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

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

Non-dopplerian cosmological redshift parameters in a model of graviton-dusty universe

Possible effects are considered which would be caused by a hypothetical superstrong interaction of photons or massive bodies with single gravitons of the graviton background. If full cosmological redshift magnitudes are caused by the interaction, then the luminosity distance in a flat non-expanding universe as a function of redshift is very similar to the specific function which fits supernova cosmology data by Riess et al. From another side, in this case every massive body, slowly moving relatively to the background, would experience a constant acceleration, proportional to the Hubble constant, of the same order as a small additional acceleration of Pioneer 10, 11.Comment: 5 pages. It was presented: at SIGRAV'2000 Congress, Italy (this version); in Proc. of the Int. Symp. "FFP 4" (9-13 Dec 2000, Hyderabad, India), Sidharth& Altaisky, Eds., Kluwer Academic/Plenum, 2001;in Proc. of the 4th Edoardo Amaldi Conference on GW (Perth, W. Australia, 8-13 July 2001

The Gravitomagnetic Influence on Gyroscopes and on the Lunar Orbit

Gravitomagnetism--a motional coupling of matter analogous to the Lorentz force in electromagnetism--has observable consequences for any scenario involving differing mass currents. Examples include gyroscopes located near a rotating massive body, and the interaction of two orbiting bodies. In the former case, the resulting precession of the gyroscope is often called ``frame dragging,'' and is the principal measurement sought by the Gravity Probe-B experiment. The latter case is realized in the earth-moon system, and the effect has in fact been confirmed via lunar laser ranging (LLR) to approximately 0.1% accuracy--better than the anticipated accuracy of the Gravity-Probe-B result. This paper shows the connnection between these seemingly disparate phenomena by employing the same gravitomagnetic term in the equation of motion to obtain both gyroscopic precession and modification of the lunar orbit. Since lunar ranging currently provides a part in a thousand fit to the gravitomagnetic contributions to the lunar orbit, this feature of post-Newtonian gravity is not adjustable to fit any anomalous result beyond the 0.1% level from Gravity Probe-B without disturbing the existing fit of theory to the 36 years of LLR data.Comment: 4 pages; accepted for publication in Physical Review Letter