More on Why Asteroid Will Miss Mars

I decided my previous post on the Mars asteroid was not clear enough.  Above is a figure from NASA's Near Earth Asteroid site  from 9 January.  The thin white line with the orange circle on it is the orbit of Mars.  The blue line is the most likely path, which corresponds to s=0 on the bell curve of the previous post.   The bunch of white dots are the possible points of closest approach given the error in the measurements (the path of the asteroid for each dot would be a line parallel to the blue line going through that dot).  

As you can see, the dots are bunched around the most probable value and taper off in either direction—in the same way that the the area under a bell curve decreases away from the center.  s, the distance from the blue line to Mars divided by the size of the error, is 3.7, giving a probability of 10,000:1.

 

Here is what the asteroid figure looked like two weeks ago:

Notice that the scale here is 500,000 km, so this is zoomed out by a factor of 5 from the 9 January picture.  Two things have happened in the fortnight.  First, the position of the blue line has changed a little.  More importantly, the size of the error was a lot bigger two weeks ago.  Back then the error was large enough so that the distance from the blue line to Mars divided by the error was only 2.2, giving a probability of 25:1.

So the probability changed from 25:1 to 10,000:1 over the last two weeks mainly because the error in the path decreased, making  s  increase (again, s is the distance from the blue line to Mars divided by the error, and it is also the position on the bell curve of the previous post).