Internet connectivity using low earth orbit (LEO) satellites is gaining significant traction, with nearly 3 million users worldwide. While these networks promise to provide universal broadband connectivity, they suffer from large throughput fluctuations over short time scales. We conduct an extensive evaluation of Starlink's throughput across three devices in different countries, with measurement durations ranging from one to six months. We identify various factors that cause throughput variations at varying timescales. Given our analysis, we design StarNet, a new learning-based throughput prediction system. StarNet incorporates satellite network-specific insights and accurately predicts future throughput for end users. We demonstrate that StarNet's accurate predictions can improve the experience of end user applications like video streaming.