Small satellites are widely used today as cost effective means to perform Earth observation and other tasks that generate large amounts of high-dimensional data, such as multispectral imagery. These satellites typically operate in low earth orbit, which poses significant challenges for data transmission due to short contact times with ground stations, low bandwidth, and high packet loss probabilities. In this paper, we introduce JSCC-SAT, which applies joint source-and-channel coding using neural networks to provide efficient and robust transmission of compressed image data for satellite applications. We evaluate our mechanism against traditional transmission schemes with separate source and channel coding and demonstrate that it outperforms the existing approaches when applied to Earth observation data of the Sentinel-2 mission.