Newton thought it was instantaneous, Einstein assumed it travelled at the speed of light, but no one really knew how fast gravity goes till now. Radio astronomer Ed Fomalont and theoretical physicist Sergei Kopeikin tell the story of how they discovered the answer

� IF AN alien spacecraft suddenly plucked the Sun from the centre of the Solar System, how would the Earth respond? We know that the sky would become dark after 8.3 minutes, the time it takes light to travel from the Sun to the Earth. But what about the Sun's gravitational force?

Most scientists assume that gravity also travels at the speed of light. So the Earth would remain in orbit for 8.3 minutes and then, suddenly feeling no gravity, would continue off into space in a straight line. This assumption is implicit in the general theory of relativity, which Einstein devised in 1915 and is still our best working theory of space-time. But an assumption is all it is. It has never been tested.

Even worse, the assumption has come under pressure from the modern interest in what are called �brane worlds�. These theories are a type of string theory that envisage extra spatial dimensions in addition to the space-time in which ordinary matter exists. In these theories, the extra dimensions are rolled up extremely small. Gravity can take a short cut through these dimensions, while light is confined to the world of ordinary matter, known as the �main brane�.

If this is the way things work, gravitational waves could appear to travel faster than the speed of light in our world and yet not violate the equations of general relativity. So determining the speed of gravity could provide important evidence about the existence and compactness of these higher dimensions, and help to put some of the competing theoretical brane worlds to the test.

When an opportunity came up last year to measure the speed of gravity, through a combination of theoretical insight by one of us (Kopeikin) and an experimental technique developed by the other (Fomalont), we leapt at the chance. The opportunity came on 8 September 2002, when the planet Jupiter passed nearly in front of a bright radio quasar called J0842+1835. Our plan was to use the world's most powerful intercontinental array of radio telescopes to measure the apparent change in the quasar's position and thus to determine the speed of gravity. Now, after four months analysing our observations, we know the answer.

It is no secret why the assumed speed of gravity remained untested and unchallenged for so long. Most physicists thought that the speed of gravity shows itself only in the propagation of gravitational waves through space. And since no one has even detected gravitational waves, measuring how fast they travel was not on the agenda.

But people were missing something. Kopeikin realised that Einstein's theory could be reformulated in a way that made gravity analogous to electromagnetic radiation. Physicists have known for more than a century that a uniformly moving charge generates a constant electric and magnetic field whose strength depends on the magnitude of the charge, its velocity and the speed of light. The relationship is expressed in what are known to every physicist as Maxwell's equations. Crucially, this means that it is possible to calculate the speed of light from measurements of the electric and magnetic field of a moving charge, without having to detect electromagnetic waves directly.

In the same way, Kopeikin's reworking of general relativity expresses the gravitational field produced by a moving body in terms of the mass of the body, its velocity and the speed of gravity. If we could just get detailed information on the gravitational field of a massive moving body, we could use this to work out the speed of gravity.

The trouble is, getting hold of this information is not at all easy. One obvious probe might be to use �gravitational lensing�. This is the apparent shift in position of a distant object that occurs when its light is deflected on the way to Earth as the rays pass through the gravitational field of a massive body. If that body is moving, measurement of the lensing effect should give us the information we require.

But there are problems. Although physicists have known for some time how a stationary body, or one moving at a uniform speed, lenses light, the equations that describe the deflection of light around a rotating, orbiting body looked totally intractable. Then in 1999 Kopeikin, who was then at the University of Jena in Germany, made a crucial breakthrough. To the surprise of physicists worldwide, he came up with an exact solution to these equations.

Being able to probe the gravitational field of a moving body is a start, but there are other problems, too. We also need to know the exact mass and orbit of the body that is lensing the light. Although the sky is full of stars and dark clusters that move in front of other light sources and deflect the light from them, we do not know the mass and velocity of most of these �cosmic lenses� nearly well enough.

One body for which we do have this information is Jupiter. Thanks to fly-bys by the Pioneer, Voyager and Galileo spacecraft, we know the planet's mass and orbital velocity with unparalleled precision. So to find the speed of gravity, all we need is an occasion where Jupiter moves in front of a good strong light source, lensing the rays on their way to Earth.

In 2000 Kopeikin compared the orbit of Jupiter for the next 30 years with catalogues of suitable radio sources. A close encounter of Jupiter with a radio source is a rare event, happening only about once every decade. But a close passage of Jupiter to the strong radio quasar J0842+1835 was due on 8 September 2002. Time was tight!

The two of us had met briefly in Tokyo in 1996. When Kopeikin was looking around for someone to help him make his observations, he recalled that Fomalont had been part of a team that some 20 years earlier had been taking accurate measurement of the bending of radio waves as they passed near the Sun. This sort of experience was just what was needed for the experiment. So Kopeikin contacted his old acquaintance and our partnership was born.

The lensing effect we were planning to measure would cause the apparent position of the quasar J0842 to shift slightly . The best way we have to measure this is to observe the quasar using an array of radio telescopes spaced as far apart as possible. From the time it takes for the distant body's radio signals to reach each telescope we can work out its position in the sky: put simply, if one telescope receives a signal before the other, the quasar must be closer to the telescope at which the signal arrives first.

