Gravity Probe B Research Articles

Flight and ground demonstration of reproducibility and stability of photoelectric properties for passive charge management using LEDs

Charges as small as 1 pC degrade the performance of high precision inertial reference instruments when accumulated on their test masses (TMs). Non-contact charge management systems are required for the most sensitive of these instruments, with the TMs free-floating, and their charges compensated by photoelectrons in a feedback loop with a TM charge measurement. Three space missions have successfully demonstrated this technique: the Relativity Mission, Gravity Probe-B launched in 2004, the LISA Pathfinder launched in 2015, and the UV-LED mission launched on SaudiSat 4 in 2014; with the first two using the 254 nm Hg discharge line and the last one a set of 255 nm UV-LEDs. UV-LEDs represent a significant improvement over the discharge sources, in terms of reliability, lifetime, switching speeds, power consumption, weight, and volume. Charge management techniques that eliminate the charge measurement and feedback systems, referred henceforth as passive, reduce the complexities and disturbance effects introduced by these systems, and are thus the subject of active research and development work. Passive charge management (PCM) depends critically on the stability and reproducibility of the photoemission properties of a given system. In support of this work, we present comprehensive flight characterization data for a suite of 16 UV-LEDs in various configurations and 255 ± 1 nm center wavelength. Flight data was acquired between December 2014 and December 2015 with the UV-LED instrument flown on SaudiSat 4. We back up our results with ground-based measurements performed in configurations comparable to the flight one between 4 September 2020, and 8 October 2020. All results confirm the excellent reliability of the UV-LEDs in the space environment, are fully consistent with the findings of ground studies, and support the approach of using LEDs for PCM. We find that the equilibrium potential of the TM, under illumination by the 255 nm LEDs, is independent of the UV intensity and reproduceable to about ≅±6 mV, or ±6 fC pF−1, over periods of up to six months. The value of the equilibrium potential is dependent on the geometry of the electric field between the TM and its enclosure, and thus on the exact configuration of the PCM instrument.

Constraints on ultralight axions, vector gauge bosons, and unparticles from geodetic and frame-dragging measurements

The geodetic and frame-dragging effects are the direct consequences of the spacetime curvature near Earth which can be probed from the Gravity probe B (GP-B) satellite. The satellite result matches quite well with Einstein’s general relativistic result. The gyroscope of the satellite which measures the spacetime curvature near Earth contains lots of electrons and nucleons. Ultralight axions, vector gauge bosons, and unparticles can interact with these electrons and nucleons through different spin-dependent and spin-independent operators and change the drift rate of the gyroscope. Some of these ultralight particles can either behave as a long range force between some dark sector or Earth and the gyroscope or they can behave as a background oscillating dark matter fields or both. These ultralight particles can contribute an additional precession of the gyroscopes, limited to be no larger than the uncertainty in the GP-B measurements. Compared with the experimental results, we obtain bounds on different operator couplings.

Gravitomagnetism and the significance of the curvature scalar invariants

The curvature invariants have been subject of interest due to the debate concerning the notions of intrinsic/extrinsic frame-dragging, the use of the electromagnetic analogy in such classification, and the question of whether there is a fundamental difference between the gravitomagnetic fields arising from the translational and rotational motions of the sources (which have been subject of observational and experimental tests, including the dedicated Gravity Probe-B and LARES space missions). In this work we clarify both the algebraic and physical meaning of the curvature invariants and their electromagnetic counterparts. They are seen to yield conditions for the existence of observers measuring vanishing electric/magnetic fields and gravitoelectric/gravitomagnetic tidal tensors, respectively. We determine these observers (in the gravitational sector and in the presence of sources, for the more relevant gravitomagnetic case) obtaining their velocities explicitly in terms of the fields/tidal tensors as measured by an arbitrary observer. The structure of the invariants of the astrophysical setups of interest is studied in detail, and its relationship with the gravitomagnetic effects is dissected. Finally, a new classification for intrinsic/extrinsic gravitomagnetism is proposed.

Is There Still Something Left That Gravity Probe B Can Measure?

