# [ExI] Life must be everywhere!

Anders Sandberg anders at aleph.se
Sat Apr 14 22:26:13 UTC 2012

```An initial velocity of 42 km/s is no real guarantee it will be
sterilized on impact. Remember that in space only relative velocity
matters: an escaping rock might enter a solar system moving away from it
in such a way that it loses plenty of velocity, and similarly for
planets. I think there is a nice research paper in doing a Monte Carlo
simulation of the velocity distributions here.

The survival of small impactor is a bit complicated. If I remember the
literature right very small ones vaporize far up, likely burning all
spores (they heat up in the very thin high atmosphere, where they are
not strongly slowed). Larger impactors have a hot crust but reach denser
lower atmosphere, where they reach terminal velocity and are even cooled
by the surrounding air. Even larger impactors are subject to enough
force that they can split apart, with fragments of different sizes and
temperatures, some of which hit the ground and have fairly low
temperatures. Even bigger "pancake" and explode - and then the biggest
ones hit the ground.

On 2012-04-14 22:21, Kelly Anderson wrote:
> On Fri, Apr 13, 2012 at 4:14 AM, Anders Sandberg<anders at aleph.se>  wrote:
>> I don't think anybody
>> knows how to calculate the denaturating effects, but they are likely severe.
>
> Undoubtedly, but we have recently learned that they can withstand
> 20,000 Gs of shock, which is rather amazing!

Bacteria have been grown under 100,000 Gs. It is not the shock that is
the problem. The problem is any temperature above (say) 200 degrees C.

A simple problem: a spherical granite pebble of radius R starts out with
a core temperature ~300 K and a surface that is molten, ~1500 K. How
long will it take for the core to become 500 K hot, and is this time
shorter than the time it takes to cool the surface in a space
environment down to around 300 K?

It is too late in my evening for me to try to solve the spherical heat
equation for the initial value or with a Stefan law boundary
condition... but it might be fun when I am awake.

But let's assume the temperature gradient is linear. Then the heat flux
is F=k*delta T/R Watts, where k is the thermal conductivity of granite
(1.7-4.0 W/mK) and delta T is the temperature difference between core
and surface. The core will heat up as F/CM, where C is the heat capacity
of granite, 790 J/kg K and M is the mass of the core. Let's make it
equal to a fourth of the volume, giving a mass M=pi*rho*R^3/3, with rho
the granite density 2691 kg/m^3. Putting it all together, the initial
heat flux will make the core temperature go up by 3*k*delta T/(C
pi*rho*R^2) = (0.00107/R^2) Kelvin/s. If R=1e-2, a pebble, the
temperature rise will be 10.7 degrees per second. So unless the pebble
has cooled significantly in the first 20 seconds the core will be
denaturated.

Now, how fast is radiative cooling of ejecta? I am too sleepy to solve
that differential equation right now. But I bet it is slower than 20
seconds.

--
Anders Sandberg
Future of Humanity Institute
Oxford University

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