ON 8 December 1990, NASA鈥檚 flew past the Earth on its roundabout path to Jupiter. It was the first of two such manoeuvres, designed to boost its speed and give it sufficient oomph to reach its destination. The probe skimmed just 960 kilometres above the cloud tops at its closest point before slingshotting back into deep space. Everything went to plan 鈥� almost. As Galileo raced away from Earth, NASA鈥檚 space-flight engineers began to scratch their heads. To their bafflement, the probe was travelling 3.9 millimetres per second faster than it had any right to be travelling. That may seem a paltry amount, but in fact such a change is startling.
And Galileo is not alone. Almost every spacecraft that has swung around the Earth to speed it on its journey into space has recorded an inexplicable velocity change. The biggest, in 1998, affected NASA鈥檚 spacecraft, whose speed was boosted by an additional 13.5 millimetres per second. 鈥淭he fly-by anomalies appear to be real,鈥� says John Anderson, who recently retired from (JPL) in Pasadena, California. 鈥淵et we don鈥檛 have a clue what鈥檚 causing them.鈥�
The findings may call into question our understanding of gravity. Could these anomalies yield the first tangible connection between quantum mechanics and relativity, a link that theorists would dearly love to find? Or is there some mysterious, unseen body of matter tugging at our spacecraft? Whatever the answer, these anomalies may compel us to re-examine the forces at work in space.
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Planetary fly-by manoeuvres were first proposed in 1961 by Mike Minovitch, then a summer student at JPL. They are a way for spacecraft to boost their speed en route to planets in the outer solar system, battling the pull of the sun as they go. On journeys to the inner planets 鈥� which inevitably entails falling ever faster towards the sun 鈥� fly-bys can be used to shed enough speed to enable a probe to drop safely into orbit around its target planet. Or they can be used merely to change direction. For space-flight engineers, fly-bys are the ultimate fuel saver because they exploit the planet鈥檚 gravitational tug to a spacecraft along its route.
How such manoeuvres work is not obvious, as the speed of the spacecraft with respect to the fly-by planet remains unchanged. Nevertheless, it is possible to choose an incoming trajectory such that the planet鈥檚 speed relative to the sun either adds to or subtracts from the space probe鈥檚 speed.
Galileo was the first spacecraft to take advantage of Earth鈥檚 gravity in a fly-by manoeuvre. NASA had originally planned to take Galileo into Earth鈥檚 orbit in the space shuttle鈥檚 cargo bay and then use a powerful liquid-fuel rocket to fire it into an orbit that would take it unassisted to Jupiter. But the in 1986 scotched that plan due to safety concerns about the rocket fuel. Engineers were then limited to using a safer, solid-fuel rocket which would have had insufficient power on its own to reach Jupiter. Searching for an alternative route, they found that they could achieve enough speed to get to the gas giant by first swinging the probe around Venus and then twice around Earth.
Galileo was merely the first to show an anomaly. There have now been a total of six Earth fly-bys by space probes. On 23 January 1998, the NEAR Shoemaker spacecraft recorded an unexpected boost as it swooped by Earth on its way to the asteroid Eros. On 4 March 2005, the European Space Agency鈥檚 spacecraft 鈥� bound for comet 67P/Churyumov-Gerasimenko 鈥� sped up by about 1.8 millimetres per second. 鈥淭hese three space probes show the most unambiguous effect,鈥� says Anderson, who this year, with colleagues at JPL, published a detailed study of the anomalies in the journal Physical Review Letters ().
鈥淕alileo was merely the first spacecraft to show an anomaly鈥�
Anderson learned of Galileo鈥檚 anomalous velocity immediately after its first fly-by in 1990. Mission controllers on Earth monitor the speed of a spacecraft by listening for the beeps broadcast by its radio transmitter. By measuring the change in frequency caused by its motion, they can determine the spacecraft鈥檚 speed to an accuracy better than 1 millimetre per second. Spacecraft engineers expect to see a probe performing a fly-by to recede from the Earth at exactly the same speed as it approaches. And this is why the extra change in speed relative to the sun is such a startling and inexplicable thing to see.
Then in 1998, Anderson heard the Galileo engineers mention the anomaly at a conference in Boston, where they also pointed out the NEAR Shoemaker fly-by anomaly. 鈥淪ince it didn鈥檛 affect their missions, they didn鈥檛 think much more about it and left it at that,鈥� he recalls.
Anderson may have left it too, had he not been one of the principal investigators for NASA鈥檚 missions. He and his colleagues had just gone public with some puzzling results showing that the twin Pioneer craft were moving slightly slower than they should be. It was as if the two spacecraft, launched in opposite directions relative to the sun in 1972 and 1973, respectively, were experiencing a small tug back towards the sun in addition to the force of gravity. The effect became known as the Pioneer anomaly and remains unexplained to this day.
