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In this paper we describe a machine learning based framework for spacecraft swarm trajectory planning. In particular, we focus on coordinating motions of multi-spacecraft in formation flying through passive relative orbit(PRO) transfers. Accounting for spacecraft dynamics while avoiding collisions between the agents makes spacecraft swarm trajectory planning difficult. Centralized approaches can be used to solve this problem, but are computationally demanding and scale poorly with the number of agents in the swarm. As a result, centralized algorithms are ill-suited for real time trajectory planning on board small spacecraft (e.g. CubeSats) comprising the swarm. In our approach a neural network is used to approximate solutions of a centralized method. The necessary training data is generated using a centralized convex optimization framework through which several instances of the n=10 spacecraft swarm trajectory planning problem are solved. We are interested in answering the following questions which will give insight on the potential utility of deep learning-based approaches to the multi-spacecraft motion planning problem: 1) Can neural networks produce feasible trajectories that satisfy safety constraints (e.g. collision avoidance) and low in fuel cost? 2) Can a neural network trained using n spacecraft data be used to solve problems for spacecraft swarms of differing size?