## 1 Introduction
The manoeuvre should be conducted at the right moment. In the atypical conditions of an orbital flight, the movement is different from the one that we are used to on Earth's surface (and even in the air or on the orbit). A rocket engine is extremely powerful and works for very short periods, so that the change in the orbital velocity is, in fact, instantaneous. In general, the issue of optimisation of orbit manoeuvres may be discussed as a type of orbit design problem [8; 9; 10]. For many years, a great number of studies have been conducted with the aim to analyse the issues related to orbit design. For example, [PERSON] et al. [11] analysed the problem of the determination of the minimum manoeuvring duration on an Earth orbit with the use of a low-thrust engine during an eclipse with great accuracy. The problem of changing the orbit was presented as a multi-phase optimum control issue, in which the spacecraft may only be propelled during those phases when the Sun remains within its reach. A method was developed to generate the initial assumptions in order to create the appropriate approximation. Then, the approximate locations where the spacecraft exits and enters Earth's shadow were analysed. A similar issue was discussedby [PERSON] et al. [12]. In their article, the authors presented the problem of optimising the minimum fuel consumption for low-thrust propulsion in the context of orbit manoeuvres using three bodies of a limited weight. On the other hand, [PERSON] et al. [13] presented a numerical convex optimisation method to solve the problem of an orbit manoeuvre conducted in the minimum time with the use of low thrust. Considering the uncertainty of the application of the previous methods, [PERSON] et al. [14] proposed a new method for the optimisation of impulse orbit manoeuvres. This study combines genetic algorithm, Monte Carlo sampling, and a substitute model so as to enable optimisation at the maximum speed. At the same time, it provides the most efficient solutions possible that are free from limitations and enables reaching the appropriate balance between optimisation accuracy and its duration. In one of the most recent studies, [PERSON] et al. [15] proposed an optimum trajectory for changing the altitude of the orbit, which takes into account chemical, electric, and hybrid propulsion systems. [PERSON] et al. [16] proposed an optimum approach to controlling a spacecraft in real time. This method employs deep learning technologies in order to achieve the optimum trajectory of the spacecraft with a solar sail in the minimum amount of time for the purposes of an orbit manoeuvre. However, a major part of the problems that are related to orbit design is solved by striving to achieve the optimum orbit to improve its efficiency (e.g., the time when the satellite is positioned above the target as well as fuel consumption) [8; 9; 17]. These studies assume that the satellite is moving constantly on a single orbit, without doing any orbit manoeuvres, and that the elements of the orbit are changeable. There are a few studies that consider the orbit manoeuvres that focus only on changing the position of satellite constellations. Orbital manoeuvres, as opposed to orbit adjustment manoeuvres, are seldom performed, and, apart from that, they require significant amounts of fuel to perform every single operation. The aim of the manoeuvres is to achieve the desired configuration of the constellation that will meet the requirements related to reach [18; 19; 20]. [PERSON] et al. [21] developed a method of physical programming with a genetic algorithm to solve the multi-task problem of the configuration of a constellation of satellites for disaster monitoring. [PERSON] et al. [22] proposed to eliminate the disadvantages of traditional methods, such as long computation time, which usually limit engineering applications, by an innovative optimisation method: an algorithm for hybrid-resampling particle swarm optimisation (HRPSO) that improves the efficiency of constellation design.