For flybys where the angle is very different for the incoming and outgoing parts of the trajectory – such as the 1998 NEAR flyby – both the formula and the observations give a large anomaly.

But for flybys where incoming and outgoing angles are similar, the anomaly predicts the anomaly to be very small, and in some cases too small to be detected. Both the 2005 flyby of NASA's Messenger spacecraft en route to Mercury and the 2007 flyby of Europe's Rosetta spacecraft on its way to a comet had very similar incoming and outgoing angles, and neither showed a detectable anomaly.

Team member Frank Jordan stumbled on the formula, after trying out many other possibilities that did not work. He says he was playing with different ideas for a formula when it occurred to him to use trajectory angles. "It just worked so well, I was amazed," he told New Scientist. "I immediately called everyone else [on the team] and people did independent computations" showing the formula worked, he says.

Although the team has been unable to come up with an underlying physical explanation for the anomaly, Anderson thinks the formula suggests some sort of connection to Earth's rotation.
First step

That is because the angles in the formula are defined with respect to Earth's equator, which is perpendicular to the planet's spin axis. "That suggests to me that the effect is related to the Earth's spin direction, or perhaps to the rotation of the Earth," Anderson told New Scientist.

But how could Earth's rotation influence the trajectories of spacecraft? One possibility that the team investigated comes from Einstein's general theory of relativity, which predicts that spinning objects distort the fabric of space around them. This effect could in principle influence the trajectory of objects near a spinning body like Earth, but the team's calculations show it would be far too weak an influence to explain the flyby anomalies.

Even though the team has not come up with a physical explanation, having the formula could be an important step towards one, because it gives physicists something to aim for

TB referred to frame-dragging as a possible explanation, but as noted above, they tried it, and it didn't work. So we seem to have some REAL and unexplained (but subtle) physics here.

It's from subtle effects that sometimes we find out radically new things. If we can later build some device that concentrates or magnifies this effect, then we may have a new trick to play with space-time and gravity...

(or it could be as "useful" as magnetically levitating a frog)