Gravity Probe B (GP-B) was a satellite-based experiment to test two unverified predictions of general relativity: the geodetic effect and frame-dragging. This was to be accomplished by measuring, very precisely, tiny changes in the direction of spin of four gyroscopes contained in an Earth-orbiting satellite at 650km (400mi) of altitude, crossing directly over the poles.
The satellite was launched on 20 April 2004 on a Delta II rocket.[4] The spaceflight phase lasted until ;[5] Its aim was to measure spacetime curvature near Earth, and thereby the stress–energy tensor (which is related to the distribution and the motion of matter in space) in and near Earth. This provided a test of general relativity, gravitomagnetism and related models. The principal investigator was Francis Everitt.
Initial results confirmed the expected geodetic effect to an accuracy of about 1%. The expected frame-dragging effect was similar in magnitude to the current noise level (the noise being dominated by initially unmodeled effects due to nonuniform coatings on the gyroscopes). Work continued to model and account for these sources of error, thus permitting extraction of the frame-dragging signal. By , the frame-dragging effect had been confirmed to within 15% of the expected result,[6] and the NASA report indicated that the geodetic effect was confirmed to be better than 0.5%.[7]
In an article published in the journal Physical Review Letters in , the authors reported analysis of the data from all four gyroscopes results in a geodetic drift rate of −6601.8±18.3mas/yr and a frame-dragging drift rate of −37.2±7.2mas/yr, in good agreement with the general relativity predictions of −6606.1±0.28%mas/yr and −39.2±0.19%mas/yr, respectively.[8]
Overview
Gravity Probe B was a relativity gyroscope experiment funded by NASA. Efforts were led by the Stanford University physics department with Lockheed Martin as the primary subcontractor. Mission scientists viewed it as the second relativity experiment in space, following the successful launch of Gravity Probe A (GP-A) in .
The mission plans were to test two unverified predictions of general relativity: the geodetic effect and frame-dragging. This was to be accomplished by measuring, very precisely, tiny changes in the direction of spin of four gyroscopes contained in an Earth satellite orbiting at 650km (400mi) altitude, crossing directly over the poles. The gyroscopes were intended to be so free from disturbance that they would provide a near-perfect spacetime reference system. This would allow them to reveal how space and time are "warped" by the presence of the Earth, and by how much the Earth's rotation "drags" space-time around with it.
The geodetic effect is an effect caused by space-time being "curved" by the mass of the Earth. A gyroscope's axis when parallel transported around the Earth in one complete revolution does not end up pointing in exactly the same direction as before. The angle "missing" may be thought of as the amount the gyroscope "leans over" into the slope of the space-time curvature. A more precise explanation for the space curvature part of the geodetic precession is obtained by using a nearly flat cone to model the space curvature of the Earth's gravitational field. Such a cone is made by cutting out a thin "pie-slice" from a circle and gluing the cut edges together. The spatial geodetic precession is a measure of the missing "pie-slice" angle. Gravity Probe B was expected to measure this effect to an accuracy of one part in 10,000, the most stringent check on general relativistic predictions to date.
The much smaller frame-dragging effect is an example of gravitomagnetism. It is an analog of magnetism in classical electrodynamics, but caused by rotating masses rather than rotating electric charges. Previously, only two analyses of the laser-ranging data obtained by the two LAGEOS satellites, published in and , claimed to have found the frame-dragging effect with an accuracy of about 20% and 10% respectively,[9][10][11] whereas Gravity Probe B aimed to measure the frame dragging effect to a precision of 1%.[12] However, Lorenzo Iorio claimed that the level of total uncertainty of the tests conducted with the two LAGEOS satellites has likely been greatly underestimated.[13][14][15][16][17][18] A recent analysis of Mars Global Surveyor data has claimed to have confirmed the frame dragging effect to a precision of 0.5%,[19] although the accuracy of this claim is disputed.[20][21] Also the Lense–Thirring effect of the Sun has been recently investigated in view of a possible detection with the inner planets in the near future.[22]
The launch was planned for at Vandenberg Air Force Base but was scrubbed within 5 minutes of the scheduled launch window due to changing winds in the upper atmosphere. An unusual feature of the mission is that it only had a one-second launch window due to the precise orbit required by the experiment. On PDT ( UTC) the spacecraft was launched successfully. The satellite was placed in orbit at AM ( UTC) after a cruise period over the south pole and a short second burn. The mission lasted 16 months.
Some preliminary results were presented at a special session during the American Physical Society meeting in . NASA initially requested a proposal for extending the GP-B data analysis phase through . The data analysis phase was further extended to using funding from Richard Fairbank, Stanford and NASA, and beyond that point using non-NASA funding only.[6] Final science results were reported in .
