The problem of intercept of a maneuverable satellite by a pursuing interceptor is considered from the standpoint of differential games as developed by Isaacs. The payoff in the games considered is either distance between vehicles at the end of a fixed time, or time to intercept. In both cases the evader desires to maximize the payoff and the pursuer to minimize it. Under the assumption of planar motion and constant gravitational field, an optimal steering strategy is determined for both players. For the intercept cases, it is found that both evader and pursuer thrust in the same constant direction. In the terminal range payoff case, the steering is a function only of the initial position and velocity The analysis is extended to the case of rendezvous, both uncooperative and cooperative, with a payoff of time to rendezvous. The resulting optimum steering for the uncooperative vehicles is again to thrust in identical directions. For the cooperative rendezvous, the optimal policy requires thrusting in opposite directions.