Making sure that the Pioneer anomaly was real took a painstaking analysis of 11 years of data, from 1977 to 1988. The Pioneer team finally published their findings in 1998 (Physical Review Letters, ). 鈥淭en years after we first noticed the Pioneer anomaly, suddenly another spacecraft anomaly turns up,鈥� says Anderson.
He and his colleagues at JPL were less sure about the other spacecraft. Galileo, NEAR Shoemaker and Rosetta showed the clearest effect, but NASA鈥檚 Mercury-bound spacecraft , which performed a fly-by of Earth on 2 August 2005, showed a negligible anomaly. On the other hand, Galileo, which flew by the Earth for a second time on 8 December 1992, was slowed by about 4.6 millimetres per second on that occasion. And , which flew by the Earth on 18 August 1999 on its way to Saturn, showed a small reduction in speed of about 2 millimetres per second.
In the latter two cases, according to Anderson, the fly-by anomaly may have been swamped by other factors. For instance, Galileo鈥檚 second fly-by was at an altitude of 303 kilometres, much lower than its first. 鈥淒rag from the atmosphere could plausibly have reduced the spacecraft鈥檚 speed,鈥� he says.
But while such swamping might explain the reductions in speed, it could not explain the increases. In 2006, Claus L盲mmerzahl at the University of Bremen, Germany, and his colleagues a number of possible mundane explanations for them. These included atmospheric drag, gravitational tugs caused by terrestrial tides, and the interaction of the spacecraft with Earth鈥檚 magnetic field.
The team ruled out atmospheric drag because it could only slow, not speed up a spacecraft. They also dismissed variations in the planet鈥檚 gravity due to the tidal bulge of the oceans and the mass distribution within the Earth鈥檚 crust 鈥� these could not produce sufficiently large velocity changes. Finally they rejected the idea that the probe had acquired an electric charge or a magnetic moment so large that its interaction with the Earth鈥檚 magnetic field might significantly change its velocity.
Dark matter cloud
So what else could be behind the anomalies? To find out, Anderson and his colleagues have been poring over the trajectory data for each spacecraft, looking for clues. They wanted to see which orbital parameters appear to affect the anomaly. Their most striking find turned out to be the angles of the incoming trajectory and the outgoing trajectory with respect to the equator. The team discovered a simple empirical formula that relates to these angles and the rotational velocity of Earth. The formula fits each of the six fly-by anomalies. 鈥淚n lay terms, this shows that the more symmetric the incoming and outgoing trajectory about the Earth鈥檚 equator, the smaller the anomaly,鈥� says Anderson.
This immediately shed light on why the NEAR Shoemaker probe showed the biggest anomaly. 鈥淚t had the most asymmetric trajectory with respect to the Earth鈥檚 equator,鈥� says Anderson (see diagram). On the other hand, the most symmetric trajectory is that of Messenger. The formula gives a velocity change of less than 0.06 millimetres per second, says Anderson, which is close to the value mission engineers measured (see chart).
Using their formula, Anderson and his colleagues were able to make a prediction for the second fly-by of Rosetta on 13 November 2007. They expect to see small boost of just under 1 millimetre per second. So far, they have yet to see and analyse the detailed data for this fly-by. 鈥淚t will be a crucial test of our formula,鈥� says Anderson.
Despite its success so far, the physics behind the formula remains a complete mystery. Earth鈥檚 rotation is a key part of the formula, but in Newtonian gravity this should have no effect on the trajectory of a spacecraft. In Einstein鈥檚 improved theory of gravity 鈥� his general theory of relativity 鈥� the rotating Earth drags space-time around with it. In fact, NASA鈥檚 was launched in 2004 precisely to measure this effect. 鈥淗owever, it is far too small to explain fly-by anomalies,鈥� says Anderson.
The only other effect connected with the Earth鈥檚 rotation relates to the Earth鈥檚 magnetic field. 鈥淏ut the force this would exert on a tiny metal spacecraft is also too small to explain the anomalies,鈥� says Anderson. He admits he is at something of a loss. 鈥淚t鈥檚 difficult to come up with mundane explanations,鈥� he says. 鈥淭he alternative is that it is new physics, possibly a consequence of a more general, quantum, theory of gravity which we do not yet have. But I鈥檓 reluctant to make such a bold claim.鈥�
鈥淚t鈥檚 difficult to come up with mundane explanations for the fly-by anomaly鈥�
Another possible indication of physics beyond general relativity might come from the motion of stars orbiting in spiral galaxies. These appear to whirl around the centre of their respective galaxies so fast that gravity should not be able to hold onto them.