Experimental setup
At the time, the fused quartz gyroscopes created for Gravity Probe B were the most nearly perfect spheres ever created by humans. The gyroscopes differ from a perfect sphere by no more than 40 atoms of thickness. One is pictured here refracting the image of Albert Einstein in background.
The Gravity Probe B experiment comprised four London moment gyroscopes and a reference telescope sighted on IM Pegasi, a binary star in the constellation Pegasus. In polar orbit, with the gyro spin directions also pointing toward IM Pegasi, the frame-dragging and geodetic effects came out at right angles, each gyroscope measuring both.
The gyroscopes were housed in a dewar of superfluid helium, maintaining a temperature of under 2 kelvins (−271°C; −456°F). Near-absolute zero temperatures were required to minimize molecular interference, and enable the lead and niobium components of the gyroscope mechanisms to become superconductive.
At the time of their manufacture, the gyroscopes were the most nearly spherical objects ever made (two gyroscopes still hold that record, but third place has been taken by the silicon spheres made by the Avogadro project). Approximately the size of ping pong balls, they were perfectly round to within forty atoms (less than 10nm). If one of these spheres were scaled to the size of the Earth, the tallest mountains and deepest ocean trench would measure only 2.4m (8ft) high.[24] The spheres were made of fused quartz and coated with an extremely thin layer of niobium. A primary concern was minimizing any influence on their spin, so the gyroscopes could never touch their containing compartment. They were held suspended with electric fields, spun up using a flow of helium gas, and their spin axes were sensed by monitoring the magnetic field of the superconductive niobium layer with SQUIDs. (A spinning superconductor generates a magnetic field precisely aligned with the rotation axis; see London moment.)
IM Pegasi was chosen as the guide star for multiple reasons. First, it needed to be bright enough to be usable for sightings. Then it was close to the ideal positions near the celestial equator. Also important was its well-understood motion in the sky, which was helped by the fact that this star emits relatively strong radio signals. In preparation for the setup of this mission, astronomers analyzed the radio-based position measurements with respect to far distant quasars taken over several years to understand its motion as precisely as needed.
History
A representation of the geodetic effect.
The conceptual design for this mission was first proposed by an MIT professor, George Pugh, who was working with the U.S. Department of Defense in and later discussed by Leonard Schiff (Stanford) in at Pugh's suggestion, based partly on a theoretical paper about detecting frame dragging that Schiff had written in . It was proposed to NASA in , and they supported the project with funds in . This grant ended in after a long phase of engineering research into the basic requirements and tools for the satellite.
In NASA changed plans for the Space Shuttle, which forced the mission team to switch from a shuttle-based launch design to one that was based on the Delta 2, and in tests planned of a prototype on a shuttle flight were cancelled as well.
Gravity Probe B marks the first time that Stanford University has been in control of the development and operations of a space satellite funded by NASA.
The total cost of the project was about $750 million.[25]
This is a list of major events for the GP-B experiment.
Launch of GP-B from Vandenberg AFB and successful insertion into polar orbit.
GP-B entered its science phase. On mission day 129 all systems were configured to be ready for data collection, with the only exception being gyro 4, which needed further spin axis alignment.
The science phase of the mission ended and the spacecraft instruments transitioned to the final calibration mode.
The calibration phase ended with liquid helium still in the dewar. The spacecraft was returned to science mode pending the depletion of liquid helium.
Phase I of data analysis complete
Analysis team realised that more error analysis was necessary (particularly around the polhode motion of the gyros) than could be done in the time to and applied to NASA for an extension of funding to the end of .
Completion of Phase III of data analysis
Announcement of best results obtained to date. Francis Everitt gave a plenary talk at the meeting of the American Physical Society announcing initial results:[26] "The data from the GP-B gyroscopes clearly confirm Einstein's predicted geodetic effect to a precision of better than 1 percent. However, the frame-dragging effect is 170 times smaller than the geodetic effect, and Stanford scientists are still extracting its signature from the spacecraft data."[27]
GP-B spacecraft decommissioned, left in its 642km (399mi) polar orbit.[28]
GP-B Final experimental results were announced. In a public press and media event at NASA Headquarters, GP-B Principal Investigator, Francis Everitt presented the final results of Gravity Probe B.[29]
On , it was announced that a number of unexpected signals had been received and that these would need to be separated out before final results could be released. In it was announced that the spin axes of the gyroscopes were affected by torque, in a manner that varied over time, requiring further analysis to allow the results to be corrected for this source of error. Consequently, the date for the final release of data was pushed back several times. In the data for the frame-dragging results presented at the meeting of the American Physical Society, the random errors were much larger than the theoretical expected value and scattered on both the positive and negative sides of a null result, therefore causing skepticism as to whether any useful data could be extracted in the future to test this effect.
