On earth-moon transfer trajectory with gravitational capture

Approaching from outside the sphere of influence, a particle may attain low relative velocity was a celestial body and even rotate around it temporarily, without utilizing any other effects than gravitational force. This mechanism is called gravitational capture (i.e. ballistic capture) and it has been considered to be one of the mechanisms which can explain the origin of planetary satellites. In astrodynamics field, lunar gravitational capture is applied to earth-moon transfer trajectory along with positive use of solar perturbation, paying attention to small delta-V required at lunar orbit insertion. In this paper, from the viewpoint of local two-body energy variation, the mechanism of gravitational capture is analytically investigated. Furthermore, a systematic design method for earth-moon transfer trajectory followed by gravitational capture is established.