Quantum key distribution (QKD) is a pioneering quantum technology on the brink of widespread deployment. Nevertheless, the distribution of secret keys beyond a few 100 kilometers at practical rates remains a major challenge. One approach to circumvent lossy terrestrial transmission of entangled photon pairs is the deployment of optical satellite links. Optimizing these non-static quantum links to yield the highest possible key rate is essential for their successful operation. We therefore developed a high-brightness polarization-entangled photon pair source and a receiver module with a fast steering mirror capable of satellite tracking. We employed this state-of-the-art hardware to distribute photons over a terrestrial free-space link with a distance of 143 km, and extracted secure key rates up to 300 bits per second. Contrary to fiber-based links, the channel loss in satellite downlinks is time-varying and the link time is limited to a few minutes. We therefore propose a model-based optimization of link parameters based on current channel and receiver conditions. This model and our field test will prove helpful in the design and operation of future satellite missions and advance the distribution of secret keys at high rates on a global scale.