Big data analytics for Earth observation has been playing an increasingly important role in supporting environmental monitoring, disaster early warning, and sustainable development through timely analysis of massive multi-source data collected by satellites. With the growing need for such timely Big Data analysis, Space Edge Computing (SEC) networks have been proposed to provide in-orbit analytic services for users worldwide, by integrating computing capability through Low-Earth-Orbit (LEO) satellites. However, the monitoring frequency of LEO satellites over specific target areas remains limited due to orbital constraints, making it difficult to meet the high-frequency data acquisition demands of Big Data analytics. Satellite inclination maneuver is a promising method to cover a wide range of target areas and enhance monitoring frequency by adjusting orbital inclination of satellites. Although such maneuvering enables satellites to timely process datasets, reducing energy wastage caused by inter-satellite data transmission, it consumes propulsion fuel, which is limited and difficult to replenish in a timely manner. Therefore, balancing the energy consumed for data processing and the fuel consumed for maneuvering is essential for efficient and sustainable Big Data analytics in SEC networks. In this paper, we aim to optimize Big Data query evaluation problem with satellite maneuver in an SEC network, focusing on minimizing the weighted sum of energy consumed for processing and fuel consumed for maneuvering. Specifically, we consider that each Earth observation service needs to guarantee a certain level of monitoring frequency, which may not always be satisfied by the original orbital coverage of LEO satellites. In such cases, some satellites will be selected to perform inclination maneuvers for additional monitoring and processing to guarantee the quality of Earth observation services. To this end, we first propose an approximation algorithm with a provable approximation ratio for the offline query evaluation problem, which leverages a customized auxiliary graph to jointly minimize energy and fuel consumption. We then devise an online learning algorithm, referred to as the customized Lipschitz bandit learning algorithm, with a bounded regret for the online Big Data query evaluation problem in an SEC network. We finally evaluate the performance of the proposed algorithms in a real SEC network topology. Experiment results show that the performance of the proposed algorithms achieve 11% lower energy consumption and 10.6% lower fuel consumption than those of their comparison counterparts.