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In a few hours NASA's NEAR Shoemaker probe will "touchdown" on the surface of the asteroid eros. Bearing in mind that NASA will underestimate them, I've been trying to guess the chances of survival. Here's what I've come up with:

starting principles:
G(earth) = 9.81 ms-2
Near's impact speed = 5 mph or 2.22 m/s

Some useful formulas:
(a) v = u+at
(b) d = u*t+(a*t^2)/2

solve (a) for t
t = (u-v)/a
 but u = 0 so it becomes:
t = -v/a
 substitute into (b)
d = u*(-v/a) + (a*(-v/a)^2)/2
 again u = 0, so:
d = (a*(-v/a)^2)/2
 with actual values:
d = (9.81*(-2.22/9.81)^2)/2
d = 25 cm
or 10 inches
Now take a look at it ( http://near.jhuapl.edu/resources/Nearcraft_lg.jpg ) and try to imagine it being dropped from 25cm on Earth. Bear in mind that the surface of Eros is probably soft and sandy, and that it's uncertain what angle it will strike at.

Anyone running a book?


Update:
Well, as you probably heard, NEAR survived beautifully. The actual impact speed was closer to 4mph, or the equivalent of a drop of 19cm on Earth. NEAR has been deactivated, but providing it is in sunlight it may be reactivated in the future.


Further update:
Attempts to reactive NEAR have not been succesful.

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