We have already noticed how the present arrangement of the earth-moon
system enables us to calculate the earth’s age; Jeffreys estimates that
the system must have taken something of the order of 4000 million years
to reach its present configuration (p. 155).
This period, which seems so long when judged by terrestrial standards,
is only a moment in the life of a star. The components of the true
binary star attain a configuration like that of the earth-moon system
in a brief fraction of their lives, and, passing on, reach in time
the configuration in which each perpetually turns the same face to
the other. Up to now, tidal friction has been driving the masses
ever further apart, but as soon as this stage is attained, the tides
become stationary on both components, so that tidal friction goes out
of operation. Thus the separation produced by tidal friction has now
reached its limit, and, so far as tidal friction is concerned, the two
bodies might rotate in the way just described to all eternity.
LOSS OF WEIGHT. As tidal friction becomes inoperative, a new agency
takes hold. We have calculated that the sun is losing weight at the
rate of 250 million tons a minute, that it has been losing weight at
this rate, or some comparable rate, for millions of millions of years,
and will continue so to do for millions of millions of years yet to
come. The earth is at its present distance from the sun because this
distance is exactly suited to the present weight of the sun. If the
sun’s weight were suddenly reduced to half, its gravitational pull on
the earth would also be reduced to half, and the earth would move to a
greater distance from the sun[22].
[22] Although the details are unimportant, the actual course of events
would be that the earth would begin to describe an elliptic instead of
a circular orbit about the sun, the earth’s _average_ distance being
greater than now.
The sun’s weight is not likely to be suddenly reduced to half, but it
has been reduced by a thousand million tons in the last four minutes,
with the result that its gravitational grip on the earth has been
weakened and the earth has moved out to a wider orbit; at this moment
the radius of the earth’s orbit is greater than it was four minutes
ago. The details can be traced out mathematically with complete
precision. It appears that the earth’s orbit round the sun is not a
circle, or even an ellipse of small eccentricity; it is a spiral curve,
like an uncoiled watch spring. Every year the earth moves a tiny step
further out into the outer cold and darkness; exact calculation shews
that its average distance from the sun increases at the rate of about
a metre (39·37 inches) a century. The effect is of course of precisely
the same kind as we have seen must be produced in the galactic system
by the loss of weight of the stars. The only difference is that in the
galaxy a system of thousands of millions of stars is expanding, whereas
the sun-earth system consists of only two members.
Public-domain text, read in full here on John Shaqi.
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