Geodetic Precession Research Articles

Gravity Probe B: Final Results of a Space Experiment to Test General Relativity

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).

Constraining spacetime torsion with the Moon and Mercury

We report a search for new gravitational physics phenomena based on Riemann-Cartan theory of general relativity including spacetime torsion. Starting from the parametrized torsion framework of Mao, Tegmark, Guth, and Cabi, we analyze the motion of test bodies in the presence of torsion, and, in particular, we compute the corrections to the perihelion advance and to the orbital geodetic precession of a satellite. We consider the motion of a test body in a spherically symmetric field, and the motion of a satellite in the gravitational field of the Sun and the Earth. We describe the torsion field by means of three parameters, and we make use of the autoparallel trajectories, which in general differ from geodesics when torsion is present. We derive the specific approximate expression of the corresponding system of ordinary differential equations, which are then solved with methods of celestial mechanics. We calculate the secular variations of the longitudes of the node and of the pericenter of the satellite. The computed secular variations show how the corrections to the perihelion advance and to the orbital de Sitter effect depend on the torsion parameters. All computations are performed under the assumptions of weak field and slow motion. To test our predictions, we use the measurements of the Moon's geodetic precession from lunar laser ranging data, and the measurements of Mercury's perihelion advance from planetary radar ranging data. These measurements are then used to constrain suitable linear combinations of the torsion parameters.

Geodetic precession and frame dragging observed far from massive objects and close to a gyroscope

Abstract Total precession (geodetic precession and frame dragging) depends on the velocity of each source of gravitation, which means that it depends on the choice of the coordinate system. We consider the latter as an anomaly specifically in the Gravity Probe B experiment, we investigated it and solved this anomaly. Thus, we proved that if our present expression for the geodetic precession is correct, then the frame dragging should be 25% less than its predicted value.

Geodetic precession and strong gravitational lensing in dynamical Chern–Simons-modified gravity

We have investigated the geodetic precession and the strong gravitational lensing in the slowly rotating black hole in the dynamical Chern–Simons-modified gravity theory. We present the formulas of the orbital period T and the geodetic precession angle ΔΘ for the timelike particles in the circular orbits around the black hole, which shows that the change of the geodetic precession angle with the Chern–Simons coupling parameter ξ is converse to the change of the orbital period with ξ for fixed a. We also discuss the effects of the Chern–Simons coupling parameter on the strong gravitational lensing when the light rays pass close to the black hole and obtain that for the stronger Chern–Simons coupling the prograde photons may be captured more easily, and conversely, the retrograde photons are harder to capture in the slowly rotating black hole in the dynamical Chern–Simons-modified gravity. Supposing that the gravitational field of the supermassive central object of the Galaxy can be described by this metric, we estimated the numerical values of the main observables for gravitational lensing in the strong field limit.

Research of Gravitation in Flat Minkowski Space

In this paper it is introduced and studied an alternative theory of gravitation in flat Minkowski space. Using an antisymmetric tensor, which is analogous to the tensor of electromagnetic field, a non-linear connection is introduced. It is very convenient for studying the perihelion/periastron shift, deflection of the light rays near the Sun and the frame dragging together with geodetic precession, i.e. effects where angles are involved. Although the corresponding results are obtained in rather different way, they are the same as in the General Relativity. The results about the barycenter of two bodies are also the same as in the General Relativity. Comparing the derived equations of motion for the $n$-body problem with the Einstein-Infeld-Hoffmann equations, it is found that they differ from the EIH equations by Lorentz invariant terms of order $c^{-2}$.

