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The Pioneer 10 and 11 spacecraft yielded the most precise navigation in deep space to date. These spacecraft had exceptional acceleration sensitivity. However, analysis of their radio-metric tracking data has consistently indicated that at heliocentric distances of $\sim 20-70$ astronomical units, the orbit determinations indicated the presence of a small, anomalous, Doppler frequency drift. The drift is a blue-shift, uniformly changing with a rate of $\sim(5.99 \pm 0.01)\times 10^{-9}$ Hz/s, which can be interpreted as a constant sunward acceleration of each particular spacecraft of $a_P = (8.74 \pm 1.33)\times 10^{-10} {\rm m/s^2}$. This signal has become known as the Pioneer anomaly. The inability to explain the anomalous behavior of the Pioneers with conventional physics has contributed to growing discussion about its origin. There is now an increasing number of proposals that attempt to explain the anomaly outside conventional physics. This progress emphasizes the need for a new experiment to explore the detected signal. Furthermore, the recent extensive efforts led to the conclusion that only a dedicated experiment could ultimately determine the nature of the found signal. We discuss the Pioneer anomaly and present the next steps towards an understanding of its origin. We specifically focus on the development of a mission to explore the Pioneer Anomaly in a dedicated experiment conducted in deep space., Comment: 8 pages, 9 figures; invited talk given at the 2005 ESLAB Symposium "Trends in Space Science and Cosmic Vision 2020", 19-21 April 2005, ESTEC, Noordwijk, The Netherlands

We review the results from {\it Mariner 10} regarding Mercury's gravity field and the results from radar ranging regarding topography. We discuss the implications of improving these results, including a determination of the polar component, as well as the opportunity to perform relativistic gravity tests with a future {\it Mercury Orbiter}. With a spacecraft placed in orbit with periherm at 400 km altitude, apherm at 16,800 km, period 13.45 hr and latitude of periherm at +30 deg, one can expect a significant improvement in our knowledge of Mercury's gravity field and geophysical properties. The 2000 Plus mission that evolved during the European Space Agency (ESA) {\it Mercury Orbiter} assessment study can provide a global gravity field complete through the 25th degree and order in spherical harmonics. If after completion of the main mission, the periherm could be lowered to 200 km altitude, the gravity field could be extended to 50th degree and order. We discuss the possibility that a search for a Hermean ionosphere could be performed during the mission phases featuring Earth occultations. Because of its relatively large eccentricity and close proximity to the Sun, Mercury's orbital motion provides one of the best solar-system tests of general relativity. Consequently, we emphasize the number of feasible relativistic gravity tests that can be performed within the context of the parameterized post-Newtonian formalism - a useful framework for testing modern gravitational theories. We pointed out that current results on relativistic precession of Mercury's perihelion are uncertain by 0.5 %, and we discuss the expected improvement using {\it Mercury Orbiter}. We discuss the importance of {\it Mercury Orbiter} for setting limits on a possible time variation in the, Comment: 23 pages, LaTeX, no figures

On February 29, 2012 the twin NASA Gravity Recovery And Interior Laboratory (GRAIL) spacecraft, Ebb and flow, achieved precise synchronized formation for collecting highly sensitive lunar gravity data. This was accomplished after performing a total of 27 propulsive maneuvers between the two spacecraft (13 on Ebb, 14 on Flow) over six months. Each 300 kg GRAIL spacecraft independently flew a 3.8-month, low-energy trajectory to reach the Moon after separation from the launch vehicle on September 10, 2011. The space craft were captured into 11.5 hr co- planar polar orbits after performing Lunar Orbit Insertion (LOI) maneuvers on New Years Eve (Dec 31, 2011) and New Years Day (Jan 1, 2012), respectively for Ebb, and Flow. Once captured, each spacecraft performed clusters of period reduction maneuvers to bring their orbit periods down to just less than 2 hrs. Finally, the orbiters we replaced into science formation by performing five strategic maneuvers (2 on Ebb, 3 on Flow). These maneuvers ensured 3 months of orbit life time with mean altitudes of 55 km and separations of 82-217 km by targeting the orbits' eccentricity vectors to specific locations. This paper will discuss the navigation strategy and performance of the twin GRAIL spacecraft from the September 10, 2011 launch through the end of the Prime Mission Science Phase in June 2012.

