The operation of an intelligent reflecting surface (IRS) under predictable receiver mobility is investigated. We develop a continuous time system model for multipath channels and discuss the optimal IRS configuration with respect to received power, Doppler spread, and delay spread. It is shown that the received power can be maximized without adding Doppler spread to the system. In a numerical case study, we show that an IRS having the size of just two large billboards can improve the link budget of ground to Low Earth Orbit (LEO) satellite links by up to 6dB. It also adds a second, almost equivalently strong, communication path that improves the link reliability.