Design and analysis of quasi-halo orbits and optimal transfers from the Earth under different Sun–Earth frameworks using differential evolution

In general, the initial designs of periodic orbits around the Lagrangian points and transfers to them from the Earth are generated under the Circular Restricted Three Body Problem (CRTBP) framework and used as reference designs to generate realistic designs under Ephemeris models. The realistic ephemeris designs are quasi-periodic multi-revolution orbits. So, the use of periodic orbits, which are multi-revolution in nature can be explored as reference designs as an alternative. Although, the periodic orbits generated in the Elliptical Restricted Three Body Problem (ERTBP) framework are multi-revolution in nature, in the Sun–Earth system, these orbits have large in-plane and out-of-plane amplitudes and hence, these are not suitable for scientific missions. For viable smaller amplitudes, only quasi-halo orbits do exist around the Sun–Earth Lagrangian point L₁ in the ERTBP framework. Hence, as an alternative to the periodic orbits under the CRTBP framework, the quasi-halo orbits under the ERTBP framework are designed and used as reference designs to generate ephemeris designs. These quasi-halo orbits are generated using a methodology, proposed in this paper, which involves differential evolution, an evolutionary optimization technique. Using a similar approach based on the differential evolution technique, the quasi-halo orbits are designed in the Ephemeris model also. The methodology could generate quasi-halo orbits that do not require any theoretical velocity corrections for about five years (10 revolutions). The pros and cons of reference designs in generating ephemeris design are analyzed. It is found that the design in the Ephemeris model is close to both the initial designs in CRTBP and ERTBP frameworks. However, the use of ERTBP design as the reference design does not result in a reduction in computational time. Furthermore, optimal two-impulse transfers to the quasi-halo orbit from an Earth parking orbit, are generated under the ERTBP framework and the Ephemeris model. The location of insertion and the components of orbit insertion velocity are treated as unknowns and determined using differential evolution. The transfer cost in the Ephemeris model is found to be less compared to transfers in CRTBP and ERTBP frameworks.