The Measurement of the Hubble Constant H_0 in the Solar System

Abstract

This paper discusses the methodology necessary to measure the Hubble constant Ho to a high degree of accuracy based upon Doppler tracking of spacecraft in the solar system. Using this methodology with available published data we determine a model independent value of the Hubble constant for the current epoch in the solar system to be Ho = 2.59 \pm 0.05 x 10^-18 (s^-1) or as 79.8 \pm 1.7 (km/s/Mpc). We calculate the direct effect of the Cosmic Redshift on Doppler tracking of spacecraft in the solar system. It is shown that with current tracking systems, such as NASA's Deep Space Tracking Network, when the return trip light time of the Doppler signal exceeds a certain threshold, imposed by the stability of the frequency standard, the effect of the Cosmic Redshift is coherently conserved in the returning Doppler signal. We demonstrate that in an underdetermined orbit, one determined by line of sight Doppler alone, that if this Cosmic Redshift term is not accounted for, the orbit determination program (ODP) miscalculates the actual recessional velocity of the spacecraft from the measured recessional velocity causing a mismatch between the actual and the predicted trajectory of the spacecraft. One consequence is that the ODP will generate Doppler residuals, the difference between the actual trajectory and the predicted trajectory which show an anomalous force. When this effect is integrated in long arc solutions, it can grow to considerable magnitude. We show that the ODP residuals uniquely separate the Cosmic Redshift term from velocity Doppler sources and that the solution can provide an accurate determination of Ho.