To describe such motion, in 1983 Mordehai Milgrom of the Weizmann Institute of Science in Rehovot, Israel, published a controversial theory called modified Newtonian dynamics (MOND). It posits that the stars experience gravity more strongly than expected at ultra-small accelerations. Even Milgrom is baffled by the fly-by anomalies, though. 鈥淚 looked quite closely at this paper when it appeared but couldn鈥檛 find a connection with MOND or come up with another explanation,鈥� he says. 鈥淚t does sound very interesting, and I keep coming back to it from time to time.鈥�
One extraordinary suggestion for the origin of the anomaly has come from theorist Stephen Adler of the Institute for Advanced Study in Princeton, New Jersey. In an as-yet-unpublished paper, he suggests that the fly-by anomalies are caused by the drag the spacecraft experiences from a cloud of invisible dark matter clumped around the Earth (). The clump cannot extend as far as the moon or we would have seen its effect on the moon鈥檚 orbital motion, and it cannot come too close to the Earth or it would have affected the orbits of artificial satellites.
Admittedly, Adler鈥檚 model appears contrived: his dark matter cloud needs two components orbiting differently in order to explain why some spacecraft increase in speed and others reduce. Even more seriously, it would require a density of dark matter much higher than most astronomers believe is even possible. These very significant constraints notwithstanding, such clumped dark matter would be compatible with an experiment in Gran Sasso, Italy, called , which is designed to detect the presence of dark matter. The DAMA team claims to show a larger-than-expected amount of dark matter impacting on the Earth, though their result, too, is controversial.
One of the most interesting questions that can be asked about the fly-by anomaly is whether it is connected with the Pioneer anomaly? 鈥淚t鈥檚 hard to believe there are two separate spacecraft anomalies,鈥� says Anderson. 鈥淚t seems too unlikely.鈥�
Intriguingly, both Pioneer 10 and 11 performed planetary fly-bys before the Pioneer anomaly became apparent 鈥� around Jupiter and Saturn respectively. And there is no known reason why fly-by anomalies should be confined to the planet Earth. Though probes have performed fly-bys of Venus, Jupiter, Saturn and even giant moons in the outer solar system, no anomalies have been observed. There are two reasons for this, says Anderson. First, because mission control is always on Earth, the speed measurements of a probe approaching and receding from its fly-by target are less accurate for planets other than our own. Second, we do not have as good models for the gravitational fields of other planets as we do for the Earth, where the motion of satellites reveals the gravitational landscape in great detail. Were any anomalous velocity change measured, it could as easily be a result of our ignorance of a given planet鈥檚 gravity field as a real effect.
The relevant Pioneer 11 data for its 47-day Saturn fly-by was retrieved by Slava Turyshev of JPL just before it was due to be tossed into a skip (快猫短视频, 3 June 2006, p 46). 鈥淚t might be good enough to analyse,鈥� says Anderson. 鈥淚t will be fascinating if we see no anomaly before Saturn, only after.鈥�
Close encounters
Anderson is not alone in thinking there is a pressing need to investigate fly-by anomalies. Theorist Karl Svozil at the Vienna University of Technology in Austria has even proposed a to test the effect. Instead of a rotating planet, he suggests using a massive, spinning stack of magnetic discs to mimic Earth鈥檚 mass and magnetic field. To imitate the spacecraft, he proposes firing a beam of neutral particles past the stack and measuring its trajectory. According to the known laws of physics, the beam should be unaffected. If it is knocked off course, then new physics is at play. 鈥淚n principle, the experiment could look for a gravitational and an electromagnetic origin of the fly-by anomaly,鈥� says Svozil.
Anderson is intrigued by this suggested experiment, but suspects it would be hard to execute. 鈥淚t took 40 years to iron out the technicalities with Gravity Probe B, which involves spinning superconducting niobium spheres,鈥� he says.
Not surprisingly, Svozil is more upbeat. 鈥淚n my view, the experiment can be performed and should be done as soon as possible,鈥� he says. 鈥淚t would even be cheap, involving components which are readily available.鈥�
The best bet to solve the problem, according to Anderson, is simply to observe more fly-bys. By a stroke of good fortune, Rosetta is due to make its third and final Earth fly-by on 13 November 2009. According to Anderson, the upcoming encounter is more favourable than the one in 2007 because it is at an altitude of almost 2500 kilometres, compared with over 5000 kilometres for the second fly-by. 鈥淭hat may have been too high to reveal the anomaly,鈥� he says.
Anderson and his team are already armed with their prediction. 鈥淥ur formula predicts about 1 millimetre per second for both the second and the next fly-by,鈥� says Anderson. 鈥淔ingers crossed, in 2009 we鈥檒l see it.鈥�
