The Planetary Society has an article up about the "Flyby Anomaly", wherein scientists at JPL have discovered that space exploration probes that use the earth as a gravitational slingshot are gaining a tiny amount of speed that exceeds the gain expected by the maneuver.
This amount is small, "only about one millionth the velocity of the spacecraft", but that's still detectable.
(That ain't much, right? How much of an effect could that possibly have?)
According to the article, the effect was first detected when the Jupiter probe Galileo got its first gravitational assist from the Earth back in 1990. It was subsequently detected on similar maneuvers by the NEAR and ROSETTA spacecraft, to varying degrees. (Two other spacecraft, Cassini and MESSENGER, also swung by Earth as part of their trajectories, but the anomaly was not detected, though for reasons that are understood.)
So I got to thinking--exactly what does "one millionth [of] the velocity of the spacecraft" actually add up to? And is it really that likely to have any kind of significant effect?
Caveat: I'm not an astronomer or an orbital mechanics guy, so I'm just going by the numbers I found in the article and web searches. I mean, you're only going to get "so" accurate when you're going by "about a millionth" :-)
According to a ROSETTA press release, it made its March 5, 2005 Earth flyby at a speed of around 38,000 kph. I'm going to use that velocity for these calculations, knowing full well that the purpose of the flyby was to increase the speed of the spacecraft, but that number will serve for what I'm trying to show regarding the scale of the anomalous speed gain.
So what is one millionth of 38,000 kph? Well, 0.038 kph, or 38 meters/hour. In non-metric terms this converts to 0.0236 miles per hour.
That may not seem like much, especially when compared with the vast distances a spacecraft, even an interplanetary one, must travel to reach its destination. On the other hand, because of those vast distances, flight times are usually quite lengthy, which gives such small values plenty of time to grow into significant ones.
So the small ROSETTA velocity discrepancy grew within one day to 0.5664 miles. Yikes, that means it's already half a mile further along in its trajectory than it was expected to be. Within a week it's nearly 4 miles further along.
Now the destination of the ROSETTA craft is the comet 67P/Churyumov-Gerasimenko, which is itself only 5 km by 3 km size (3 x 1.8 miles), so a week after the flyby ROSETTA would already be off in its expected position by more than a full span of its target's size. And since ROSETTA is on a 10 year trajectory, this discrepancy would keep adding up with each subsequent year, at 206+ miles per year, making the "flyby anomaly" quite a significant factor in mission planning and success.
Obviously the mission planners have taken this all into account now, and we can look forward to a successful ROSETTA flight and mission.
But this certainly does demonstrate that being off by "about a millionth" can have some real consequences, despite how insignificant that sounds.