At the end of the last century the illustrious French mathematician
Laplace undertook a new investigation of the famous problem, and was
rewarded with a success which for a long time appeared to be quite
complete. Let us suppose that the moon lies directly between the
earth and the sun, then both earth and moon are pulled towards the
sun by the solar attraction; as, however, the moon is the nearer of
the two bodies to the attracting centre it is pulled the more
energetically, and consequently there is an increase in the distance
between the earth and the moon. Similarly when the moon happens to
lie on the other side of the earth, so that the earth is interposed
directly between the moon and the sun, the solar attraction exerted
upon the earth is more powerful than the same influence upon the
moon. Consequently in this case, also, the distance of the moon from
the earth is increased by the solar disturbance. These instances
will illustrate the general truth, that, as one of the consequences
of the disturbing influence exerted by the sun upon the earth-moon
system, there is an increase in the dimensions of the average orbit
which the moon describes around the earth. As the time required by
the moon to accomplish a journey round the earth depends upon its
distance from the earth, it follows that among the influences of the
sun upon the moon there must be an enlargement of the periodic time,
from what it would have been had there been no solar disturbing
action.
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