Many different cosmic bodies, from small planets to massive stars, possess magnetic fields. The Earth's magnetic field protects us from the harmful solar wind (a stream of particles emitted from the Sun), Jupiter's is the largest object in the solar system, and those of exoplanets may offer a new detection method. They are particularly interesting to study since the analyses of these many different types of body are mutually illuminating, i.e. we can learn much about distant astrophysical bodies by studying objects much closer to home, and vice versa. This proposal is thus a holistic study of the dynamics of planetary magnetic fields in our solar system and others, through a ubiquitous phenomenon: the 'northern lights', or aurora. Auroras on other planets in the solar system can be studied with the Hubble Space Telescope (HST), and they act as 'TV screens' in the upper atmospheres telling us how energy flows through the space controlled by the planets' magnetic fields. There are some fundamental gaps in our knowledge about Saturn's magnetic field. Most planets' magnetic fields wobble like tilting spinning tops as the planets spin. Saturn's is unique in that it does not, and yet strangely many phenomena associated with the magnetic field, like the aurora, pulse near the spin period. This could be due to a difference in conditions in the upper atmosphere at the summer and winter poles, however HST has only ever observed the southern auroras. In addition, Saturn's upper atmosphere is much hotter than models predict. I will obtain HST images of the northern auroras, which, in conjunction with in situ Cassini measurements, will provide the data required to resolve these problems. Despite the 'spinning top' wobble in most planets' magnetic fields, the models which describe how auroras are generated by the rapid rotation of Jupiter assume no wobble at all, i.e. symmetry in longitude about the spin axis. This is a fundamental omission, since Jupiter's auroras are clearly not longitudinally symmetric, and Jupiter is the source of various pulsing emissions which must be caused by a longitudinal asymmetry. I will thus develop the models to include this asymmetry, and also determine how the shape of the magnetic field and auroral processes are interdependent. These studies of the dynamics of Jupiter's tilted magnetic field will act as stepping stones toward developing models for the highly asymmetric magnetic fields of Uranus and Neptune, about which very little is known. These models will therefore make discoveries about how these enigmatic magnetic fields work. Many hundreds of planets of roughly Jupiter's mass have been discovered orbiting other stars. Most of these orbit very close to the star, since present detection methods are best at finding close planets. The buffeting of these planets by stellar winds has been suggested to generate auroral radio waves powerful enough to be detected across tens of lightyears. However, I have recently shown that rapidly-spinning planets orbiting hot stars at the equivalent of Saturn's orbital distance could equally generate such detectable radio emissions. I will thus develop this model to determine exactly what configurations of this presently-overlooked class of planet are detectable, and also search radio telescope data for detections. The possibility of detecting potentially life-friendly magnetospheres of planets orbiting other stars is particularly exciting and of significant relevance to wider society.