129.1 Sept 2, 2002 Gravity Speed Test 

Sept 2, 2002 Gravity Speed Test

04/22/04 Propagation Speed of Gravity and the Relativistic Time Delay by Clifford M. Will (PDF)

Go To Cosmic Log Results as of 12/17/02

Go To The Associated Press Study: Speed of Gravity, Light Match By Paul Recer 09/01/03

Kopeikin and the Speed of Gravity, Meta Research Press Release 2003/01/08

Van Flandern immediately rejects the Kopeikin Summary, as I do.

(Note: I predict speed of propagation of gravity, tested by the measuring instruments, will be claimed to be limited to the speed of light, that limit also being the limit of the measuring instruments. If a Lorentz Relativity was used here, I learned, some time ago, that Lorentz Transform guage is the only one that does not allow measurement or detection of velocities more than the velocity of, supposed light, actually of space, or of any cause before effect phenomena.

However, knowing that gravity is also the cosmic NOW (Instant Renewal), or the 4th Dimension (SuperSpectrum), which has no velocity and does communicate instantly, I have claimed, and do claim gravity communicates instantly, far beyond any measure of it, but it does not "travel". The phenomena of gravity should be accurately defined as the disappearance of space Aether between any two units of mass. As the Aether disappears into matter, naturally the matter seems to approach each other, so there is not an actual pull of mass, nor is there an actual push of gravity either. We could say that gravity is the rate of flow of space Aether into mass. This experiment of attempting to measure, with instruments limited to light velocity, a gravity phenomena that has no velocity and does not push or pull or move, in reality, seems to point to a lack of understanding and hence, a coming erroneous result. MetPhys)

Go Right to The Test Setup (From pdf to Text Document)
General relativistic model for experimental measurement of the speed of propagation of gravity by VLBI.

What is Gravity? Select Gravity Excerpts from 100's Studied
Where is it in the SuperSpectrum?

Results in Mid-November: Earthfiles Report of the Experiment by Linda M. Howe

Alen Boyle: Cosmic Log
Sept. 5, 2002 / 4 p.m. ET
How fast is gravity? The question seems so simple, but it actually generates a cosmic debate inside and outside the scientific mainstream. This weekend, astronomers will take a big step toward calculating the speed of gravity.

Relativity theory dictates that nothing can travel faster than the speed of light, and that such a cosmic speed limit would apply to gravitational influences as well. But there's never been a definitive experimental test of that claim.

As it so happens, a line-of-sight encounter between Jupiter and a distant quasar at 12:30 p.m. ET Sunday represents the best opportunity in a decade for such a test, according to Sergei Kopeikin of the University of Missouri at Columbia and Ed Fomalont of the National Radio Astronomy Observatory.

The astronomers expect their data to confirm that gravitational effects move at the speed of light, and they hope to have the results ready to present to the American Astronomical Society in January. But if they come up with an unexpected answer, it could send shock waves through the scientific community and beyond.

In the days and hours surrounding Sunday's encounter, the 10 radio telescopes of the NRAO's Very Long Baseline Array and the Max Planck Institute's 100-meter radio telescope in Effelsberg, Germany, will measure how Jupiter's passage affects radio waves from the quasar.

Fomalont said the radio signature should be "bent by the gravitational field of Jupiter, not where it is now, but where it was a little bit earlier, because it took some time for that gravitational field to travel from Jupiter to where the radio wave is."

Kopeikin explained, "The apparent position of the quasar as Jupiter is moving will make a small loop in the sky. That loop will be a circle, if gravity propagates at infinite speed. But if gravity propagates at infinite speed, that loop will be an ellipse."

The observations are incredibly tricky, not only because the effect is very small but also because the astronomers have to adjust for the effects of Jupiter's magnetic field, the jitters caused by Earth's atmosphere and what Fomalont calls the "natural perversities" in the quasar's radio emissions.

"Only now are we able to reach such a high precision in measuring the position of astronomical bodies," Kopeikin said. A similar observation, conducted a decade ago, was inconclusive because the precision was 100 times worse, he said.

The paper setting the stage for this weekend's experiment was published in The Astrophysical Journal last year. You need a subscription to read that paper, but if you have Adobe Acrobat, you can read this version, which was presented at a symposium in June.

