Spatial-Time Relationships When Measuring The Range And The Velocity Of Spacecrafts

The problem of determining the range and the radial velocity of space crafts in the middle and deep space by a monostatic radar is considered. The tested determination method is based on the calculations concerning the relayed signal reception moment and its delay relative to both the emission moment and the Doppler shift of the carrier frequency from the emitted signal frequency (active mode). The results of the determination of the radial velocity only by calculating the Doppler shift of the onboard generator carrier frequency (passive mode) are also examined. The analysis of the space-time relationships during the curvilinear movement of the radar in an inertial geocentric system is conducted and it allows testing the radar as an autonomous measuring device that measures the range to the spacecraft in a certain coordinate system and then matches the measurement result with the estimated time suggested by this system. It is shown that practically the same result is obtained in the station coordinate system for the mean time between the signal emission and the reception relative to the calculated point that does not coincide with the radar location but changes its position with the measured signal delay depending on the time of the day and time of the year. It is established that when the range and the velocity in the station coordinate system (active operation mode) are measured simultaneously, the radial velocity is calculated relative to the target point, while the measured value depends on the angular direction set for the spacecraft. In the passive mode of operation (one-sided emission), to calculate the direction and the components of the velocity vector accurately, one needs a knowledge of the spacecraft coordinates and the scalar of orbital velocity.