From Solar System to Earth System: The Symbiotic Sciences of Astronomy and Meteorology Professor Ian Roulstone 110 years ago, weather forecasting was for the first time described as a problem in mathematics and physics. We shall show how, since that time and right up to current supercomputer simulations of the Earth System, mathematics has assisted in quantifying and enhancing our understanding of weather and climate. Crucially, many of the early advances in weather forecasting were stimulated by the success of astronomers in solving problems of celestial mechanics, and we discuss the implications of these developments in the context of modern Earth System modelling. (No specialist mathematical background will be assumed.) Ian Roulstone is professor of mathematics at the University of Surrey.