scores during the defined time period is less than the threshold value; as a consequence of having determined that the number of beams of the antenna having non-zero beam scores during the defined time period is less than the threshold value: accessing a set of beam weights for each of multiple different candidate beam patterns, each set of beam weights having a weight corresponding to each of the antenna's beams; for each set of weights: multiplying individual beam weights by corresponding beam scores for beams of the antenna during the defined time period, and generating a candidate beam pattern score by calculating a sum of the products of the beam weights and corresponding beam scores; comparing the candidate beam pattern scores for the different candidate beam patterns; selecting, based on having compared the candidate beam pattern scores for the different candidate beam patterns, a particular one of the candidate beam patterns; and scheduling the selected beam pattern for the beams of the antenna for the defined time period.