To make our measurements as accurate as possible, we arranged to take measurements on the largest array we could get access to. We began with the US National Radio Astronomy Observatory's Very Long Baseline Array. It is made up of a series of 10 radio telescopes, each one 25 metres in diameter, stretching from Saint Croix in the US Virgin Islands in the east to Mauna Kea, Hawaii, in the west. To that we added the 100-metre radio telescope in Effelsberg, Germany, giving us a array that extended over 10,000 kilometres.

This should be able to pin down the position of a quasar to an accuracy of 10 microarcseconds, or about 5 billionths of the diameter of the full Moon. That is a resolution three times as high as anyone had previously achieved, yet it is the bare minimum needed to be able to tell whether Jupiter's gravity reaches Earth instantaneously, travelling at infinite speed, or takes a finite amount of time for the journey.

Although we knew it was possible in principle to do our experiment, there were a worryingly large number of ways it could go wrong. Tiny changes in the locations of the telescopes due to continental drift and variations in the Earth's rotation rate could affect our measurements. A more serious problem was that the weather above each telescope could ruin them entirely: as the wind moves clouds over the various telescopes, the radio source can appear to jitter, masking the much smaller effect from Jupiter's gravity.

The key to dealing with these uncertainties was to find sources near J0842+1835 that would not be lensed by Jupiter on 8 September but were close enough in the sky to be subject to similar atmospheric conditions. With fast-alternating observations of several radio sources, we could measure the difference in positions much more accurately than the position of each one alone. In the end we picked two quasars to use as reference sources on the day.

We had five observing days on the array of telescopes, each lasting 10 hours. The crucial day was, of course, 8 September, when the closest passage of Jupiter to J0842 occurred at 16.30 GMT. But that alone would not have been enough. Quasars are caused by outbursts of energy from a black hole in the centre of a galaxy, and this phenomenon can vary over time. So we also made observations on days when the effect of Jupiter's gravitational field on J0842 would be negligible, and also to check that our sources were not jittering in a way that might confound our measurements.

Perhaps our most serious worry concerned what was happening on Jupiter itself, or to be more precise, in its large and variable magnetosphere. This is a plasma of fast-moving electrons from the solar wind that become trapped by the Jovian magnetic field. Our fear was that the quasar radio waves passing near the planet's surface on 8 September could be warped by the magnetosphere. We were worried that if the magnetosphere was very active, this effect would be as large as the gravitational bending we were looking for.

We could have overcome this problem by observing at two different frequencies simultaneously, but this would have added complexity to the experiment, and decreased its overall accuracy, so we decided instead to bank on good Jovian weather.

The bet paid off, and everything did go well � until the big day itself. To our horror, on 8 September, the telescope at Saint Croix malfunctioned because of serious tape recording problems. Fortunately, it turned out that the data from other telescopes could compensate for the loss. We also had to discard about 15 per cent of our data because of bad weather.

Happily, this still left enough data for us to carry out the analysis. Comparing the position of J0842 on 8 September with its average position on the off-Jupiter days and plugging this into Kopeikin's formula for the gravitational field of the moving Jupiter gave us the answer we were looking for. We became the first two people to know the speed of gravity, one of the fundamental constants of nature.

Here it is: gravity does move at the same speed as light. Our actual figure was 1.06 times the speed of light, but we have an error of plus or minus 0.21. We are planning to announce our results this week at the American Astronomical Society's annual meeting in Seattle.

Our result rules out the possibility that gravity travels instantaneously, as Newton imagined. If it did, we would have seen a minutely different shift in the position of the quasar on the night of 8 September. This vindicates Einstein's instinct when formulating his general theory of relativity, which was to assume the speed of gravity was equal to the speed of light.

Our result also puts stringent limitations on the parameters of brane-world theories: in particular, it restricts how many extra dimensions there may be, and their size. The more compact the extra dimensions, the less able gravity is to take a short cut through them and the closer the speed of gravity must be to the speed of light.

We look forward to new theoretical efforts to unify fundamental forces with gravity that take this into account. We also hope that over the next decade Russia, Japan and the US will succeed in extending the largest radio telescope arrays beyond the diameter of the Earth by putting large radio telescopes in orbit, and that this will confirm and greatly increase the accuracy of our result.

�We became the first two people to know the speed of gravity, one of the fundamental constants of nature�

PHOTO (COLOR): The world's most powerful radio telescopes watched as Jupiter almost eclipsed a distant quasar

PHOTO (COLOR): On 8 September 2002, Jupiter passed almost in front of a distant quasor, putting Einstein's assumption to the test

PHOTO (COLOR): The very long Baseline Array of raidio telescopes stretches from Hwaii (left) to the Caribbean

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By Ed Fomalont, Ed Fomalont is a scientist at the National Radio Astronomy Observatory in Charlottesville, Virginia. and Sergei Kopeikin, Sergei Kopeikin is a professor of theoretical physics at the University of Missouri-Columbia