We perform a full analytical and numerical treatment, to the first post-Newtonian (1pN) order, of the general relativistic long-term spin precession of an orbiting gyroscope due to the mass quadrupole moment J 2 of its primary without any restriction on either the gyro’s orbital configuration and the orientation in space of the symmetry axis k ^ of the central body. We apply our results to the past spaceborne Gravity Probe B (GP-B) mission by finding a secular rate of its spin’s declination δ which may be as large as ≲30–40 milliarcseconds per year mas yr − 1 , depending on the initial orbital phase f 0 . Both our analytical calculation and our simultaneous integration of the equations for the parallel transport of the spin 4-vector S and of the geodesic equations of motion of the gyroscope confirm such a finding. For GP-B, the reported mean error in measuring the spin’s declination rate amounts to σ δ ˙ GP − B = 18.3 mas yr − 1 . We also calculate the general analytical expressions of the gravitomagnetic spin precession induced by the primary’s angular momentum J . In view of their generality, our results can be extended also to other astronomical and astrophysical scenarios of interest like, e.g., stars orbiting galactic supermassive black holes, exoplanets close to their parent stars, tight binaries hosting compact stellar corpses.

Timing system design and tests for the Gravity Probe B relativity mission

In this paper, we discuss the timing system design and tests for the NASA/Stanford Gravity Probe B (GP-B) relativity mission. The primary clock of GP-B, called the 16fo clock, was an oven-controlled crystal oscillator that produced a 16.368 MHz master frequency. The 16fo clock and the 10 Hz data strobe, which was divided down from the 16fo clock, provided clock signals to all GP-B components and synchronized the data collection, transmission, and processing. The sampled data of science signals were stamped with the vehicle time, a counter of the 10 Hz data strobe. The time latency between the time of data sampling and the stamped vehicle time was compensated in the ground data processing. Two redundant global positioning system receivers onboard the GP-B satellite supplied an external reference for time transfer between the vehicle time and coordinated universal time (UTC), and the time conversion was established in the ground preprocessing of the telemetry timing data. The space flight operation showed that the error of time conversion between the vehicle time and UTC was less than 2 μs. Considering that the constant timing offsets were compensated in the ground processing of the GP-B science data, the time latency between the effective sampling time of GP-B science signals and the stamped vehicle time was verified to within 1 ms in the ground tests.

The three-fold theoretical basis of the Gravity Probe B gyro precession calculation

The Gravity Probe B (GP-B) experiment is complete and the results are in agreement with the predictions of general relativity (GR) for both the geodetic precession, 6.6 arcsec yr−1 to about 0.3%, and the Lense–Thirring precession, 39 marcsec to about 19%. This note is concerned with the theoretical basis for the predictions. The predictions depend on three elements of gravity theory, firstly that macroscopic gravity is described by a metric theory such as GR, secondly that the Lense–Thirring metric provides an approximate description of the gravitational field of the spinning Earth, and thirdly that the spin axis of a gyroscope is parallel displaced in spacetime, which gives its equation of motion. We look at each of these three elements to show how each is solidly based on previous experiments and well-tested theory. The agreement of GP-B with theory strengthens our belief that all three elements are correct and increases our confidence in applying GR to astrophysical phenomena. Conversely, if GP-B had not verified the predictions a major theoretical quandary would have occurred.

Gravity Probe B orbit determination

The Gravity Probe B (GP-B) satellite was equipped with a pair of redundant Global Positioning System (GPS) receivers used to provide navigation solutions for real-time and post-processed orbit determination (OD), as well as to establish the relation between vehicle time and coordinated universal time. The receivers performed better than the real-time position requirement of 100 m rms per axis. Post-processed solutions indicated an rms position error of 2.5 m and an rms velocity error of 2.2 mm s−1. Satellite laser ranging measurements provided independent verification of the GPS-derived GP-B orbit. We discuss the modifications and performance of the Trimble Advance Navigation System Vector III GPS receivers. We describe the GP-B precision orbit and detail the OD methodology, including ephemeris errors and the laser ranging measurements.