In , a detailed update was released explaining the cause of the problem, and the solution that was being worked on. Although electrostatic patches caused by non-uniform coating of the spheres were anticipated, and were thought to have been controlled for before the experiment, it was subsequently found that the final layer of the coating on the spheres defined two-halves of slightly different contact potential, which gave the sphere an electrostatic axis. This created a classical dipole torque on each rotor, of a magnitude similar to the expected frame dragging effect. In addition, it dissipated energy from the polhode motion by inducing currents in the housing electrodes, causing the motion to change with time. This meant that a simple time-average polhode model was insufficient, and a detailed orbit by orbit model was needed to remove the effect. As it was anticipated that "anything could go wrong", the final part of the flight mission was calibration, where amongst other activities, data was gathered with the spacecraft axis deliberately misaligned for , to exacerbate any potential problems. This data proved invaluable for identifying the effects. With the electrostatic torque modeled as a function of axis misalignment, and the polhode motion modeled at a sufficiently fine level, it was hoped to isolate the relativity torques to the originally expected resolution.
Stanford agreed to release the raw data to the public at an unspecified date in the future. It is likely that this data will be examined by independent scientists and independently reported to the public well after the final release by the project scientists. Because future interpretations of the data by scientists outside GP-B may differ from the official results, it may take several more years for all of the data received by GP-B to be completely understood.[needs update]
NASA review
A review by a panel of 15 experts commissioned by NASA recommended against extending the data analysis phase beyond . They warned that the required reduction in noise level (due to classical torques and breaks in data collection due to solar flares) "is so large that any effect ultimately detected by this experiment will have to overcome considerable (and in our opinion, well justified) skepticism in the scientific community".[31]
Data analysis after NASA
NASA funding and sponsorship of the program ended on , but GP-B secured alternative funding from King Abdulaziz City for Science and Technology in Saudi Arabia[6] that enabled the science team to continue working at least through . On , the 18th meeting of the external GP-B Science Advisory Committee was held at Stanford to report progress.
The Stanford-based analysis group and NASA announced on that the data from GP-B indeed confirms the two predictions of Albert Einstein's general theory of relativity.[32] The findings were published in the journal Physical Review Letters.[8] The prospects for further experimental measurement of frame-dragging after GP-B were commented on in the journal Europhysics Letters.[33]
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. General relativity generalises special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time or four-dimensional spacetime. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of second order partial differential equations.
A gravity assist, gravity assist maneuver, swing-by, or generally a gravitational slingshot in orbital mechanics, is a type of spaceflight flyby which makes use of the relative movement and gravity of a planet or other astronomical object to alter the path and speed of a spacecraft, typically to save propellant and reduce expense.
In theoretical physics, particularly in discussions of gravitation theories, Mach's principle is the name given by Albert Einstein to an imprecise hypothesis often credited to the physicist and philosopher Ernst Mach. The hypothesis attempted to explain how rotating objects, such as gyroscopes and spinning celestial bodies, maintain a frame of reference.
In satellite laser ranging (SLR) a global network of observation stations measures the round trip time of flight of ultrashort pulses of light to satellites equipped with retroreflectors. This provides instantaneous range measurements of millimeter level precision which can be accumulated to provide accurate measurement of orbits and a host of important scientific data. The laser pulse can also be reflected by the surface of a satellite without a retroreflector, which is used for tracking space debris.
The Pioneer anomaly, or Pioneer effect, was the observed deviation from predicted accelerations of the Pioneer 10 and Pioneer 11 spacecraft after they passed about 20 astronomical units (3×109 km; 2×109 mi) on their trajectories out of the Solar System. The apparent anomaly was a matter of much interest for many years but has been subsequently explained by anisotropic radiation pressure caused by the spacecraft's heat loss.
The Gravity Recovery and Climate Experiment (GRACE) was a joint mission of NASA and the German Aerospace Center (DLR). Twin satellites took detailed measurements of Earth's gravity field anomalies from its launch in March 2002 to the end of its science mission in October 2017. The two satellites were sometimes called Tom and Jerry, a nod to the famous cartoon. The GRACE Follow-On (GRACE-FO) is a continuation of the mission on near-identical hardware, launched in May 2018.
Tests of general relativity serve to establish observational evidence for the theory of general relativity. The first three tests, proposed by Albert Einstein in 1915, concerned the "anomalous" precession of the perihelion of Mercury, the bending of light in gravitational fields, and the gravitational redshift. The precession of Mercury was already known; experiments showing light bending in accordance with the predictions of general relativity were performed in 1919, with increasingly precise measurements made in subsequent tests; and scientists claimed to have measured the gravitational redshift in 1925, although measurements sensitive enough to actually confirm the theory were not made until 1954. A more accurate program starting in 1959 tested general relativity in the weak gravitational field limit, severely limiting possible deviations from the theory.
