Lambert problem solution in the Hill model of motion (Q1766268)

The Lambert problem (determination of a transfer orbit between two given positions during a given time) is applied to the design of transfers in an extended Earth vicinity including Lagrange points of three-body problem (Sun-Earth-spacecraft). These points are convenient for solving many scientific and applied problems related to solar-terrestial physics. The advantage of Lagrange points (particularly, of the collinear \(L_1 , L_2\) points) is that the spacecraft can stay in, say, the halo orbit around one of them as long as necessary with a very small propellant consumption. The transfer from Lagrange point vicinity back to the Earth or to another Lagrange point also can be performed with a small characteristic velocity. In this article, the authors consider the Hill variant of the restricted three-body problem. A mathematical solution of Lambert problem is described. The solution is based on the use of pre-determinant reference orbits of different types (depending on the problem) giving the first guess and defining the sought-for transfer type. The mathematical procedure provides step-by-step transformation of the reference orbit to the sought-for transfer orbit. The approach gives a possibility to solve transfer problems of different types. The standard Runge-Kutta fourth-order integrator is used in numerical simulations. Numerous families of transfer orbits are found and presented in the form of diagrams.