VLBI for Gravity Probe B: the guide star, IM Pegasi

We review the radio very long baseline interferometry (VLBI) observations of the guide star, IM Peg, and three compact extragalactic reference sources, made in support of the NASA/Stanford gyroscope relativity mission, Gravity Probe B (GP-B). The main goal of the observations was the determination of the proper motion of IM Peg relative to the distant Universe. VLBI observations made between 1997 and 2005 yield a proper motion of IM Peg of ± 0.09 mas yr−1 in α and ± 0.09 mas yr−1 in δ in a celestial reference frame of extragalactic radio galaxies and quasars virtually identical to the International Celestial Reference Frame 2 (ICRF2). They also yield a parallax for IM Peg of 10.37 ± 0.07 mas, corresponding to a distance of 96.4 ± 0.7 pc. The uncertainties are standard errors with statistical and estimated systematic contributions added in quadrature. These results met the pre-launch requirements of the GP-B mission to not discernibly degrade the estimates of the geodetic and frame-dragging effects.

Proportional helium thrusters for Gravity Probe B

The Gravity Probe B (GP-B) satellite used electrostatically suspended gyroscopes to test two predictions of general relativity. Here, we describe the satellite’s proportional thrusters, which utilized boil-off helium gas for attitude and translation Control (ATC). The evolution of the design and its successful effect on orbit performance is reported.

Porous plug for Gravity Probe B

The confinement of superfluid helium for a Dewar in space poses a unique challenge due to its propensity to minimize thermal gradients by essentially viscous-free counterflow. This poses the risk of losing liquid through a vent pipe, reducing the efficiency of the cooling process. To confine the liquid helium in the Gravity Probe B (GP-B) flight Dewar, a porous plug technique was invented at Stanford University. Here, we review the history of the porous plug and its development, and describe the physics underlying its operation. We summarize a few missions that employed porous plugs, some of which preceded the launch of GP-B. The design, manufacture and flight performance of the GP-B plug are described, and its use resulted in the successful operation of the 2441 l flight Dewar on-orbit for 17.3 months.

The Gravity Probe B electrostatic gyroscope suspension system (GSS)

A spaceflight electrostatic suspension system was developed for the Gravity Probe B (GP-B) Relativity Mission’s cryogenic electrostatic vacuum gyroscopes which serve as an indicator of the local inertial frame about Earth. The Gyroscope Suspension System (GSS) regulates the translational position of the gyroscope rotors within their housings, while (1) minimizing classical electrostatic torques on the gyroscope to preserve the instrument’s sensitivity to effects of General Relativity, (2) handling the effects of external forces on the space vehicle, (3) providing a means of precisely aligning the spin axis of the gyroscopes after spin-up, and (4) acting as an accelerometer as part of the spacecraft’s drag-free control system. The flight design was tested using an innovative, precision gyroscope simulator Testbed that could faithfully mimic the behavior of a physical gyroscope under all operational conditions, from ground test to science data collection. Four GSS systems were built, tested, and operated successfully aboard the GP-B spacecraft from launch in 2004 to the end of the mission in 2008.

Gravity Probe B data analysis: I. Coordinate frames and analysis models

Gravity Probe B (GP-B) was a cryogenic, space-based experiment testing the geodetic and frame-dragging predictions of Einstein's theory of general relativity (GR) by means of gyroscopes in Earth orbit. This first of three data analysis papers reviews the GR predictions and details the models that provide the framework for the relativity analysis. In the second paper we describe the flight data and their preprocessing. The third paper covers the algorithms and software tools that fit the preprocessed flight data to the models to give the experimental results published in Everitt et al (2011 Phys. Rev. Lett. 106 221101–4).