The Dynamic Science investigation on the STARDUST mission has been described previously. The data delivered by the STARDUST Project is multifold, but basically it consists of radio Doppler data from the Deep Space Network (DSN) and attitude control data (ACS) from the spacecraft. Doppler data were successfully recorded by JPL's Navigation System (closed-loop data) and also by its Radio Science System (open-loop data) at DSN stations DSS43 near Canberra Australia and at DSS14 at Goldstone California. Attitude control data were also successfully delivered to the Dynamic Science Team. Here we describe a preliminary analysis of the data. Beyond a closest approach distance of 150 km, a Doppler detection of a the Wild 2 nucleus mass was not expected. The current best estimate of the closest approach distance is 236.4 km, and as expected, any mass signal in the Doppler data is hopelessly buried in the noise. We have attempted to fit the data to a mass model with no success. However, analysis of the Doppler data and the ACS data for particle impacts on the spacecraft's Whipple shields is in progress, and will be reported at the meeting. The DSS43 closed-loop Doppler residuals are plotted as a function of time from the current best estimate of the time of Wild 2 closest approach, 2 January 2004, 19:43:11.7 UTC, Earth-receive time at the station.

Radio Doppler data from two Ganymede encounters (G1 and G2) on the first two orbits in the Galileo mission have been analyzed previously for gravity information . For a satellite in hydrostatic equilibrium, its gravitational field can be modeled adequately by a truncated spherical harmonic series of degree two. However, a fourth degree field is required in order to fit the second Galileo flyby (G2). This need for a higher degree field strongly suggests that Ganymede s gravitational field is perturbed by a gravity anomaly near the G2 closest approach point (79.29 latitude, 123.68 west longitude). In fact, a plot of the Doppler residuals , after removal of the best-fit model for the zero degree term (GM) and the second degree moments (J2 and C22), suggests that if an anomaly exists, it is located downtrack of the closest approach point, closer to the equator.

Radio Doppler data from the Cassini spacecraft during its solar conjunction in June 2002 can be used to test General Relativity.

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Radio metric data from the Pioneer 10/11, Galileo, and Ulysses Spacecraft indicate an apparent anomalous, constant, acceleration acting on the spacecraft with a magnitude ~8.5 x 10(sup -8) cm/s(sup 2), directed towards the Sun.

Using radio Doppler data from a single encounter (C3) of the Galileo spacecraft with Callisto, we have reported previously that this outermost Galilean moon might be undifferentiated.

Doppler data generated with the Galileo spacecraft's radio carrier wave during two Europa encounters on 19 December 1996 (E4) and 20 February 1997 (E6) were used to measure Euroapa's external gravitational field. The measurements indicate that Europa has a predominantly water ice-liquid outer shell about 100 to 200 klilometers thick and a deep interior with a density in excess of about 4000 kilograms per cubic meter.

Before the arrival of the Galileo spacecraft in the jovian system, there was little information on the interior structures of Jupiter's four Galilean satellites. Results obtained during the Galileo Mission are described.

Galileo's first encounter with Callisto took place on 4 November 1996, and the gravity signal was detected in the radio Doppler data recorded during the encounter.

Here we report measurements by the Galileo spacecraft of Ganymede's overall density and the spherical harmonics, J2, and C22, of its gravitational field.

