A Few Chapters in Astronomy

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But the opposing tangential impulse 6, which is equal to a, would, if it acted by itself on the still undisturbed moon, cause her to describe an ellipse with its apogee very near to the octant under the letter b. These two ellipses would have a very small proportional difference as to magnitude ; although the former would be entirely outside, and the latter entirely inside, the original circular orbit. The eccen- tricities of the two ellipses would be very nearly the same. Now these two apogees... under b and c, only 90 C apart, would combine or coalesce, as is evident, into an apogee very nearly halfway between, close to the quadrature B. It is easily seen that this apogee would be above the circle in the figure ; as the former ellipse would cross the line of EB at a height above the circle due, inter alia, to the distance of three octants from the apse under the letter a ; while the other ellipse would cross EB below at a depth due to the distance of only one octant from its apse under b.

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