Large-scale disasters are very destructive to terrestrial optical networks (TONs), and most existing survivability technologies that rely solely on TONs themselves can hardly combat disasters. Satellite networks, as a promising complement to terrestrial systems, can help to improve the survivability of TONs against disasters. However, the time-varying nature of satellite networks poses new challenges to traditional survivability technologies. This paper considers the low earth orbit (LEO) satellite network-assisted shared backup path protection. Since the link-switching consumes a certain amount of time and would cause the delay jitter and the quality of transmission (QoT) fluctuation of the space lightpath, a link duration-aware shared backup path protection (LD-SBPP) scheme is proposed to search space backup lightpaths with the minimum number of link-switching. A pre-calculated snapshot continuous routing and wavelength assignment (P-SCRWA) algorithm is proposed to pre-calculate the routing and reserve spectrum resources at each continuous snapshot. Simulations show that user requests cannot be effectively protected by relying on the TON solely, while the protection can be achieved with the help of LEO satellites. The LD-SBPP scheme has high wavelength utilization efficiency, resulting in lower blocking probability. Besides, the link duration-aware strategy can greatly reduce the number of link-switching along space backup lightpaths.