Improved mathematical apparatus for determining the observed area of the landed earth region in space monitoring problems

The article proposes an improved mathematical apparatus adapted for modeling the processes of space monitoring of the earth's surface, in particular, for determining the geographic coordinates and sizes of the observed area of given regions of the Earth. In this case, a three-pronged problem is solved: finding the projection of the viewing zone of the onboard target equipment on a flat and spherical underlying surface; calculation of the area of land plots of arbitrary shape and size; calculation of the observed part of a given region of the Earth as a result of the intersection of a plurality of elements of the projection of the survey zone and elements of the entire area of the observation area. The proposed mathematical apparatus can be used to model the processes of space observations in the planning stages of space imagery and to evaluate the results of this survey, as well as in the educational process.