The Gravity Probe B gyroscope

The Gravity Probe B (GP-B) gyroscope, a unique cryogenically operated mechanical sensor, was used on-orbit to independently test two predictions of general relativity (GR). Here, we describe the development and performance of the GP-B gyroscope, its geometry and fabrication, spin-up and vacuum approach, magnetic considerations, and static charge management. The history of electrically suspended gyroscopes puts the current work in context. Fabrication and ground testing of the GP-B gyroscope are detailed, followed by a review of on-orbit initialization, calibration, operation, and performance. We find that the performance was degraded relative to the mission goals, but was still sufficient to provide excellent new tests of GR. The degradation is partially due to the existence of gyroscope torques due to an unanticipated interaction between patch potentials on the rotor and the housing. We discuss these patch potentials and describe the effect of related torques on gyro drift. It was essential to include models for the effects due to the patch potentials in the complete data analysis model to yield determinations of the two GR effects.

Constraining models of extended gravity using Gravity Probe B and LARES experiments

We consider models of extended gravity and in particular, generic models containing scalar-tensor and higher-order curvature terms, as well as a model derived from noncommutative spectral geometry. Studying, in the weak-field approximation (the Newtonian and post-Newtonian limit of the theory), the geodesic and Lense-Thirring processions, we impose constraints on the free parameters of such models by using the recent experimental results of the Gravity Probe B (GPB) and Laser Relativity Satellite (LARES) satellites. The imposed constraint by GPB and LARES is independent of the torsion-balance experiment, though it is much weaker.

The geodetic precession as a 3D Schouten precession and a gravitational Thomas precession

The Gravity Probe B (GP-B) experiment measured the geodetic precession due to parallel transport in a curved space–time metric, as predicted by de Sitter, Fokker, and Schiff. The Schiff treatment included Thomas precession and argued that it should be zero in a free fall orbit. We review the existing interpretations regarding the relation between the Thomas precession and the geodetic precession for a gyroscope in a free fall orbit. Schiff and Parker had contradictory views on the status of the Thomas precession in a free fall orbit, a contradiction that continues to exist in the literature. In the second part of this paper we derive the geodetic precession as a global Thomas precession by use of the equivalent principle and some elements of hyperbolic geometry, a derivation that allows the treatment of GP-B physics in between special and general relativity courses.

Did the Gravity Probe B Actually Prove the Einstein's General Relativity Theory?

It has been shown in an earlier publication (Hynecek, 2013) that the frame dragging effect due to the Earth's rotation, which is claimed that the Gravity Probe B (GP-B) has detected, cannot exist. In this paper it is shown that the Geodetic Precession, which the GP-B has also measured, and is typically calculated from the Einstein's General Relativity Theory (GRT), can also be calculated from a different metric. When the results of calculations are compared side by side the differences are very small, but it becomes clear that the GRT actually may not be providing the correct derivation of formula for this effect. The one reason among several others is due to the fact that the GRT derivation, as is shown in this paper, also leads to the derivation of the classical Kepler's third law for circular orbits, which is easily derived from the Newtonian physics, and should therefore hold true only in the flat space-time geometry.

VLBI FOR GRAVITY PROBE B . V. PROPER MOTION AND PARALLAX OF THE GUIDE STAR, IM PEGASI

We present the principal astrometric results of the very-long-baseline interferometry (VLBI) program undertaken in support of the Gravity Probe B (GP-B) relativity mission. VLBI observations of the GP-B guide star, the RS CVn binary IM Pegasi (HR 8703), yielded positions at 35 epochs between 1997 and 2005. We discuss the statistical assumptions behind these results and our methods for estimating the systematic errors. We find the proper motion of IM Peg in an extragalactic reference frame closely related to the International Celestial Reference Frame 2 (ICRF2) to be -20.83 +- 0.03 +- 0.09 mas/yr in right ascension and -27.27 +- 0.03 +- 0.09 mas/yr in declination. For each component the first uncertainty is the statistical standard error and the second is the total standard error (SE) including plausible systematic errors. We also obtain a parallax of 10.37 +- 0.07 mas (distance: 96.4 +- 0.7 pc), for which there is no evidence of any significant contribution of systematic error. Our parameter estimates for the ~25-day-period orbital motion of the stellar radio emission have SEs corresponding to ~0.10 mas on the sky in each coordinate. The total SE of our estimate of IM Peg's proper motion is ~30% smaller than the accuracy goal set by the GP-B project before launch: 0.14 mas/yr for each coordinate of IM Peg's proper motion. Our results ensure that the uncertainty in IM Peg's proper motion makes only a very small contribution to the uncertainty of the GP-B relativity tests.