There are other facets to the "speed of gravity" debate that may not be settled even if Kopeikin and Fomalont come up with the expected results. Iconoclastic physicist Tom Van Flandern has been saying for years that gravitational force acts at velocities far faster than the speed of light, and he engaged Kopeikin in a rather technical discussion of the quasar experiment. Suffice it to say that Van Flandern thinks this weekend's observations won't address his central claims.

This whole exercise isn't merely a dry classroom debate over Lorentzian vs. Einsteinian relativity: Any evidence that gravity works faster than the speed of light would be seized upon by creationists to bolster their claim that the universe really could have been created 6,000 years ago. We saw this debate flare up in the wake of suggestions that the speed of light might have been faster in the distant past.

Click here to see how creationists frame their arguments, or here to read a counterargument. And feel free to let me know what you think.

Alen Boyle


129.2 The Test Setup 

(From pdf Format converted to text document)

arXiv: gr- qc/ 0206022 v1 7 Jun 2002

Proceedings of the 6th European VLBI Network Symposium Ros, E., Porcas R.W., & Zensus, J.A. (eds.) June 25th-28th 2002, Bonn, Germany EUROPEAN NETWORK

PDF Version: General relativistic model for experimental measurement of the speed of propagation of gravity by VLBI

Text Version: General relativistic model for experimental measurement of the speed of propagation of gravity by VLBI
S. Kopeikin 1;3 and E. Fomalont 2

1. Department of Physics and Astronomy, University of Missouri - Columbia, 223 Physics Bldg., Columbia, Missouri, 65211, USA
2. National Radio Astronomical Observatory, 520 Edgemont Road, Charlottesville, VA 22903, USA
3. E-mail: kopeikins@missouri.edu

Abstract. A relativistic sub-picosecond model of gravitational time delay in radio astronomical observations is worked out and a new experimental test of general relativity is discussed in which the effect of retardation of gravity associated with its finite speed can be observed. As a consequence, the speed of gravity can be measured by differential VLBI observations. Retardation in propagation of gravity is a central part of the Einstein theory of general relativity which has not been tested directly so far. The idea of the proposed gravitational experiment is based on the fact that gravity in general relativity propagates with finite speed so that the detection of light caused by the body must be sensitive to the ratio of the body's velocity to the speed of gravity. The interferometric experiment can be performed, for example, during the very close angular passage of a quasar by Jupiter. Due to the finite speed of gravity and orbital motion of Jupiter, the variation in its gravitational field reaches observer on Earth not instantaneously but at the retarded instant of time and should appear as a velocity-dependent excess time delay in addition to the well-known Shapiro delay, caused by the static part of the Jupiter's gravitational field. Such Jupiter-QSO encounter events take place once in a decade. The next such event will occur on September 8, 2002 when Jupiter will pass by quasar J0842+1835 at the angular distance 3:70. If radio interferometric measurement of the quasar coordinates in the sky are done with the precision of a few picoseconds (cannot copy 5 pas) the effect of retardation of gravity and its speed of propagation may be measured with an accuracy about 10%.

1. Theoretical Background

Experimental verifications of the basic principles underlying Einstein's general relativity theory are important for fundamental physics. All previous experimental tests of general relativity in the solar system have relied upon the static Schwarzchild solution (Will 1993) and, therefore, were not sensitive to the effects entirely associated with the propagation speed of gravity. It is worth noting that gravitational waves are inherent to the radiative (far) zone of a system emitting the waves (Misner, Thorne & Wheeler 1973; Barish & Weiss 1999). However, the gravitational waves do not propagate freely through the interior of a non-radiative (near) zone of the system. Nevertheless, the process of generation of gravitational waves produces retarded effects in the near zone leading to appearance of the gravitational radiation reaction force in the relativistic equations of motion of extended bodies comprising a self gravitating astronomical system (Damour et al. 1989). Existence of this force is a consequence of the finite speed of propagation of gravity as it was experimentally confirmed by Taylor (1994). We have found (Kopeikin 2001) that the gravitational bending of light passing through the gravitational field of a moving massive object like Jupiter, though being dominated by the spherically-symmetric component of its gravitational field, also contains terms associated with the - finite speed of propagation of gravity. Our calculations reveal that electromagnetic signals interact with the lightray detecting bodies only through the retarded gravitational fields { the observational effect which must be accounted for in precise data processing algorithms adopted for the microarcsecond space astrometry. This gravitational light-propagation theory, in the case of a static spherically-symmetric field, gives the same result as that predicted by Einstein for the bending of light, E ' 4GM=(c 2 R ), where M is the mass of the lightray de ecting body, R is the distance from observer to the body, and is the (small) angle in the sky between the undisturbed geometric positions of the source of light and the center of mass of the massive body. Furthermore, this theory allows to calculate the correction, PG, to the Einstein detection E related to the variability of the gravitational field produced by the motion of the light-ray detecting body. We were successful in proving (Kopeikin 2001) that these corrections in the bending of light are inherently associated with the finite speed of propagation of gravity and in case of slowly moving bod- ies can be parameterized as PG ' (1 + )( E= )(v=c), where v is the orbital velocity of the light-ray detecting body with respect to the barycenter of the solar system projected on the plane of the sky, and = cg=c 1 is a tting parameter used in data analysis. It is chosen such that = 0, if the speed of gravity cg equals the speed of light c.•S. Kopeikin and E. Fomalont: Relativistic model for experimental measurement of the speed of gravity Parameter is a close analogue of the parameter 2 = (cg=c) 2 1 of the parameterized post-newtonian (PPN) formalism which quanties possible violation of the local Lorentz invariance (Will 1993) 1 . It was shown (Nordtvedt 1987) that 2 < 4 10 7 under the (rather restrictive) assumption that the preferred frame is real- ized by the cosmological Hubble ow. If one abandons any anthropic assumption about the speed of the solar system with respect to an (actually unknown) preferred frame the limit on 2 < 0:1 can be obtained from the analysis of the anomalous perihelion shifts of inner planets (Will 1993).

