Abstract Attention is paid to the problem of predicting accurately (a) the orbital elements of a balloon satellite over long periods of time, and (b) the time the satellite will pass through a given point in the orbit, a few days or weeks in advance of the event. It is shown that by computing the solar radiation pressure and gravitational perturbations of the orbit of the balloon satellite Echo 2, the orbital elements can be predicted reasonably accurately several months in advance. For the balloon satellite Explorer 19, allowing for air drag at perigee, computed from a simple atmospheric model in addition to the effect of solar radiation pressure, results in significant improvement in predicting the period of revolution a few months in advance. Finally, by numerically integrating the air-drag effect round the orbit, it is shown that a considerable improvement can be made in the accuracy of predicting the time at which a satellite will pass through a given point on the orbit.