Celestial reference frames and the gauge freedom in the post-Newtonian mechanics of the Earth–Moon system

We introduce the Jacobi coordinates adopted to the advanced theoretical analysis of the relativistic Celestial Mechanics of the Earth–Moon system. Theoretical derivation utilizes the relativistic resolutions on reference frames adopted by the International Astronomical Union (IAU) in 2000. The resolutions assume that the Solar System is isolated and space-time is asymptotically flat at infinity and the primary reference frame covers the entire space-time, has its origin at the Solar System barycenter (SSB) with spatial axes stretching up to infinity. The SSB frame is not rotating with respect to a set of distant quasars that are assumed to be at rest on the sky forming the International Celestial Reference Frame (ICRF). The second reference frame has its origin at the Earth–Moon barycenter (EMB). The EMB frame is locally inertial and is not rotating dynamically in the sense that equation of motion of a test particle moving with respect to the EMB frame, does not contain the Coriolis and centripetal forces. Two other local frames—geocentric and selenocentric—have their origins at the center of mass of Earth and Moon respectively and do not rotate dynamically. Each local frame is subject to the geodetic precession both with respect to other local frames and with respect to the ICRF because of their relative motion with respect to each other. Theoretical advantage of the dynamically non-rotating local frames is in a more simple mathematical description of the metric tensor and relative equations of motion of the Moon with respect to Earth. Each local frame can be converted to kinematically non-rotating one after alignment with the axes of ICRF by applying the matrix of the relativistic precession as recommended by the IAU resolutions. The set of one global and three local frames is introduced in order to decouple physical effects of gravity from the gauge-dependent effects in the equations of relative motion of the Moon with respect to Earth.

Post-Newtonian Reference Frames for Advanced Theory of the Lunar Motion and for a New Generation of Lunar Laser Ranging

Post-Newtonian Reference Frames for Advanced Theory of the Lunar Motion and for a New Generation of Lunar Laser RangingWe overview a set of post-Newtonian reference frames for a comprehensive study of the orbital dynamics and rotational motion of Moon and Earth by means of lunar laser ranging (LLR). We employ a scalar-tensor theory of gravity depending on two post-Newtonian parameters, β and γ, and utilize the relativistic resolutions on reference frames adopted by the International Astronomical Union (IAU) in 2000. We assume that the solar system is isolated and space-time is asymptotically flat at infinity. The primary reference frame covers the entire space-time, has its origin at the solar-system barycenter (SSB) and spatial axes stretching up to infinity. The SSB frame is not rotating with respect to a set of distant quasars that are forming the International Celestial Reference Frame (ICRF). The secondary reference frame has its origin at the Earth-Moon barycenter (EMB). The EMB frame is locally-inertial and is not rotating dynamically in the sense that equation of motion of a test particle moving with respect to the EMB frame, does not contain the Coriolis and centripetal forces. Two other local frames - geocentric (GRF) and selenocentric (SRF) - have their origins at the center of mass of Earth and Moon respectively and do not rotate dynamically. Each local frame is subject to the geodetic precession both with respect to other local frames and with respect to the ICRF because of their relative motion with respect to each other. Theoretical advantage of the dynamically non-rotating local frames is in a more simple mathematical description. Each local frame can be aligned with the axes of ICRF after applying the matrix of the relativistic precession. The set of one global and three local frames is introduced in order to fully decouple the relative motion of Moon with respect to Earth from the orbital motion of the Earth-Moon barycenter as well as to connect the coordinate description of the lunar motion, an observer on Earth, and a retro-reflector on Moon to directly measurable quantities such as the proper time and the round-trip laser-light distance. We solve the gravity field equations and find out the metric tensor and the scalar field in all frames which description includes the post-Newtonian multipole moments of the gravitational field of Earth and Moon. We also derive the post-Newtonian coordinate transformations between the frames and analyze the residual gauge freedom.

Gravity Probe B experiment and gravitomagnetism

Gravitomagnetism is a low velocity and weak gravitational field approximation of general relativity. It provides a simple approach to post-Newtonian gravitational phenomena via electromagnetic analogy. Intended for advanced undergraduate students, the present paper applies gravitomagnetism to the quantitative study of the geodetic precession and frame dragging effects, both verified recently in the Gravity Probe B experiment. The result obtained is identical with Schiff's formula.