The primary purpose of our experiment is, however, to observe directly the effect of retardation in propagation of gravitational field in the solar system rather than improving limits on 2. Nevertheless, we would like to emphasize that relativistic effects in propagation of light through time dependent gravitational fields are also sensitive to vi- olation of local Lorentz invariance.

The largest measurable contribution to the variable, time-dependent part of the solar system gravitational field comes out from the orbital motion of Jupiter. The min- imal value of the impact parameter of an incoming light ray from a quasar that can be achieved for Jupiter is also the least possible amongst all the solar system bodies. Therefore, it is highly sensible to make an attempt for detection of the "gravity retardation" effect by observing very accurately the gravitational detection of light from a background source (quasar) caused by the motion of Jupiter around the barycenter of the solar system. As ex- plained in (Kopeikin 2001) the magnitude of the observed effect is directly translated to the measured value of the propagation speed of gravity cg. This is the essence of the new test of general relativity which has never been done before with suffcient accuracy.

Radio astronomical methods of VLBI are the most accurate for measuring gravitational detection of elec- tromagnetic waves. The two most precise measure- ments of the bending of radio waves near the sun (Lebach et al. 1995; Robertson, Carter & Dillinger 1991) were accurate to about 0.1%. However, these observations were insensitive to the speed of gravity effect PG because of the relatively large impact parameter of the incoming light ray. Even at the solar limb, the magnitude of PG is ý 10 5 of the static gravitational bending E = 1:750 and is totally unobservable because of the highly turbulent solar magnetosphere.

On September 8, 2002 Jupiter will pass at an angu- lar distance of 3:70 from the quasar J0842+1835 making an ideal celestial configuration for measuring the speed of propagation of gravity by using the phase-referencing VLBI technique (Fomalont & Kopeikin 2002). The encounter in 2002 is especially favorable because: (1) it occurs when Jupiter is relatively far from the Sun (the next near occultation which occurs is a few degrees from the Sun), and (2) the five critical hours of the closest approach

1 One notices that = 2=2 in the first approximation. occur when Jupiter is near the transit line for VLBA ob- servations.

We have estimated that for this Jupiter-quasar encounter the de ection from the static gravitational field and from the propagation of gravity are, respectively, E = 1:26 mas and PG = 53 as 2 both in the plane of the sky with the static bending radially from Jupiter and the propagation bending in the direction of Jupiter's motion (see Eqs. (7) and (8) in Sec. 3). As one can see the ratio j PG j = E ' 0:04 is much larger for Jupiter than for the Sun which is explained by the ability to get a smaller impact parameter for the light ray passing by Jupiter than that for the Sun.

2. Relativistic Model of VLBI Time Delay

Detection of the effect of gravity propagation requires a more advanced VLBI model for light propagating in the time dependent gravitational field of the solar system. Such a model must be valid to a precision of better than 0.1 ps. In the present paper we discuss the appropriate corrections to the standard Shapiro time delay (Shapiro 1967) which bring the accuracy of the model up to the necessary threshold.

