Obtaining the Chandrayaan-3 lander coordinates on the lunar surface by the Doppler measurements of the transmitted signal with an Earth-based receiving system

We determine the selenographic coordinates of the Chandrayaan-3 lander by Doppler measurements of its signal. The Chandrayaan-3 successfully landed in the south polar region of the Moon near the craters Manzinus and Simpelius on 23 August 2023 and had been transmitting scientific information and telemetry to Earth in the S and X-bands during 14 days. The accuracy of the obtained Doppler measurements do not allow unambiguous determination of the lander location on the lunar surface because the transmitter was degrading during the entire observing interval. For this reason, in our work we have evaluated the influence of the Doppler measurement characteristics on the accuracy of the transmitter location determination. It has been shown that for a signal with a relative frequency instability of the order of $10^{-13}$, the achievable accuracy of coordinate determination is about 34 meters.