A method for generating extended satellite ephemeris data for a satellite for use by a terminal apparatus in a satellite communication system, wherein the satellite is a minimally controlled satellite which is only infrequently corrected by small amounts, small Δυ, or only corrected by small amounts in emergency circumstances, or never corrected, the method comprising: receiving historical ephemeris data for the satellite, wherein the satellite is the minimally controlled satellite; estimating, using the received historical ephemeris data, a dynamical orbital model for the satellite, wherein estimation of the dynamical orbital model comprises modelling a time evolution of each orbital parameter of a set of orbital parameters which define an orbital model, and modelling the time evolution comprises fitting a model to each orbital parameter or jointly fitting some or all orbital parameters of the set of orbital parameters, unless a respective orbital parameter of the set of orbital parameters does not vary significantly in the received historical ephemeris data, where the respective orbital parameter is set to the respective most recent historical value, and the dynamical orbital model is used to predict future values of each orbital parameter of the set of orbital parameters storing the dynamical orbital model by the terminal apparatus or updating a dynamical orbital model stored by the terminal apparatus based on the estimated dynamical orbital model, wherein the dynamical orbital model is either received from a source external to the terminal apparatus or the dynamical orbital model is estimated by the terminal apparatus; generating, by the terminal apparatus, a set of synthetic orbital parameters at an epoch time using the dynamical orbital model, and the terminal apparatus providing the set of synthetic orbital parameters to an orbital predictor to obtain an estimate of one or more satellite pass times for a predefined terminal position, or one or more satellite locations at a predetermined future time. receiving historical ephemeris data for the satellite, wherein the satellite is the minimally controlled satellite; estimating, using the received historical ephemeris data, a dynamical orbital model for the satellite, wherein estimation of the dynamical orbital model comprises modelling a time evolution of each orbital parameter of a set of orbital parameters which define an orbital model, and modelling the time evolution comprises fitting a model to each orbital parameter or jointly fitting some or all orbital parameters of the set of orbital parameters, unless a respective orbital parameter of the set of orbital parameters does not vary significantly in the received historical ephemeris data, where the respective orbital parameter is set to the respective most recent historical value, and the dynamical orbital model is used to predict future values of each orbital parameter of the set of orbital parameters storing the dynamical orbital model by the terminal apparatus or updating a dynamical orbital model stored by the terminal apparatus based on the estimated dynamical orbital model, wherein the dynamical orbital model is either received from a source external to the terminal apparatus or the dynamical orbital model is estimated by the terminal apparatus; generating, by the terminal apparatus, a set of synthetic orbital parameters at an epoch time using the dynamical orbital model, and the terminal apparatus providing the set of synthetic orbital parameters to an orbital predictor to obtain an estimate of one or more satellite pass times for a predefined terminal position, or one or more satellite locations at a predetermined future time.