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Let us now pass on to the subject of the moon’sperturbations caused by the sun’s attraction.
Here, in the first place, I may mention a fact whicliwill perhaps seem surprising to many. Though thesun’s disturbing influence on the moon is such thatthe moon’s course around the earth is not very dif-ferent in any single revolution from that which shewould have if the sun’s attraction had no existence;yet the sun actually exerts a far more powerful in-fluence on the moon than the earth does. As weshall have to consider the relation between the twoforces, we may as well proceed at once to prove thisexcess of power on the sun’s part.
The law of gravitation enables us at once to com-
sion have nothing in common ; that, for instance, such a relation asthis can be affirmed :—
f Moon ’s mean distance! 3 I" Mean distance between 13
L from earth. J [ components of a Centauri.J
t Mood’s mean! 2 f Bum of moon’s “j I" Their period 12 T Sum of 1
period. J l_mass and earth’s. J |_of revolution. J |_their masses. J
It will be observed how the law enables us at once to compare thesums of the masses, when we know the mean distances and periods.For it may be written
M + to _ D 3 P ' 2M' + to' l / 3 P 2
Also where to and to' are both small, compared with M and Mrespectively, the law becomes simplified intoM = D 3 P ' 2M' “ D ' 3 P 2
This law is in effect applied, in what immediately follows in themain text, to the determination of the moon’s mass. It is therealso independently established, at least in the case of circularorbits.