RESUMO
Gravity Probe B, launched 20 April 2004, is a space experiment testing two fundamental predictions of Einstein's theory of general relativity (GR), the geodetic and frame-dragging effects, by means of cryogenic gyroscopes in Earth orbit. Data collection started 28 August 2004 and ended 14 August 2005. Analysis of the data from all four gyroscopes results in a geodetic drift rate of -6601.8±18.3 mas/yr and a frame-dragging drift rate of -37.2±7.2 mas/yr, to be compared with the GR predictions of -6606.1 mas/yr and -39.2 mas/yr, respectively ("mas" is milliarcsecond; 1 mas=4.848×10(-9) rad).
RESUMO
In this paper, we present a method to measure the frequency and the frequency change rate of a digital signal. This method consists of three consecutive algorithms: frequency interpolation, phase differencing, and a third algorithm specifically designed and tested by the authors. The succession of these three algorithms allowed a 5 parts in 10(10) resolution in frequency determination. The algorithm developed by the authors can be applied to a sampled scalar signal such that a model linking the harmonics of its main frequency to the underlying physical phenomenon is available. This method was developed in the framework of the gravity probe B (GP-B) mission. It was applied to the high frequency (HF) component of GP-B's superconducting quantum interference device signal, whose main frequency f(z) is close to the spin frequency of the gyroscopes used in the experiment. A 30 nHz resolution in signal frequency and a 0.1 pHz/s resolution in its decay rate were achieved out of a succession of 1.86 s-long stretches of signal sampled at 2200 Hz. This paper describes the underlying theory of the frequency measurement method as well as its application to GP-B's HF science signal.
