## 1 Introduction  
Satellite imaging is one of the most dynamically developing areas of application of space technologies. Earth observation satellite systems may acquire images via remote sensing sensors [1]. Due to their multiple advantages, including the ability to capture image data from any place on Earth, regardless of the atmospheric conditions and time of the day, the ability to observe vast areas of land, as well as the short revisit time, remote sensing satellites are used in environmental monitoring, spatial planning, supporting crisis management activities, and supporting national defence and security. In the twenty-first century, the small satellite technology has played an important role in the development of space technologies. Significant technological progress was observed in the field of small satellites, weighing from 1 to 500 kg. One of the classes of the small satellite category is the NanoSat-class (1-10 kg). Nanosatellites were generally used to test, experiment with, and analyse new space equipment or software together with new concepts, at a minimum cost [1]. Although the number of imaging satellites continues to grow, there are still some limitations that prevent the fulfilment of all requirements of the users [2]. Such an example may be the early detection of fires. In this case, images must be acquired as often as possible so that the information about new fire outbreaks is provided as early as possible. Imaging satellites in their regular orbits are unable to observe the given area at the required time [2] and in the desired resolution. Due to that, in such a case, the satellite has to be transferred to a new orbit that will allow it to achieve high-resolution data, larger terrain coverage, and a short time of revisit. This issue is referred to as the orbit optimisation problem. It has been long known that the relation between the lifespan of a satellite and the altitude of its orbit depends on several factors. These include limitations resulting from atmospheric drag, factors related to radiation, such as high-energy particles, damage caused by micrometeoroids, atomic oxygen (AO), and ultraviolet (UV) radiation. In particular, the harsh conditions prevailing in low Earth orbit (LEO) can lead to complex, mutually reinforcing surface and satellite system degradation processes. Therefore, when considering orbit optimisation, a thorough assessment of these environmental conditions should be conducted, especially in the context of extending the operational lifespan of a nanosatellite [3]. However, the limitations for circular and elliptical orbits are slightly different. All spaceports are constructed in the vicinity of the equator (as close to the equator as possible for the given country), so that the rockets that are launched to the east gain some free velocity as a result of the Earth's rotation. Equatorial space ports offer the possibility to achieve a high inclination (the angle of inclination of the orbital plane to the equatorial plane) [4]. Defining a specific orbit and conducting the orbit manoeuvres for satellites are extremely important problems in the science of orbital mechanics. As a result, the issue of transferring a spacecraft between orbits has been gaining increasing attention in recent years [5]. Many important problems in astrodynamics are related to the modification of the satellite's orbit in order to achieve a specific trajectory for the planned space mission [6]. The aim of orbit manoeuvres is to transfer the spacecraft from one orbit to another. Such manoeuvres may be radical, for example transferring the satellite from a low parking orbit to inter-planetary trajectory. However, they may also be small, like at the last stages of the meeting of two spacecrafts. Changing the orbit requires launching the rocket engines [7], e.g., by applying a short impulse. The speed and inclination of the satellite may be modified by the rocket engine thrust that is specifically directed and lasts as long as it is necessary to achieve the desired result.