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that the curvature of her path when she is “full”greatly exceeds the curvature at the time of newmoon.
It was necessary to say so much about the moon’spath round the sun, and the sun’s real influence uponour satellite, because a great deal of confusion verycommonly prevails in the student’s mind on this sub-ject. He is exceedingly apt, when his attention ischiefly (and in the first instance) directed to the sun’sperturbing influence, to suppose that our earth playsthe chief part in ruling the motions of the moon,whereas the sun’s influence is in reality paramountat all times.
In considering the moon’s motion around the earth,however, we may leave out of consideration the com-mon influence of the sun upon both these orbs, andneed consider only the difference of his influence uponthe earth and moon, since this difference can aloneaffect the moon’s motion around the earth.
Now we are enabled to deal somewhat more readilywith this case than with the general problem of threebodies, because the moon is always very close to theearth as compared with the distance of either from thesun. On this account lines drawn to the sun from theearth and moon enclose so small an angle that theymaybe regarded as appreciably parallel. Again, theselines are at all times so nearly equal, that in deter-mining the relative pull on the earth and moon we
times, or in the ratio of 110 to 103. But the attractive force onthe moon varies in the ratio of 110 to 40, as above shown.