The sun occupies just about one 94,000th part of the hemisphere of the
heavens or one 188,000th part of the whole sphere. If the whole sphere
surrounding the earth were of sun brightness, the earth would be in an
enclosure at the temperature of the sun, and would therefore be at that
temperature itself. The sphere would be sending heat at 188,000 times
the rate at which the sun is sending it, and the earth would be
radiating it at 188,000 times its present rate. But the rate at which
it radiates is proportional to the fourth power of its absolute
temperature, and therefore its temperature would be the fourth root of
188,000 times its present temperature, _i.e._ 20.8 times. If the
radiating or absorbing power of the earth's surface be taken as 9/10,
which is somewhere near the mark, {54} the calculation gives the number
21.5 instead of 20.8. The average temperature of the earth's surface
is probably about 17° C. or 290° absolute, and therefore the
temperature of the sun is 290 x 21.5, _i.e._ about 6200° absolute.
It is easy to see that if we had known the temperature of the sun and
not of the earth, we could have calculated that of the earth by
reversing the process.
By this means we can estimate the temperatures of the other planets, at
any rate of those for which we may make the same assumptions as for the
earth. Probably those planets which are very much larger than the
earth are still radiating a considerable amount of heat of their own,
and therefore to them the calculation will not apply; but the smaller
planets Mercury, Venus and Mars have probably already radiated nearly
all their own heat and are now radiating only such heat as they receive
from the sun. The temperatures calculated in this way are--
Average
Absolute Temperature
Mercury . . . . . . . . . 467°
Venus . . . . . . . . . . 342°
Earth . . . . . . . . . . 290°
Mars . . . . . . . . . . 235°
Since the freezing point of water is 273° absolute, we see that the
average temperature of Mars is 38° C. below freezing, and it is almost
certain that no part of Mars ever gets above freezing point.
In a very similar way we may find the temperature to which a
non-conducting surface reaches when it is exposed to full sunlight by
equating the heat absorbed to the heat radiated, and the result comes
{55} to 412° absolute, _i.e._ 139° C., or considerably above boiling
point. This would be the upper limit to the temperature of the surface
of the moon at a point where the sun is at its zenith.
Public-domain text, read in full here on John Shaqi.
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