Abstract. A mathematical approach is proposed to calculate the duration of survey by a spacecraft equipped with a synthetic aperture radar to assess the potential capabilities of the observation system. The geometry of the radar survey is characterized by a system of three equations governing the slant range, the rotation ellipsoid, and the Doppler frequency of the received signal, which are specified in a three-dimensional inertial coordinate system associated with the Earth. This system of equations does not have an explicit solution, therefore, a variant of solving the problem of identifying the analytical relationship between the parameters characterizing the position of the spacecraft on the trajectory and the angles of its rotation, the angles of deflection of the antenna pattern, and the parameters of probing pulses is proposed. To simplify the solution, the local sphericity of the Earth is assumed in the survey area with a known local radius. Determination of the survey duration is required to select the necessary radar operation mode in order to obtain a radar image of the observation area with the wanted resolution within a given capture band. A technique for planning an area survey with a radar based on calculation of the observation duration is presented. Relationships are obtained that make it possible to evaluate the capabilities of a radar in solving survey problems or in designing a surveillance system, as well as to determine reasonable requirements for choosing the main characteristics of a radar and ballistic parameters of a spacecraft constellation.

Keywords: observation duration, space surveillance system, synthetic aperture radar, radar survey, survey mode, survey parameters, photogrammetry

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