The general formula for the relativistic time delay T in the eld of a system of moving bodies is given in (Kopeikin 2001) T = (1 + ) G c 3 N X a=1 ma Z s s0 1 1 c k va( ) 2 ( ) d t + 1 c k xa( ) ; (1) where ( ) = 1= p 1 c 2 v 2 a ( ) is the Lorentz factor, is the PPN parameter (Will 1993), ma is the mass of the ath(?) body, t is the time of the closest approach of electro- magnetic signal to the barycenter of the Solar system 3 , xa(t) are coordinates of the ath(?) body, va(t) = dxa(t)=dt is the (non-constant) velocity of the ath(?) light-ray detecting body, k is the unit vector from the point of emission to the point of observation, s is a retarded time obtained by solving the gravitational null cone equation for the time of observation of photon t = s + c 1 g j x xa(s) j , and s0 is found by solving the same equation written down for the time of emission of the photon t0 = s0 +c 1 g j x0 xa(s0) j . One emphasizes that the equations for the retarded times depend on the speed of gravity cg, but not the speed of light c. This is because they were obtained by solving Einstein equations for the space-time metric perturbations by making use of retarded Lienard-Wiechert tensor potentials (Kopeikin & Sch•afer 1999). These retarded gravitational potentials describe propagation of gravity without any relation to the problem of propagation of light in the gravitational field. In general relativity cg = c numerically.

2 It corresponds to the time delays 122.2 and 5.1 picoseconds respectively on a baseline b = 6000 km.

3 The time t is used in calculations as a mathematical tool only. It has no real physical meaning because of its dependence on the choice of a coordinate system.•S. Kopeikin and E. Fomalont: Relativistic model for experimental measurement of the speed of gravity However, when light propagates through time-dependent gravitation field, in principle, one can separate relativistic effects associated with propagation of light and gravity.

The Earth and Sun also contribute signifcantly to the gravitational time delay and must be included in the data processing algorithm in order to extract accurately the effect of retardation of gravity. Precise calculation of the integral (1) for two radio antennas gives the differential VLBI time delay = 2T 1T = + + J + JPG : (2)

The first term in the right hand side of (2) describes the gravitational (Shapiro) time delay due to the gravitational eld of the Earth = (1 + ) GM c 3 ln X1 + K X1 X2 + K X2 : (3)

It can reach 21 ps for the baseline b = 6000 km.

The second term in the right hand side of (2) describes the gravitational (Shapiro) time delay due to the Sun = (1 + ) GM c 3 ln r1 + K r1 r2 + K r2 : (4)

It can vary (for b = 6000 km) from 17 10 4 ps for the light ray grazing the Sun's limb to only 17 ps when direction to the source of light is opposite to the Sun.

The third term in the right hand side of (2) is the Shapiro time delay due to the static part of the gravita- tional field of Jupiter J = (1 + ) GMJ c 3 (1 + K vJ ) ln r1J + K r1J r2J + K r2J : (5)

Finally, the forth term in the right hand side of (2) is the time delay caused by the finite speed of gravity as predicted by general relativity theory (Kopeikin 2001) JPG = 2(1 + ) GMJ c 4 b vJ + (b N1J)(K vJ) r1J + K r1J : (6)

In formulas (3){(6) we use the following notations: M { mass of the Earth, M { mass of the Sun, MJ { mass of Jupiter, vJ(t1) { the barycentric velocity of Jupiter, and K { the unit vector from the barycenter of the solar system to the quasar observed. Also, for each i = 1; 2, one has the baseline vector b = X1 X2, ri = j ri j , riJ = j riJ j , N1J = r1J=r1J, ri = xi(ti) x (ti), riJ = xi(ti) xJ(ti), xi = x (ti) + Xi(ti), where Xi(ti) are the geocentric coordinates of i-th VLBI sta- tion, x { the barycentric coordinates of the geocenter, x { barycentric coordinates of the Sun, xJ { barycentric coordinates of Jupiter, and ti is time of arrival of the plane front of electromagnetic wave from quasar to the ith(?) VLBI station.

