A fast calculation method for asteroid exploration window based on optimal and sub-optimal two-impulse transfer orbits

Abstract For impulse transfers, the solution of two-impulse rendezvous is generally obtained by solving the Lambert orbit problem, and the search for the exploration window of the target celestial body is a two-dimensional optimization based on velocity increment calculation. In order to assess the accessibility and exploration window of large-number asteroids, this paper approximates the transfer orbit from the Earth to the target asteroid as a co-planar two-impulse transfer orbit and gives an effective method. Based on the theory of cotangential transfer orbit, this paper proposes a method to express the transfer orbit with one single variable (the aphelion argument of the transfer orbit, θT), which can also determine the start time of the transfer. After that, the paper combines the two-impulse orbit transfer theory (without considering the rendezvous) with the calculation method of the exploration window (considering the rendezvous), proposing the concept of the rendezvous difference angle eR. eR is defined as the mean anomaly angle difference between the spacecraft and the target object when the spacecraft enters the target orbit. The rendezvous difference angle eR has the same minimum point as the velocity increment in exploration window search, while it can be directly calculated from the transfer orbit and the transfer time. When cotangential transfer orbits are used, eR can be expressed as a function of θT. Taking eR as the optimal target variable, the exploration window search can be simplified to a one-dimensional problem. This method is suitable for the large-scale accessibility calculation for asteroids with low inclinations, so as to quickly determine the accessible target group.