Satellite internet (Sat-Net) enables high-speed con-nectivity with low latency and extensive coverage. However, it faces challenges related to data security and reliable networking. Blockchain technology, with its decentralized and tamper-proof nature, offers a promising solution to these challenges. However, applying blockchain to the Sat-Net topology is difficult due to its highly dynamic structure, which results in restricted communication periods between satellites and ground stations. To address these issues and adapt to the Sat-Net topology, we propose a solution called RelSharding, which utilizes relayer satellites to relieve concurrent transmission pressure of ground stations by collecting and transmitting data transactions from client satellites. Through caching block headers and Merkle trees in relayer satellites, RelSharding can also reduce authentication latency between satellites utilizing simplified payment verification (SPV). Conducted on the modified SimBlock framework, our experiments indicate that RelSharding can enhance throughput up to 45x and decrease latency by 292x compared to existing blockchain solutions.