No abstract

We describe the method of representation the aerodynamic torque in problems of mathematical modeling uncontrolled attitude motion of spacecraft Progress. The components of the torque are calculated in the nodes of the grid on the two-dimensional sphere. The calculations were based on the detailed geometric model of the spacecraft external surface. The found arrays of torque data were approximated by the segments of the Fourier series by spherical functions up to the order (8,8) inclusive. These approximations are used in the equations of attitude motion of the spacecraft. We describe the use of such equations in reconstruction of the motion of spacecraft Progress MS-07, MS-08 in the gravitational orientation mode by measurements of their angular rates and in the prognosis of electric charge from the solar arrays of the spacecraft in the mode of its single-axis solar orientation.

During deep space missions, planning and realization of dynamic operations (orbit and attitude correction manoeuvres, landing in target areas, etc.) require fast determination of spacecraft position. Due to the objective difficulties of interplanetary communication, it is interesting to solve this problem using the data from onboard sensors (in particular, the optical ones). What is more, most “transportable” of these devices give out “angular” (or quaternion) representation of reference objects’ positions instead of rectangular coordinates or at least distances. Thus, one faces the problem of determination of spacecraft state vector (in a rectangular coordinate system) from the data in “angular” coordinates in the coordinate system of measurement devices. We suggest to determine the spacecraft state vector at the required time as a solution to the problem of minimizing the quadratic cost that determines the difference between the “simulated” measurements (i.e., those that would have been made on the “simulated” trajectory generated by a current state vector approximation) and the real ones (i.e., those that were obtained from on-board sensors). To find a solution, we use a software implementation of the Levenberg-Marquardt method and a prototype of a software package that allows one to configure spacecraft sensors set and the measurement series parameters.