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3-4. For the major parameters of the problem, the phase angles at departure, and the phase angles at arrival are shown in Table 3 for clockwise LMO departure and Table 4 for counterclockwise LMO departure. Also for the optimal Design of Moon Missions 49 trajectory in Moon-Earth space, near-Moon space, and near-Earth space is shown in Fig. 3 for clockwise LMO departure and Fig. 4 for counterclockwise LMO departure. Major comments are as follows: (i) the accelerating velocity impulse decreases as the orbital altitude over the Moon surface increases (see Ref.

3. Earth-Moon Flight We study the LEO-to-LMO transfer of the spacecraft under the following conditions: (i) tangential, accelerating velocity impulse from circular velocity at LEO; (ii) tangential, braking velocity impulse to circular velocity at LMO. 1. Departure Conditions. Because of Assumption (A1), Earth fixed in space, the relative-to-Earth coordinates are the same as the inertial coordinates As a consequence, corresponding to counterclockwise departure from LEO with tangential, accelerating Design of Moon Missions 37 velocity impulse, the departure conditions (t = 0) can be written as follows: or alternatively, where Here, is the radius of the low Earth orbit and is the altitude of the low Earth orbit over the Earth surface; is the spacecraft velocity in the low Earth orbit (circular velocity) before application of the tangential velocity impulse; is the accelerating velocity impulse; is the spacecraft velocity after application of the tangential velocity impulse.

For further details on topics covered in this paper, see Ref. 18. 2. System Description The present study is based on a simplified version of the restricted three-body problem. More precisely, with reference to the motion of a spacecraft in Earth-Moon space, the following assumptions are employed: (A1) the Earth is fixed in space; (A2) the eccentricity of the Moon orbit around Earth is neglected; (A3) the flight of the spacecraft takes place in the Moon orbital plane; (A4) the spacecraft is subject to only the gravitational fields of Earth and Moon; the gravitational fields of Earth and Moon are central and obey (A5) the inverse square law; (A6) the class of two-impulse trajectories, departing with an accelerating velocity impulse tangential to the spacecraft velocity relative to Earth [Moon] and arriving with a braking velocity impulse tangential to the spacecraft velocity relative to Moon [Earth], is considered.

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