VLBI FOR GRAVITY PROBE B . I. OVERVIEW

We describe the NASA/Stanford gyroscope relativity mission, Gravity Probe B (GP-B), and provide an overview of the following series of six astrometric and astrophysical papers that report on our radio observations and analyses made in support of this mission. The main goal of this 8.5 year program of differential VLBI astrometry was to determine the proper motion of the guide star of the GP-B mission, the RS CVn binary IM Pegasi (IM Peg; HR 8703). This proper motion is determined with respect to compact, extragalactic reference sources. The results are: -20.833 +- 0.090 mas/yr and -27.267 +- 0.095 mas/yr for, respectively, the right ascension and declination, in local Cartesian coordinates, of IM Peg's proper motion, and 10.370 +- 0.074 mas (i.e., 96.43 +- 0.69 pc) for its parallax (and distance). Each quoted uncertainty is meant to represent an ~70% confidence interval that includes the estimated contribution from systematic error. These results are accurate enough not to discernibly degrade the GP-B estimates of its gyroscopes' relativistic precessions: the frame-dragging and geodetic effects.

VLBI FOR GRAVITY PROBE B . II. MONITORING OF THE STRUCTURE OF THE REFERENCE SOURCES 3C 454.3, B2250+194, AND B2252+172

We used 8.4 GHz VLBI images obtained at up to 35 epochs between 1997 and 2005 to examine the radio structures of the main reference source, 3C 454.3, and two secondary reference sources, B2250+194 and B2252+172, for the guide star for the NASA/Stanford relativity mission Gravity Probe B (GP-B). For one epoch in 2004 May, we also obtained images at 5.0 and 15.4 GHz. The 35 8.4 GHz images for quasar 3C 454.3 confirm a complex, evolving, core-jet structure. We identified at each epoch a component, C1, near the easternmost edge of the core region. Simulations of the core region showed that C1 is located, on average, 0.18 +- 0.06 mas west of the unresolved "core" identified in 43 GHz images. We also identified in 3C 454.3 at 8.4 GHz several additional components which moved away from C1 with proper motions ranging in magnitude between 0.9c and 5c. The detailed motions of the components exhibit two distinct bends in the jet axis located ~3 and ~5.5 mas west of C1. The spectra between 5.0 and 15.4 GHz for the "moving" components are steeper than that for C1. The 8.4 GHz images of B2250+194 and B2252+172, in contrast to those of 3C 454.3, reveal compact structures. The spectrum between 5.0 and 15.4 GHz for B2250+194 is inverted while that for B2252+172 is flat. Based on its position near the easternmost edge of the 8.4 GHz radio structure, close spatial association with the 43 GHz core, and relatively flat spectrum, we believe 3C 454.3 component C1 to be the best choice for the ultimate reference point for the GP-B guide star. The compact structures and inverted to flat spectra of B2250+194 and B2252+172 make these objects valuable secondary reference sources

Nanohertz frequency determination for the gravity probe B high frequency superconducting quantum interference device signal

In this paper, we present a method to measure the frequency and the frequency change rate of a digital signal. This method consists of three consecutive algorithms: frequency interpolation, phase differencing, and a third algorithm specifically designed and tested by the authors. The succession of these three algorithms allowed a 5 parts in 10(10) resolution in frequency determination. The algorithm developed by the authors can be applied to a sampled scalar signal such that a model linking the harmonics of its main frequency to the underlying physical phenomenon is available. This method was developed in the framework of the gravity probe B (GP-B) mission. It was applied to the high frequency (HF) component of GP-B's superconducting quantum interference device signal, whose main frequency f(z) is close to the spin frequency of the gyroscopes used in the experiment. A 30 nHz resolution in signal frequency and a 0.1 pHz/s resolution in its decay rate were achieved out of a succession of 1.86 s-long stretches of signal sampled at 2200 Hz. This paper describes the underlying theory of the frequency measurement method as well as its application to GP-B's HF science signal.