With the rapid advancement of earth observation technologies in recent years, agile earth observation satellites (AEOS) equipped with advanced attitude adjustment capabilities have attracted widespread attention. The scheduling of AEOS involves time-dependent transition times, which generates a complex time-dependent multi-objective scheduling problem in multi-satellite, multi-orbit, and multi-demand observation scenarios. To solve this problem, we first formulate a mathematical programming model based on the problem characteristics and optimization objectives. Subsequently, a distributed meta-$Q $-learning co-evolutionary framework is proposed, which consists of a pretraining phase and an evolutionary search phase. In the pretraining phase, distributed $Q $-learning is used to enhance the pretraining efficiency, while the evolutionary search phase leverages the pretrained distributed $Q $-learning model to adaptively select the evolutionary operators. Based on the proposed evolutionary framework and problem characteristics, different evolutionary operators and a dynamic population division strategy are designed. Further, a distributed meta-$Q $-learning co-evolutionary algorithm (DMCEA) is constructed. Finally, computational experiments validate the effectiveness of the DMCEA in solving the problem under consideration.