We notice there are two relativistic parameters to be measured in order to test validity of general relativity theory - the PPN parameter , and the speed of gravity parameter = cg=c

1. The best experimental measurement of parameter had been conducted by Lebach et al. (1995) who obtained = 0:9996 0:0017 in an excellent agreement with general relativity. The primary goal of the new experimental test of general relativity is to measure the parameter which will set up limits on the numerical value of the speed of gravity cg (Fomalont & Kopeikin 2002). During the passage of Jupiter near the quasar the time-dependent impact parameter ý(t) of the light ray with respect to Jupiter will be always small as compared with the distance from Earth to Jupiter which will be approximately 6 AU. It is convenient to introduce the unit vector n = ý= j ý j along the direction of the impact parameter according to definition sin n = (K (N1J K)); where is a small angle between the unperturbed astrometric position of the quasar and that of Jupiter. Making use of the (impact parameter ) expansion N1J = (1 2 =2)K+ n+O( 3 ); we obtain the functional structure of the Shapiro time delay J and the speed of gravity delay JPG in a more explicit form (assuming for simplicity = 1) J = 4GMJ c 3 r1J n B + (n B) 2 r1J 2 (K B) 2 2r1J 2 ; (7) JPG = (1 + ) 4GMJ c 4 r1J b vJ (K vJ)(K b) 2 ; (8)

where B = b c 1 (K b)(v2 vJ) + O(c 2 ) ; and all quantities in the right sides of Eqs. (7){(8) are taken at the time t1.

3. The Effect of the Magnetosphere of Jupiter

In addition to various special and general relativistic effects in the time of propagation of electromagnetic waves from the quasar to the VLBI antenna network, we must account for the effects produced by the jovian magnetosphere. Measurements obtained during the occultations of Galileo by Jupiter indicate (Flasar et al. 1997) that near the surface of Jupiter the electron plasma density reaches the peak intensity N0 = 1:0 10 10 m 3 . We shall assume that the jovian magnetosphere is spherical 4 and a radial drop-o of the plasma density N(r) is proportional to 1=r 2+A where r is the distance from the center of Jupiter. The guess is that A 0, and we will assume that A = 0 for the worst possible case. Hence, radial dependence of the electron plasma density is taken as N(r) = N0(RJ=r) 2+A , where RJ = 7:1 10 7 m is the mean radius of Jupiter. The plasma produces a delay T in the time of propagation of radio signal which is proportional to the column plasma density in the line of sight given by integral (Yakovlev 1989) Nl = Z r0 d N(r) dr r A+1 pr 2 d 2 + Z r1 d N(r) dr r A+1 pr 2 d 2 ; (9)

4 In reality the magnetosphere has a dipole structure and we speculate that our model which assumes circular symmetry grossly underestimates the plasma content along the polar direction where the closest approach occurs.•S. Kopeikin and E. Fomalont: Relativistic model for experimental measurement of the speed of gravity where r0 and r1 are radial distances of quasar and radio antenna from Jupiter respectively, and d = j ý j is the impact parameter of the light ray from the quasar to Jupiter

5 . In the experiment under discussion the impact parameter is much less than both r0 and r1. Hence, Nl (m 2 ) = N0RJ RJ d A+1 pˇ A+1 2 1 + A 2 ; (10)

where (z) is the Euler gamma-function. The plasma time delay T (s) = 40:4 c 1 2 Nl ; (11) where c is the speed of light in vacuum measured in m/sec, is the frequency of electromagnetic signal measured in Hz.

It is worthwhile noting that, in fact, the VLBI array measures difference in path length between the radio telescopes. Hence, one has to differentiate Nl in expression (11) with respect to the impact parameter d and project the result on the plane of the sky. This gives a magnetospheric VLBI time delay of JM(ps) = 6:3 10 7 (A + 1) Nl d 0 2 n b c ; (12) normalized to the frequency 0 = 8:0 GHz. Substituting d = 13RJ and taking the baseline b = 6000 km we find JM = 2:34 ( 0= ) 2 ps (A = 0) ; (13) JM = 0:13 ( 0= ) 2 ps (A = 1) ; (14) JM = 0:03 ( 0= ) 2 ps (A = 2) : (15)

This represents the pure bending from Jupiter's magnetosphere which should be compared with the propagation of gravity time delay JPG = 5:1 ps at closest approach. If we observe at the dual frequencies at 2.3 GHz and 8.4 GHz in the normal geodetic mode, we certainly can determine the ionospheric (both from Jupiter and from the Earth) effects. However, our sensitivity at 8.4 GHz will be decreased because of only one polarization and only half the total bandwidth. The noise in the ionosphere/magnetosphere bending may also be a limit. As a rough order of magnitude, the position error per day is 10 as at 8.4 GHz and 30 as at 2.3 GHz. Whatever bending we obtain at 2.3 GHz, about 10% is removed from the 8.4 GHz bending. Thus, the ionosphere/magnetosphere correction will have an error of 3 to 4 as. Only in the worst case scenario will the effects of Jupiter's magnetosphere be signi cant at 8 GHz observing. Perhaps we should observe at two widely spaced frequencies in the 8 GHz band, say at 8.0 GHz and 8.5 GHz, then, independently reduce the data at the two frequencies. The gravitational bending delay (7) and gravitational retardation of gravity delay (8) are both independent of frequency. Any plasma delay should scale inversely with

