Abstract
This paper proposes a basic method for constructing a formation flight based on Hill's equations of motion. It proposes a trajectory design of minimum fuel consumption for spacecraft relative position change by two impulses. Focusing on enlarging the formation size, we consider a problem to obtain the time and the phase of the second impulse when the phase of the first impulse is given. First, the phase of the second impulse is obtained as a function of the time of the second impulse. Then, the time of the second impulse is obtained to minimize the total fuel consumption. There are three ways to give two impulses for the minimum fuel consumption, which depends on the phase of the first impulse. Numerical studies of enlarging the formation size by two impulses are executed in order to verify the trajectory design.
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