Spacecraft insertion into halo orbits around the Luna-Earth libration point L2 is necessary for the lunar exploration programs, especially for solving problems of studying the far side of the Moon by using landing vehicles. The paper proposes a new method for calculating the transfer trajectories to such halo orbits. Considered two flight sachems: conventional transfer and transfer with ballistic capture. A numerical method has been developed for solving the problems. It consists in inserting invariant manifolds of halo orbits and calculating two-impulse trajectories from an initial circular earth orbit to the insertion point of this stable manifold. The problem of transfer orbit calculation is reduced to calculating the transfer trajectory between the LEO and a given entry point to the stable manifold. For solving the boundary value problem, the parameter continuation method is used, which based on Newtonian homotopy between the solutions of the unperturbed and perturbed boundary value problems. And a hybrid algorithm for optimizing the insertion point of the manifold for trajectories with ballistic capture is proposed, the numerical examples are given.

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