Families of Two-Impulse Transfers to Sun–Earth Triangular Libration Points

The growing demand for space weather monitoring at the Sun–Earth triangular libration points (TLPs) demonstrates the critical need for efficient transfer trajectories. While previous studies have provided preliminary results, a systematic investigation remains lacking. This paper presents a systematic investigation of two-impulse transfers from low Earth orbit (LEO) to periodic orbits near Sun–Earth TLPs, with the [Formula: see text] point serving as a representative case. Assuming fixed departure and arrival points, the solution space of point-to-point transfers is comprehensively mapped from a family-oriented perspective. A novel classification scheme is developed to deconstruct and analyze the characteristics. Building upon low-energy point-to-point transfer families as initial guesses, a “coordinate [Formula: see text]” method is proposed to obtain fuel-optimal trajectories between orbital states (orbit-to-orbit transfers). Subsequently, the results are extended to short periodic orbits (SPOs) with varying amplitudes and validated in a high-fidelity ephemeris model. Remarkably, an approximately 0.03 astronomical unit (AU) amplitude consistently yields a local minimum in the magnitude of the total velocity impulse ([Formula: see text]) across the entire time-of-flight (TOF) range (0.2–5.5 years). The global minimum [Formula: see text] achieves [Formula: see text] with a TOF of 5.1638 years. These insights and results establish reliable and practical references for future mission design and engineering applications. Furthermore, the proposed framework incorporates the global solution characteristics, enabling more systematic and complete optimization. This framework is also applicable to other transfer problems.