Gravitation; An Elementary Explanation of the Principal Perturbations in the Solar System

Cover Gravitation; An Elementary Explanation of the Principal Perturbations in the Solar System
Gravitation; An Elementary Explanation of the Principal Perturbations in the Solar System
Sir George Biddell Airy
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upon B is f of the attraction upon A, and the disturbing force is i of the attraction upon A.
The disturbmg force in the first case is, therefore.
Digitized by VjOOQIC GREATER THAN AT OPPOSITION. 67 greater than in the second case^in the proportion of 3 to l-, or 27 to 5. This remark applies to nearly all the cases of planet€u>y disturbance where the disturbing planet is exterior to the orbit of the disturbed planet^ the ratio between these distances from the sun being a ratio of not very great
... inequality. But it scarcely applies to the moon. For the sun^s distance from the earth is nearly 400 times the moon's distance: conse- quently when the moon is between the sun and the earthy the attraction of the sun on the moon is (i^)* X the attraction of the sun on the earthy OT \tUU par^» of A® sun's attraction on the earthj and the disturbing force therefore is t/AVt parts of the sun'^s attraction on the earth : but when the moon is on that side farthest from the sun^ the sun's attraction on the moon is (iff)* or HHff parts of the sun's attraction on the earthy and the disturbing force is ttWs-t parts of the sun's attraction on the earthy which is very little less than the former.

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