Multiband Photometry of the Chromospherically Active & Spotted Binary System IM Peg—the Guide Star for the Gravity Probe B Mission

ABSTRACTWe report on the starspot properties of IM Pegasi—the guide star of the Gravity Probe B (GP-B) satellite. GP-B’s mission is to measure two predicted consequences of general relativity—the frame-dragging and geodetic effects—via its extremely precise onboard gyroscopes. However, IM Peg is a chomospherically active binary system with a luminous K2 III primary star showing rotationally modulated (Prot ≈ 24.5 days) light variations from starspots. The starspots can potentially cause problems as GP-B can erroneously interpret a change in starspot coverage (and corresponding shifts in the light center) as the star’s movement. This apparent shift can also be exacerbated by possible changes in the light center (photocenter) of the binary system arising from changes in the light balance with the fainter ∼1 M⊙(main-sequence early G-type star) component. Since 2000, we have carried out multiband high-precision photoelectric photometry of IM Peg to determine its activity and starspot coverage. Our photometry uses Strömgren uvby intermediate-band filters, VRI filters, and TiO (720/750 nm) narrowband filter sets. Measurements were made relative to nearby comparison and check stars using 0.8 m and 0.25 m telescopes. Analysis of TiO and multiband continuum photometry constrains the starspot areas, temperatures, and surface distributions. The photometry has been modeled using the maximum entropy and Tikhonov regularizations to determine the properties of starspots and to evaluate the effects of changing starspot areas and distributions on the light center of the binary. Our results indicate that IM Peg’s activity should not affect the GP-B mission. We also present a study of IM Peg’s long-term starspot cycle, which shows evidence of being 20 yr long. Lastly, we have determined the intrinsic (unspotted) brightness of the star to be V mag = 5.62 ± 0.03.

On the1/cexpansion off(R)gravity

We derive for applications to isolated systems - on the scale of the Solar System - the first relativistic terms in the $1/c$ expansion of the space time metric $g_{\mu\nu}$ for metric $f(R)$ gravity theories, where $f$ is assumed to be analytic at $R=0$. For our purpose it suffices to take into account up to quadratic terms in the expansion of $f(R)$, thus we can approximate $f(R) = R + aR^2$ with a positive dimensional parameter $a$. In the non-relativistic limit, we get an additional Yukawa correction with coupling strength $G/3$ and Compton wave length $\sqrt{6a}$ to the Newtonian potential, which is a known result in the literature. As an application, we derive to the same order the correction to the geodetic precession of a gyroscope in a gravitational field and the precession of binary pulsars. The result of the Gravity Probe B experiment yields the limit $a \lesssim 5 \times 10^{11} \, \mathrm{m}^2$, whereas for the pulsar B in the PSR J0737-3039 system we get a bound which is about $10^4$ times larger. On the other hand the E\"ot-Wash experiment provides the best laboratory bound $a \lesssim 10^{-10} \, \mathrm{m}^2$. Although the former bounds from geodesic precession are much larger than the laboratory ones, they are still meaningful in the case some type of chameleon effect is present and thus the effective values could be different at different length scales.

Observational constraints on the completeness of space near astrophysical objects

We consider the observational effects of a deficit angle, w, in the topology of the solar system and in the 'double pulsar' system PSR J0737-3039A/B. Using observations of the perihelion precession of Mercury, and the gravitational deflection of light due to the Sun, we constrain the magnitude of such a deficit angle in the solar system to be 2*pi*(1-w), with 0<(1-w)<10^(-9) at 95% confidence. We calculate the effects of a deficit angle on the periastron advance, geodetic precession rate and inclination angle of the double pulsar system and use the observational data to obtain the constraint 0<(1-w)<2.4*10^(-8) at 95% confidence. Although this result is weaker than the solar system bound, it is in a very different physical environment, where accumulating data is likely to lead to tighter constraints in the future.

