Astrophysics/Asteroid strike calculation
I assume this should be a fairly easy (back of the envelope) calculation for an astrophysicist yet an answer may finally bring much appreciated closure to a surprisingly heated debate in my household.
This all started with the movie 'Seeking a Friend for the End of the World' (spoiler alerts). The movie opens with the announcement that, in three weeks time, an asteroid will be impacting the Earth. Approx. 2 weeks later another announcement was made that the original calculations were incorrect, and that the asteroid was now going to hit in sixteen hours (approx. one week early).
THIS sparked a HEATED 4 hour debate that desperately could have used Isaac Newton as a mediator.
The only information we have about the asteroid is that its "70 miles wide", and it was close enough (and traveling at a speed conducive enough) for us to send a manned mission to try to stop it.
My friend's (AND his girlfriend's) position: There is ABSOLUTELY NO WAY that the asteroid would now impact the Earth. They argue that the slightest calculation error in velocity and/or trajectory under the given conditions would result in a non-impact with the originally calculated target.
My position: There simply isn't enough data to support their theory. I don't assume to know a scenario that would still result in an Earth impact, but I don't feel we were given enough information to make such a bold/absolute assertion (I then I remind him that only a Sith deals in absolutes... I completely expect an astrophysicist to get that reference).
My question is (if you haven't figured it out yet...), who gets to perform the sacred victory dance of righteousness in the other party's face???
I greatly appreciate and respect your time (and knowledge of physics/calculus). Thank you!
Well, the problem begins with the movie. If they calculate that an asteroid is going to strike us in three weeks, they mean three weeks. These measurements are very precise, indeed. The only reason that's even remotely possible is if (this is kind of typical) the object dipped into and out of our orbit. For example, this asteroid: http://neo.jpl.nasa.gov/risk/2014ux34.html
has two chances to hit us in 2063 (see the table). The risks are small. Sometimes the elliptical orbits are like that. The only way for the impact date to be moved up is if further observations to have confirmed an earlier one over a later one. Objects this large are pretty well-monitored (http://neo.jpl.nasa.gov/risk
) but you do see the objects in the "recently observed" list move up and down in probability all the time. So the idea that we would get it so wrong if the impact was so close is ridiculous, but technically possible if the actual possible impact shifted. The Apophis asteroid, for example, has two chances to hit us in 2068, separated by months (April and October). http://neo.jpl.nasa.gov/risk/a99942.html
So an orbit like that is technically possible, but a real close-in impact would be so well-measured that we wouldn't just pop up and say "hey, you have two days." The numbers for the movie scenario are technically possible, but it wouldn't take more than a day to correct the measurement...there's no way that every telescope on Earth (and the Hubble, no clouds) wouldn't be tasked to track that thing.