From: dsg@impmh.uucp (Dave Gordon)
Subject: Re: Physical Constants List
Organization: Integrated Micro Products Ltd
Date: Wed, 27 Jan 1993 18:54:05 GMT

In <1993Jan21.194306.12763@ncsu.edu> bjbisset@eos.ncsu.edu (BILLY JOE BISSETTE) writes:
>
>dsg@impmh.uucp (Dave Gordon) writes:
>>Thus a mirror in Earth orbit could collect well over *1GW* per square
>>kilometre, even after allowing for losses. That's a lot of power - surely
>>someone can find an application for it (diverting asteroids springs to mind)!
>
>Divert?!  Why would we want to divert asteroids?
>This is alt.destroy.the.earth.
>There are much better uses for that much power.
>We could have a gaint bar-b-cue... 8)
>
>PS: nice work on the data, but why did you write m/s as m s^-1, I mean m/s is
>so much more pleasant to the eye...

To answer your last point first, for consistency and to avoid ambiguity.

With a mixture of upper and lower case letters for units, plus SI
prefixes, plus multi-character symbols that have to be spelled out
because of the limitations of ASCII (e.g. pi), plus named free
variables such as "r" and "m1" in my formulae, I decided that the
only unambiguous solution was to write explicit multiply and power
operations (thus E=m*c^2 rather than E=mc2).  Negative powers followed
naturally from there.  Names of basic units are separated by a space
when forming derived units to distinguish them from compound names,
thus N m (newton-metres) vs. nm (nanometres).

I just hated the idea of people confusing (for example) J K^-1
(joules-per-kelvin) with kJ (kilojoules), or (worse still) a formula
containing the term "delta_temp*k J" (temperature change times
Boltzmann's constant, giving joules) being misread as "delta_temp kJ".

Now, about that bar-b-cue ...

One of the purposes of posting the "Physical Constants List" was to
give people a sense of *scale*; most people don't seem to realise
just how *big* a planet is!

Focussed onto an area 1m*1m, 1GW would easily vapourise most earthly
materials (e.g. rock) at a rate of several tons per second. But if
spread over 10m*10m, it will merely raise the temperature by about 200K
(perhaps this is the 'big barbecue' you meant).  Over an area 100m*100m,
the temperature rise would be a few tens of degrees, while if the beam
were defocussed to 1km*1km, a rise of 10K is all you could expect.
(1GW km^-2 is approximately what the tropical regions of the earth
already receive).

ObOutrageousCalculation:

Suppose the *entire* output of the Sun were used to heat the earth.
Assuming no radiation to space, and that the temperature increase
is uniform throughout the entire volume of the planet, how long would
it take for the average surface temperature to reach boiling point?

Here are the figures we need:

Mass of the Earth		m(E)		6e24		kg
Total solar radiation		o(S)		4e26		W (J s^-1)

Plus some assumptions:

Average surface temperature of the earth
				ts(E)		283		K
(i.e. 10 degrees Celsius/Centigrade)

Average specific heat capacity of the earth	
				shc(E)		4e3		J kg^-1 K^-1
(this is probably a bit low; water has a SHC of 4.2e3, but I don't
have the figure for iron to hand; at least it will probably be the
same order of magnitude).

Then, the energy needed to raise the average surface temperature to boiling
point (373K) is

	shc(E)*m(E)*(373-ts(E))

and the time taken is

	shc(E)*m(E)*(373-ts(E))
	-----------------------
		o(S)

which comes to

	(4e3*6e24*90)/4e26	= 5400 s, or 1.5 hours!

This seems an outrageously long time; if a *star* would take hours or
even days to vapourise a planet, what chance for mankind's puny efforts?

BTW, there's a handy memorable result hidden in that calculation:
THE SUN'S *ENTIRE* OUTPUT COULD HEAT UP THE EARTH AT A MERE 1 DEGREE PER MINUTE!

(the calculation of the K.E. of the asteroid that we could divert with
a 1GW beam is left as an exercise for the reader).
-- 

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