Eclipses and orbital modulations in binary pulsar PSR J0737-3039

Binary radio pulsar system J0737-3039 provides an exceptional opportunity to study innermost structure of pulsar magnetospheres due to very tight orbit, favorable directions of pulsars’ rotation and magnetic axes and extremely fortuitous orientation of the orbit. In this system the millisecond pulsar A is eclipsed once per orbit. During eclipse a clear modulation at the 2.77 s period of pulsar B is seen, pointing unambiguously to magnetospheric origin of eclipses. A simple geometric model, based on the idea that the radio pulses are attenuated by synchrotron absorption on the closed magnetic field lines of pulsar B, can successfully reproduces the eclipse light curves down to intricate details. This detailed agreement confirms the dipolar structure of the neutron star’s magnetic field. The model gives clear predictions for temporal evolution of eclipse profile due to geodetic precession of pulsar B. In addition, pulsar B shows orbital modulations of intensity, being especially bright at two short orbital phases. We showed that these modulations are due to distortion of pulsar B magnetosphere by pulsar A wind which produces orbital phase-dependent changes of the direction along which radio waves are emitted. Thus, pulsar B is intrinsically bright at all times but its radiation beam misses the Earth at most orbital phases.

Magnetospheric interactions and emission properties in the double pulsar system

Our ability to observe both pulsars in the double-pulsar system, PSR J0737–3039A/B, combined with its short binary period and almost edge-on orbit, provides an unique opportunity to study pulsar magnetospheric interactions and the pulse emission mechanism. Pulses from J0737–3039A (A) are eclipsed by the magnetosphere of PSR J0737–3039B (B) which is believed to be highly distorted by the relativistic wind from A. In addition, pulses from B are modulated at the A rotational period, revealing an interaction between radiation from A and the B pulse emission mechanism. Relativistic geodetic precession of the spin axes of the two pulsars is expected. Surprisingly, no precessional effects have been observed in A, but secular changes in the B pulse profile and orbital modulation are seen. Finally, based on polarisation observations, we discuss the inclination of A’s magnetic axis relative to its spin axis.

Comments on the unique gravity probe-b experiment

The results from an experimental verification of the general relativity theory on board a satellite are considered. The idea behind the experiment (Schiff, Stanford, 1960), the geodetic precession of the cryogenic gyroscope, the criticism of the experiment (Mathey and Paris, 1967), the crisis of the idea of cryogenic gyroscopy, the disproof of Mathey’s idea (Institute for Problems in Mechanics (IPM), Moscow, 1975), Lense—Thirring precession, the effect of the Moon and the Sun, Tomas precession, Logunov’s kinematic precession of a gyroscope in the Earth’s gravitational field, and the final behavior of the results from an experiment done nearly 50 years ago are described.

The nature of pulsar radio emission

High-quality averaged radio profiles of some pulsars exhibit double, highly symmetric features both in emission and in absorption. It is shown that both types of feature are produced by a split fan beam of extraordinary-mode curvature radiation that is emitted/absorbed by radially extended streams of magnetospheric plasma. With no emissivity in the plane of the stream, such a beam produces bifurcated emission components (BFCs) when our line of sight passes through the plane. An example of a double component created in this way is present in the averaged profile of the 5-ms pulsar J1012+5307. We show that the component can indeed be very well fitted by the textbook formula for the non-coherent beam of curvature radiation in the polarization state that is orthogonal to the plane of electron trajectory. The observed width of the BFC decreases with increasing frequency at a rate that confirms the curvature origin. Likewise, the double absorption features (double notches) are produced by the same beam of the extraordinary-mode curvature radiation, when it is eclipsed by thin plasma streams. The intrinsic property of curvature radiation to create bifurcated fan beams explains the double features in terms of a very natural geometry and implies the curvature origin of pulsar radio emission. Similarly, the ‘double conal’ profiles of class D result from a cut through a wider stream with finite extent in magnetic azimuth. Therefore, their width reacts very slowly to changes of viewing geometry resulting from geodetic precession. The stream-cut interpretation implies a highly non-orthodox origin of both the famous S-swing of polarization angle and the low-frequency pulse broadening in D profiles. The azimuthal structure of polarization modes in the curvature radiation beam provides an explanation for the polarized ‘multiple imaging’ and the edge depolarization of pulsar profiles.

