paha arkkitehti wrote:So the next question is how much did the length of year change because of Rosetta stealing Earth's momentum in the flybys?
Without going into the math, it'll change our year about as noticeably as this girl
will change our day.
With some very approximate math...
Momentum robbed from earth is added to the orbiter. (Assume losslessly, because spherical cows rock.)
mass of orbiter = 3000 kg at launch (it's probably burned some fuel since then, but whatever.)
mass of earth = 5.97e24 kg
velocity of earth = 108000 km/hour
So how fast do we want to go? Our comet target is going 135000 km/hour, so that's a reasonable speed to think about. If we were to get all
of it from slingshotting around the earth:
Keeping everything in kg, km, and hours, we steal (135000 x 3000) = 4.05e8 of momentum from earth, slowing it down by (4.05e8 / 5.97e24) = 6.78e-17 km/hour.
Since the length of our year is proportional to our speed around the sun, that's a change of 6.78e-17/108000 = 6.28e-22 of a year (or 6.28e-20 percent of a year, if you like percentages.)
A year is about 365.25 days or 31557600 seconds, so we've added about (31557600 x 6.28e-22) = 1.98e-14 seconds, or about 20 femtoseconds seconds to a year to do this.
I'd say having to adjust for this by subtracting a leap-second once every 50 trillion years counts as "meh", since the sun will go red-giant and burn all our pin-up calendars a mere 5 billion years from now.
(Disclaimer: even basic arithmetic performed at 4AM is likely to be miscalculated.)