By means of a topographic Legendre expansion complete through the second

We report a search for waves from supermassive coalescing binaries using a 10.5 day Pioneer 10 data set taken in 1988. Depending on the time to coalescence, the initial frequency of the wave, and the length of the observing interval, a coalescing binary waveform appears in the tracking record either as a sinusoid, a 'chirp', or as a more complicated signal. We searched our data for coalescing binary waveforms in all three regimes. We successfully detected a (fortuitous) 'chirp' signal caused by the varying spin rate of the spacecraft; this nicely served as a calibration of the data quality and as a test of our analysis procedures on real data. We did not detect any signals of astronomical origin in the millihertz band to an upper limit of about 7 x 10 exp -15 (rms amplitude). This is the first time spacecraft Doppler data have been analyzed for coalescing binary waveforms, and the upper limits reported here are the best to date for any waveform in the millihertz band.

The gravitation and celestial mechanics investigations that are to be conducted during the cruise and Orbiter phases of the Galileo Mission cover four investigation categories: (1) the gravity fields of Jupiter and its four major satellites; (2) a search for gravitational radiation; (3) mathematical modeling of general relativistic effects on Doppler ranging data; and (4) improvements of the Jupiter ephemeris via Orbiter ranging. Also noted are two secondary objectives, involving a range fix during Venus flyby and the determination of the earth's mass on the bases of the two earth gravity assists used by the mission.

Results are presented from the analysis of solar-system astrometric data, notably the range data to the Viking landers on Mars. A least-squares fit of the parameters of the solar system model to these data limits a simple time variation in the effective Newtonian gravitational constant to (2 + or - 4) x 10 to the -12th/yr and a rate of drift of atomic clocks relative to the implicit clock of relativistic dynamics to (1 + or - 8) x 10 to the -12th/yr. The error limits quoted are the result of uncertainties in the masses of the asteroids.

Improved gravity coefficients for Saturn, its satellites and rings are calculated on the basis of a combination of Pioneer 11 spacecraft Doppler tracking data and earth-based determinations of Saturn natural satellite apse and node rates. Solutions are first obtained separately from the coherent Doppler tracking data obtained for the interval from August 20 to September 4, surrounding the time of closest approach, with the effects of solar plasma on radio signal propagation taken into account, and from secular rates for Mimas, Enceladus, Tethys, Dione, Rhea and Titan determined from astrometric data by Kozai (1957, 1976) and Garcia (1972). Combination of the data by the use of the Pioneer solution and corresponding unadjusted covariance matrix as a priori information for a secular rate analysis results in values for the total ring mass of essentially zero at a standard error level of 1.7 x 10 to the -6th Saturn masses, a ratio of solar mass to that of the Saturn system of 3498.09 + or - 0.22, masses of Rhea, Titan and Iapetus of 4.0 + or - 0.9, 238.8 + or - 3, and 3.4 + or - 1.3 x 10 to the -6th Saturn masses, respectively, and second and fourth zonal harmonics of 16,479 + or - 18 and -937 + or - 38, respectively. The harmonic coefficients are noted to be important as boundary conditions in the modeling of the Saturn interior.

The Cottrell gravity research observatory and work in progress are described. Equipment in place and equipment to be installed, the cryogenic gravity meter (CGM), concrete pads to support the vertical seismometer, CGM, and guest experiments, techniques of data analysis, and improvements needed in the CGM are discussed. Harmonic earth eigenvibrations with multipole moments are examined and their compatibility with a fictitious black hole binary system (of which the primary central mass is assigned a value one million solar masses) located 400 light-years away is shown by calculations.

The application of MACSYMA to general first order perturbation theory in celestial mechanics is explored. Methods of derivation of small variations in the Keplerian orbital elements are developed. As an example of the methods, the small general relativistic perturbations on the two-body Newtonian motion, resulting from the rotation of the central body, are developed in detail.

Current least squares fits to solar system data, including transit circle observations of the terrestrial and giant planets, radar observations of the terrestrial planets, Mariner 9 range fixes to Mars, and Pioneer 10/11 range fixes to Jupiter, have yielded some new results of interest to experimental relativity. Solutions have been obtained for the parameterized post-Newtonian (PPN) parameters beta and gamma, the solar gravitational quadrupole moment J2, a time variation in the gravitational constant G, and four Nordtvedt parameters.