Geodetic precession in squashed Kaluza-Klein black hole spacetimes

We investigate the geodetic precession effect of a parallelly transported spin vector along a circular geodesic in five-dimensional squashed Kaluza-Klein black hole spacetime. Then we derive the higher-dimensional correction of the precession angle to general relativity. We find that the correction is proportional to the square of (size of extra dimension)/(gravitational radius of central object).

Gravity Probe B Data Analysis

This is the first of five connected papers detailing progress on the Gravity Probe B (GP-B) Relativity Mission. GP-B, launched 20 April 2004, is a landmark physics experiment in space to test two fundamental predictions of Einstein’s general relativity theory, the geodetic and frame-dragging effects, by means of cryogenic gyroscopes in Earth orbit. Data collection began 28 August 2004 and science operations were completed 29 September 2005. The data analysis has proven deeper than expected as a result of two mutually reinforcing complications in gyroscope performance: (1) a changing polhode path affecting the calibration of the gyroscope scale factor C g against the aberration of starlight and (2) two larger than expected manifestations of a Newtonian gyro torque due to patch potentials on the rotor and housing. In earlier papers, we reported two methods, ‘geometric’ and ‘algebraic’, for identifying and removing the first Newtonian effect (‘misalignment torque’), and also a preliminary method of treating the second (‘roll-polhode resonance torque’). Central to the progress in both torque modeling and C g determination has been an extended effort on “Trapped Flux Mapping” commenced in November 2006. A turning point came in August 2008 when it became possible to include a detailed history of the resonance torques into the computation. The East-West (frame-dragging) effect is now plainly visible in the processed data. The current statistical uncertainty from an analysis of 155 days of data is 5.4 marc-s/yr (∼14% of the predicted effect), though it must be emphasized that this is a preliminary result requiring rigorous investigation of systematics by methods discussed in the accompanying paper by Muhlfelder et al. A covariance analysis incorporating models of the patch effect torques indicates that a 3–5% determination of frame-dragging is possible with more complete, computationally intensive data analysis.

The Gravity Probe B Data Analysis Filtering Approach

A simple pre-flight strategy of the Gravity Probe B (GP-B) data analysis has evolved in the elaborate multi-level structure after the discovery of the complex polhode motion, and of the patch effect torques. We describe a cascade of estimators (filters) that reduce the science data (SQUID and telescope signals) to the estimates of the relativistic drift rates. Those estimators, structured in two “floors”, are based on the polhode-related models for the readout scale factor and patch effect torque. Results of the 1st Floor processing—gyro orientation profiles—manifest clearly the strong geodetic effect but also the presence of classical torque. Modeling of the patch effect torque at the 2nd Floor provides a successful compensation of the torque contributions, and leads to consistent estimates of the relativistic drift rates.

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 the Earth. This curvature is characterized by the Eddington parameter γ — the most fundamental relativistic gravity parameter and a direct measure for the presence of new physical interactions. BEACON will achieve an accuracy of 1 × 10-9 in measuring the parameter γ, 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 respectively, (ii) the first measurement of gravity's nonlinear effects on light and the corresponding second 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. It 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.

APOLLO: A new push in solar-system tests of gravity

AbstractLunar laser ranging (LLR) has long provided many of our best measurements on the fundamental nature of gravity, including the strong equivalence principle, time -rate-of-change of the gravitational constant, the inverse square law, geodetic precession, and gravitomagnetism. This paper serves as a brief overview of APOLLO: a recently operational LLR experiment capable of millimeter-level range precision.