The flyby anomaly is a discrepancy between current scientific models and the actual increase in speed observed during a planetary flyby by a spacecraft. In multiple cases, spacecraft have been observed to gain greater speed than scientists had predicted, but thus far no convincing explanation has been found. This anomaly has been observed as shifts in the S-band and X-band Doppler and ranging telemetry. The largest discrepancy noticed during a flyby has been 13.46 mm/s.
The geodetic effect represents the effect of the curvature of spacetime, predicted by general relativity, on a vector carried along with an orbiting body. For example, the vector could be the angular momentum of a gyroscope orbiting the Earth, as carried out by the Gravity Probe B experiment. The geodetic effect was first predicted by Willem de Sitter in 1916, who provided relativistic corrections to the Earth–Moon system's motion. De Sitter's work was extended in 1918 by Jan Schouten and in 1920 by Adriaan Fokker. It can also be applied to a particular secular precession of astronomical orbits, equivalent to the rotation of the Laplace–Runge–Lenz vector.
The Gravity Probe B mission timeline describes the events during the flight of Gravity Probe B, the science phase of its experimental campaign, and the analysis of the recorded data.
In general relativity, Lense–Thirring precession or the Lense–Thirring effect is a relativistic correction to the precession of a gyroscope near a large rotating mass such as the Earth. It is a gravitomagnetic frame-dragging effect. It is a prediction of general relativity consisting of secular precessions of the longitude of the ascending node and the argument of pericenter of a test particle freely orbiting a central spinning mass endowed with angular momentum .
Gravitoelectromagnetism, abbreviated GEM, refers to a set of formal analogies between the equations for electromagnetism and relativistic gravitation; specifically: between Maxwell's field equations and an approximation, valid under certain conditions, to the Einstein field equations for general relativity. Gravitomagnetism is a widely used term referring specifically to the kinetic effects of gravity, in analogy to the magnetic effects of moving electric charge. The most common version of GEM is valid only far from isolated sources, and for slowly moving test particles.
Charles William Francis Everitt is a US-based English physicist working on experimental testing of general relativity.
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LARES is a passive satellite system of the Italian Space Agency.
Frame-dragging is an effect on spacetime, predicted by Albert Einstein's general theory of relativity, that is due to non-static stationary distributions of mass–energy. A stationary field is one that is in a steady state, but the masses causing that field may be non-static — rotating, for instance. More generally, the subject that deals with the effects caused by mass–energy currents is known as gravitoelectromagnetism, which is analogous to the magnetism of classical electromagnetism.
Ignazio Ciufolini is an Italian physicist active in the field of gravitational physics and general relativity.
PSR J1141−6545 is a pulsar in the constellation of Musca. Located at 11h 41m 07.02s −65° 45′ 19.1″, it is a binary pair composed of a white dwarf star orbiting a pulsar. Because of this unusual configuration and the close proximity of the two stars it has been used to test several of Einstein's theories.
Lorenzo Iorio, born in Bari in, is an Italian physicist working in general relativity, gravitation and related topics in astronomy and astrophysics.
↑ "Frequently asked Questions". Gravity Probe B. Stanford University. Answers to Spacecraft and Mission Operations Questions: 1.When and where was GP-B launched, and where can I find photos, video or news clips of the launch?. Retrieved 14 May 2009.
↑ "Frequently asked Questions". Gravity Probe B. Stanford University. Answers to Spacecraft and Mission Operations Questions: 4.Where is the GP-B Mission Operations Center (MOC) for controlling the spacecraft in orbit?. Retrieved 14 May 2009.
↑ Iorio, L. (2007). "An assessment of the measurement of the Lense–Thirring effect in the Earth gravity field, in reply to: "On the measurement of the Lense–Thirring effect using the nodes of the LAGEOS satellites, in reply to "On the reliability of the so far performed tests for measuring the Lense–Thirring effect with the LAGEOS satellites" by L. Iorio," by I. Ciufolini and E. Pavlis". Planetary and Space Science. 55 (4): 503–511. arXiv:gr-qc/0608119. Bibcode:2007P&SS...55..503I. doi:10.1016/j.pss.2006.08.001.
↑ Iorio, L. (2009). Recent Attempts to Measure the General Relativistic Lense–Thirring Effect with Natural and Artificial Bodies in the Solar System. Vol.017. Proceedings of Science PoS (ISFTG). arXiv:0905.0300. Bibcode:2009ftg..confE...1I.
Launches are separated by dots ( • ), payloads by commas ( , ), multiple names for the same satellite by slashes ( / ). Cubesats are smaller. Crewed flights are underlined. Launch failures are marked with the † sign. Payloads deployed from other spacecraft are (enclosed in parentheses).
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