Eugen Leitl writes:
> Apart from twiddling with the surface albedo which might be not
> enough -- we currently don't have ion drives with enough power, or at
> least we can't develop and deploy them on time,
My estimate is that, in the worst case, we have 17 years (5.4e8
seconds) to move it one earth radius, or about 6000 km (6e6 m).
a t^2/2 = x, if I remember right, so a = 2x/t^2, which is
1.2e7 m/(2.9e17 s^2), or about 4.1e-11 m/s^2, which is not a very
large acceleration, roughly equivalent to the gravitational
acceleration in these parts divided by 200000000000.  Assuming a
2km-wide --- that is, 20 000 decimeter-wide --- spherical asteroid of
specific gravity 10, 4/3 pi r^3 says it would have a volume of 4e12
cubic decimeters and thus a mass of 4e13 kg.  The force we'd have to
apply to achieve this acceleration would be roughly equivalent to the
weight of 200 kg here on Earth.
So, yeah, ion drives are probably a no-go, unless I screwed up the
calculations here; I think the force they typically exert is about
four orders of magnitude too small.
If we just wanted to hit today it with enough of an impulse that it
would miss us 17 years later, we'd need to accelerate it by about 1.1
cm/s.  A one-ton (1000kg) mass would need to hit it at about 4e9 m/s,
or about ten times the speed of light, to achieve this, so that's not
possible.  (If you could actually put enough work into a one-ton mass,
as it approached the speed of light, it would mass more, so you could
still do it with a one-ton mass; but we don't have anything
approaching that speed.)  The impulse required is inversely
proportional to the remaining time to impact, so if we were to hit it
after half the time has elapsed, we'd need to accelerate it by around
2.2 cm/s instead.
The gravitational force of an Earth-sized mass could provide
sufficient deflection if that mass were about 4.5e5 times as far away
from the asteroid as we are from Earth's center, or about 2.7e9 m, or
about 0.018 times the distance from the Earth to the Sun (0.018 AU).
(And if that mass stayed so nearby for 17 years.)
The effects of continuous acceleration benefit greatly from planning
ahead, since they scale with t^2, not t --- and thus the needed
acceleration scales with 1/t^2.  After half the time has elapsed, we'd
need four times as much acceleration to make it miss the Earth than if
we were to start accelerating it now.
All of these numbers are a little low, because the Earth presents a
slightly easier target than its physical size suggests, due to its
gravity well.  How much easier depends on the speed of the projectile
in ways I don't understand.
They're also a little high, because they assume the force is being
applied purely at right angles to the asteroid's current path, which
is a slightly suboptimal scenario (although for velocity changes five
orders of magnitude smaller than the relative velocity, the difference
is probably insignificant.)  And they assume there are no other effects on the asteroid's path.
What about electrical charges?  Could we electrically charge the
asteroid and another nearby asteroid, perhaps with electron beams, to
provide the needed acceleration?
Of course, all of this calculation could be applied in the other
direction, too.  If you want to sock a moon colony with a one-ton
asteroid, you could do it with a tiny amount of force applied over
twenty-five years to adjust its orbit.
***
About spam: I'm sorry to admit I haven't implemented any of the better
solutions, and so I'm afraid I'll have to allow non-subscriber FoRK
mail to be detained for scanning.  I hope this measure can be reversed
soon when I have time to implement better measures.  As has often been
noted by other posters, measures to reduce spam sent to the FoRK list
will not significantly decrease the spam load of FoRKposters, since
the vast majority of spam received by FoRKposters is sent to them
directly, not through the FoRK list.
--
<kragen@pobox.com>       Kragen Sitaker     <http://www.pobox.com/~kragen/>
Silence may not be golden, but at least it's quiet.  Don't speak unless you
can improve the silence.  I have often regretted my speech, never my silence.
-- ancient philosopher Syrus (?) via Adam Rifkin, <adam@cs.caltech.edu>
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