Flyby anomaly
en.wikipedia.org
en.wikipedia.org
https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_p...
https://en.wikipedia.org/wiki/List_of_unsolved_problems_in_p...
[1]: http://www.nasa.gov/feature/jpl/earth-might-have-hairy-dark-...
https://en.wikipedia.org/wiki/Gravity_Recovery_and_Climate_E...
Double checking electromagnetic forces is an excellent idea.
So we're left in a position where there's a difference between the prediction and the measurement, when the measurement is highly accurate. That means something is out, and that might be extremely important for long range flights.
I'm not too sure how to work some of these things out, but it's possible that a few mm/second difference really adds up when you're on an enormous trip. If you're out by 10mm/second here, then your next flyby will leave you even further out, then the next, etc. until you crash into a planet. Cassini was out by under 1 mm/s, but its flight path would have been 2 billion miles. These things travel for years, and can't make too many corrections.
More info on the crazy journey it took: http://www.theplanetstoday.com/cassini_flight_path.html
Another one of those questions: doesn't the acceleration of such a fly-by depend in large amount on the masses of the various objects, and if that's correct could this indicate an error in the mass of one of the objects (say, Cassini having a mass (not a weight) 1/1000000 less than we think it does)? And also, could it be indicative of a number of factors all being off by a fraction of the resulting discrepancy, or even two factors where one is a negative and the other is a slightly different positive?
OTOH this is a pretty conservative bunch.
It may "just" be something in the details (much like the Pioneer anomoly: http://www.planetary.org/blogs/bruce-betts/3459.html?referre... which was solved after 20 years of digging and LOTS of speculative ideas that did not work out).
Note, this is an important anomaly not because of its magnitude, but rather, its relation to the measurement error.
The Pioneer anomaly was solved by precise calculation of the heat radiance of spacecraft.
But of course, it might end up being a trivial explanation (something on the measurement equipment, for example)
At one point, the motion of Mercury didn't fit into the rules of mechanics, which we thought we understood. It turns out we didn't, and general relativity filled that gap.
It's far more likely the explanation is a mundane force not considered before, than new physics. But we have to look.