Study of the Pioneer Anomaly: A Problem Set

Analysis of the radio-metric tracking data from the Pioneer 10 and 11 spacecraft at distances between 20--70 astronomical units from the Sun has consistently indicated the presence of an anomalous, small, and constant Doppler frequency drift. The drift is a blue-shift, uniformly changing at the rate of (5.99 +/- 0.01) x 10^{-9} Hz/s. The signal also can be interpreted as a constant acceleration of each particular spacecraft of (8.74 +/- 1.33) x 10^{-8} cm/s^2 directed toward the Sun. This interpretation has become known as the Pioneer anomaly. We provide a problem set based on the detailed investigation of this anomaly, the nature of which remains unexplained.Comment: 14 pages, 3 figures, 5 tables, minor corrections before publicatio

Relativistic gravitational deflection of light and its impact on the modeling accuracy for the Space Interferometry Mission

We study the impact of relativistic gravitational deflection of light on the accuracy of future Space Interferometry Mission (SIM). We estimate the deflection angles caused by the monopole, quadrupole and octupole components of gravitational fields for a number of celestial bodies in the solar system. We observe that, in many cases, the magnitude of the corresponding effects is significantly larger than the 1 uas accuracy expected from SIM. This fact argues for the development of a relativistic observational model for the mission that would account for the influence of both static and time-varying effects of gravity on light propagation. Results presented here are different from the ones obtained elsewhere by the fact that we specifically account for the differential nature of the future SIM astrometric measurements. We also obtain an estimate for the accuracy of possible determination of the Eddington's parameter \gamma via SIM global astrometric campaign; we conclude that accuracy of ~7 x 10^{-6} is achievable via measurements of deflection of light by solar gravity.Comment: revtex4, 20 pages, 9 figures, 13 table