NASA's Solar Dynamics Observatory (SDO) mission collects extensive data to monitor the Sun's daily activity. In the realm of space mission design, data compression plays a crucial role in addressing the challenges posed by limited telemetry rates. The primary objective of data compression is to facilitate efficient data management and transmission to work within the constrained bandwidth, thereby ensuring that essential information is captured while optimizing the utilization of available resources. This paper introduces a neural video compression technique that achieves a high compression ratio for the SDO's image data collection. The proposed approach focuses on leveraging both temporal and spatial redundancies in the data, leading to a more efficient compression. In this work, we introduce an architecture based on the Transformer model, which is specifically designed to capture both local and global information from input images in an effective and efficient manner. Additionally, our network is equipped with an entropy model that can accurately model the probability distribution of the latent representations and improves the speed of the entropy decoding step. The entropy model leverages a channel-dependent approach and utilizes checkerboard-shaped local and global spatial contexts. By combining the Transformer-based video compression network with our entropy model, the proposed compression algorithm demonstrates superior performance over traditional video codecs like H.264 and H.265, as confirmed by our experimental results.