Optimization of the trajectory of launching the spacecraft into the geostationary orbit for transport system with specific impulse of the engine 600-900 s
The spacecraft flight from the low Earth orbit to the geostationary orbit is considered as a typical transport operation. The optimization of the interorbital flight, the control laws for the movement of the spacecraft during the flight and the flight trajectory are carried out. The main goal of the work is to provide the users who analyze the interorbital flight, the possibility of correct and simple estimation of the characteristic velocity for the transport operation in question. When optimizing the flight from the low Earth orbit to the geostationary orbit, a method based on the Pontryagin maximum principle is used. The problem of optimizing the trajectory reduces to the boundary-value problem. The boundary-value problem is solved using the evolutionary strategy with the adaptation of the covariance matrix. The characteristic velocity for the operation is considered as a function of the specific impulse of the engine and the initial reactive acceleration. Specific impulse of the engine is considered in the range of 600-900 s. The initial reactive acceleration is considered in the range 1.25-12.5 mm / s<sup>2</sup>. The results of the analysis are presented in the tables form of the characteristic velocity reactive as the function of initial reactive acceleration (the range 1.25-12.5 mm/s is considered) and the specific impulse (range 600-900 s). Such a range is typical, for example, a solar thermal rocket engine. Another result of the work is the analysis of the optimal flight, the analysis of the properties of the optimal flight and the optimal control law for the movement of the spacecraft during the interorbital flight. The results of the work can be used to analyze the space transport systems for interorbital spacecraft flight with the specific impulse of the engine in the range of 600-900 s. The characteristics of the optimal flight scheme are analyzed. The optimal flight path contains three characteristic sections. On the first of them, the SC engine operates at the perigee section of the multi-revolutions trajectory. In this area, the eccentricity of the orbit increases (the radius of the apogee increases, with a slight increase in the perigee altitude). The inclination of the orbit decreases a little due to a small yaw angle (less than 2 degrees). At the end of the first segment of the flight path, the radius of apogee appears to be substantially larger than the radius of the geostationary orbit. On the second part of the trajectory, the engine operates at the apogee sections of the trajectory. In this case, the radius of the perigee of the trajectory increases actively, the radius of apogee hardly increases. The yaw angle on the flight path provides an effective reduction in the inclination of the orbit. At the beginning of the section, the yaw angle value is large, the optimal yaw angle decreases in each revolution. At the end of the second section of the trajectory, the inclination of the orbit is practically zero. On the third part of the flight path (the duration of the section is approximately two revolutions of the trajectory) the active sections are located in the vicinity of the perigee of the orbit. The engine breaks the spacecraft, providing zero eccentricity of the final orbit.