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

A Search for New Physics with the BEACON Mission

The primary objective of the Beyond Einstein Advanced Coherent Optical Network (BEACON) mission is a search for new physics beyond general relativity by measuring the curvature of relativistic space-time around Earth. This curvature is characterized by the Eddington parameter \gamma -- the most fundamental relativistic gravity parameter and a direct measure for the presence of new physical interactions. BEACON will achieve an accuracy of 1 x 10^{-9} in measuring the parameter \gamma, thereby going a factor of 30,000 beyond the present best result involving the Cassini spacecraft. Secondary mission objectives include: (i) a direct measurement of the "frame-dragging" and geodetic precessions in the Earth's rotational gravitomagnetic field, to 0.05% and 0.03% accuracy correspondingly, (ii) first measurement of gravity's non-linear effects on light and corresponding 2nd order spatial metric's effects to 0.01% accuracy. BEACON will lead to robust advances in tests of fundamental physics -- this mission could discover a violation or extension of general relativity and/or reveal the presence of an additional long range interaction in physics. BEACON will provide crucial information to separate modern scalar-tensor theories of gravity from general relativity, probe possible ways for gravity quantization, and test modern theories of cosmological evolution.Comment: 8 pages, 2 figures, 2 table

Could the Pioneer anomaly have a gravitational origin?

If the Pioneer anomaly has a gravitational origin, it would, according to the equivalence principle, distort the motions of the planets in the Solar System. Since no anomalous motion of the planets has been detected, it is generally believed that the Pioneer anomaly can not originate from a gravitational source in the Solar System. However, this conclusion becomes less obvious when considering models that either imply modifications to gravity at long range or gravitational sources localized to the outer Solar System, given the uncertainty in the orbital parameters of the outer planets. Following the general assumption that the Pioneer spacecraft move geodesically in a spherically symmetric spacetime metric, we derive the metric disturbance that is needed in order to account for the Pioneer anomaly. We then analyze the residual effects on the astronomical observables of the three outer planets that would arise from this metric disturbance, given an arbitrary metric theory of gravity. Providing a method for comparing the computed residuals with actual residuals, our results imply that the presence of a perturbation to the gravitational field necessary to induce the Pioneer anomaly is in conflict with available data for the planets Uranus and Pluto, but not for Neptune. We therefore conclude that the motion of the Pioneer spacecraft must be non-geodesic. Since our results are model independent within the class of metric theories of gravity, they can be applied to rule out any model of the Pioneer anomaly that implies that the Pioneer spacecraft move geodesically in a perturbed spacetime metric, regardless of the origin of this metric disturbance.Comment: 16 pages, 6 figures. Rev. 3: Major revision. Accepted for publication in Phys. Rev. D. Rev. 4: Added two reference

LATOR Covariance Analysis

We present results from a covariance study for the proposed Laser Astrometric Test of Relativity (LATOR) mission. This mission would send two laser-transmitter spacecraft behind the Sun and measure the relative gravitational light bending of their signals using a hundred-meter-baseline optical interferometer to be constructed on the International Space Station. We assume that each spacecraft is equipped with a $< 1.9 \times 10^{-13} \mathrm{m} \mathrm{s}^2 \mathrm{Hz}^{-1/2}$ drag-free system and assume approximately one year of data. We conclude that the observations allow a simultaneous determination of the orbit parameters of the spacecraft and of the Parametrized Post-Newtonian (PPN) parameter $\gamma$ with an uncertainty of $2.4 \times 10^{-9}$. We also find a $6 \times 10^{-9}$ determination of the solar quadrupole moment, $J_2$, as well as the first measurement of the second-order post-PPN parameter $\delta$ to an accuracy of about $10^{-3}$.Comment: 9 pages, 3 figures. first revision: minor changes to results. Second revision: additional discussion of orbit modelling and LATOR drag-free system requirement feasibility. Added references to tables I and V (which list PPN parameter uncertainties), removed word from sentence in Section III. 3rd revision: removed 2 incorrect text fragments (referring to impact parameter as distance of closest approach) and reference to upcoming publication of ref. 2, removed spurious gamma from eq. 1 - Last error is still in cqg published versio

Effects of standard and modified gravity on interplanetary ranges

We numerically investigate the impact on the two-body range by several Newtonian and non-Newtonian dynamical effects for some Earth-planet (Mercury, Venus, Mars, Jupiter, Saturn) pairs in view of the expected cm-level accuracy in some future planned or proposed interplanetary ranging operations (abridged).Comment: LaTex, World Scientific style, 46 pages, 55 figures, 1 table, 57 references. Version in press in International Journal of Modern Physics D (IJMPD