5 This impact parameter d ' 14RJ on September 8, 2002 and corresponds to the angle = 3:70 between the quasar and Jupiter in the plane of the sky.

The frequency-squared and can be determined by looking at the difference measurements. However, this small frequency difference will produce very large errors in the estimate of the jovian bending and also be strongly affected by Earth ionospheric contamination.

If we observe at 15 GHz instead, the magnetospheric and ionospheric delays are both a factor of four smaller and almost certainly negligible. However, the system sensitivity is less and one of the calibrators may be too weak to reliable detect (J0839+1802). We are still unsure about the most optimum method to deal with the possible jovian magnetosphere component.

Time variability of the Jupiter magnetosphere could cause problems. For example, if there were very large, chaotic changes in the jovian magnetosphere, then we could lose coherence over a minute of time. However, this uctuation model is very pessimistic and unlikely, and would probably average out to the steady state model.

4. Summary

We believe that the differential VLBI experiment in September 2002 can measure the retardation effect in propagation of gravity and determine the speed cg of its propagation with 10% to 20% accuracy. If the experiment is successful it will provide a new independent test of general relativity in the solar system.

Acknowledgements. This project has been partially supported by the University of Missouri-Columbia Research Council grant URC-01-083. We thank B. Mashhoon and C.R. Gwinn for discussions and valuable comments and A. Corman for help in preparation of the manuscript.


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Dec. 11, 2002 / 7 p.m. ET

Updating the "speed of gravity": Remember that September experiment to determine whether the propagation speed for a gravitational field was equal to the speed of light? Robert from St. Petersburg does: "Is there a page of the results of the gravity velocity test?" he asked.

VIn reply, University of Missouri physicist Sergei Kopeikin said it's still too soon. "We are still working, because the data analysis is not finished," he said.

Kopeikin and Ed Fomalont of the National Radio Astronomy Observatory do have some preliminary findings, but they're embargoed until January, when the fuller report will be presented to the American Astronomical Society at its meeting in Seattle. The abstract listed for the meeting offers no clues.

A research paper on the experiment will be submitted to the Astrophysical Journal Letters and perhaps other journals, Kopeikin said.


129.4 Speed of Gravity, Light Match By Paul Recer 

Source: The Associated Press Study

SEATTLE - Einstein was right. The speed of gravity matches the speed of light, according to astronomers who took advantage of a rare planetary alignment to measure one of the fundamental forces of nature. Edward B. Fomalout of the National Radio Astronomy Observatory and Sergei Kopeikin of the University of Missouri measured the amount that light from a distant star was deflected by the gravity of Jupiter as the planet passed in front of the star.

Albert Einstein, who formulated basic theories about space, time and relativity, had assumed that gravity moved with the speed of light, about 186,000 miles per second, "but until now, no one had measured it," said Kopeikin. "Einstein was right, of course," said Fomalout.

The measurement is one of the last fundamental constants in physics to be established and Fomalout admitted, "gravity is not well understood." The researchers used 10 radio telescopes scattered across the Earth from Hawaii to Germany to precisely measure how light from a distant quasar, a type of star, was bent as it passed by Jupiter on its way to the Earth. Jupiter is in the precise position for such a measurement only once a decade.

To make the measurement, the instruments had to detect a minute deflection of the light. Fomalout compared the required precision to being able to measure the size of a silver dollar sitting on the moon's surface, or measuring the width of a human hair from 250 miles away.

Craig Hogan, a University of Washington astronomer, said the achievement "is an important advance for physics," but he predicted that new techniques will be developed that will measure gravity's speed even more accurately.

"You can expect a series of experiments now," he said. Fomalout and Kopeikin said their results are accurate within about 20 percent. Knowing the precise speed of gravity is important to physicists testing such modern ideas as the superstring, which holds that fundamental particles in the universe are made up of small vibrating loops or strings. It also affects some basic space-time theories.


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