Chameleon effect and the Pioneer anomaly

The possibility that the apparent anomalous acceleration of the Pioneer 10 and 11 spacecraft may be due, at least in part, to a chameleon field effect is examined. A small spacecraft, with no thin shell, can have a more pronounced anomalous acceleration than a large compact body, such as a planet, having a thin shell. The chameleon effect seems to present a natural way to explain the differences seen in deviations from pure Newtonian gravity for a spacecraft and for a planet, and appears to be compatible with the basic features of the Pioneer anomaly, including the appearance of a jerk term. However, estimates of the size of the chameleon effect indicate that its contribution to the anomalous acceleration is negligible. We conclude that any inverse-square component in the anomalous acceleration is more likely caused by an unmodelled reaction force from solar-radiation pressure, rather than a chameleon field effect.Comment: 16 pages; to appear in Phys.Rev.

Murphy et al. Reply to the Comment by Kopeikin on "Gravitomagnetic Influence on Gyroscopes and on the Lunar Orbit"

Lunar laser ranging analysis, as regularly performed in the solar system barycentric frame, requires the presence of the gravitomagnetic term in the equation of motion at the strength predicted by general relativity. The same term is responsible for the Lense Thirring effect. Any attempt to modify the strength of the gravitomagnetic interaction would have to do so in a way that does not destroy the fit to lunar ranging data and other observations.Comment: 1 page; accepted for publication in Physcal Review Letters; refers to gr-qc/070202

The Laser Astrometric Test of Relativity: Science, Technology, and Mission Design

The Laser Astrometric Test of Relativity (LATOR) experiment is designed to explore general theory of relativity in the close proximity to the Sun -- the most intense gravitational environment in the solar system. Using independent time-series of highly accurate measurements of the Shapiro time-delay (interplanetary laser ranging accurate to 3 mm at 2 AU) and interferometric astrometry (accurate to 0.01 picoradian), LATOR will measure gravitational deflection of light by the solar gravity with accuracy of 1 part in a billion -- a factor ~30,000 better than currently available. LATOR will perform series of highly-accurate tests in its search for cosmological remnants of scalar field in the solar system. We present science, technology and mission design for the LATOR mission.Comment: 12 pages, 4 figures. To appear in the proceedings of the International Workshop "From Quantum to Cosmos: Fundamental Physics Research in Space", 21-24 May 2006, Warrenton, Virginia, USA http://physics.jpl.nasa.gov/quantum-to-cosmos

Observational Limits on Gauss-Bonnet and Randall-Sundrum Gravities

We discuss the possibilities of experimental search for new physics predicted by the Gauss-Bonnet and the Randall-Sundrum theories of gravity. The effective four-dimensional spherically-symmetrical solutions of these theories are analyzed. We consider these solutions in the weak-field limit and in the process of the primordial black holes evaporation. We show that the predictions of discussed models are the same as of General Relativity. So, current experiments are not applicable for such search therefore different methods of observation and higher accuracy are required.Comment: 7 pages, accepted to JET

The Effect of Companions on the SIM Reference Frame

The Space Interferometry Mission (SIM) is a 10-m Michelson space-based optical interferometer designed for precision astrometry (4 microarcseconds, 3 microarcseconds/year) with better accuracy than before over a narrow field of view. One of the primary objectives of the SIM instrument is to determine accurately the directions to a grid of stars, together with their proper motions and parallax, improving a priori knowledge by nearly three orders of magnitude over Hipparcos and one order of magnitude over FAME's planned accuracy (Johnston, 2000). The instrument does not measure directly the angular separation between stars, but rather it measures the projection of each star's direction vector onto the interferometer baseline vector by measuring the pathlength delay of starlight as it passes through the two arms of the interferometer. The accuracy and stability of SIM's celestial reference frame is subject to degradation over the 5-year mission from the reflex motion induced by massive companions of the objects used to construct the celestial reference frame. The authors present the results of simulations that show the sensitivity of reference frame accuracy to companions as a function of mass and period. They assume that pre-launch ground surveys will eliminate all objects with RMS radial velocity greater than 10 m/s. They further assume that the standard astrometric parameters of position, parallax, and proper motion plus acceleration terms in right ascension and declination will be allowed to absorb reflex motion