Mechanisui and Functions in Celestial Mechanics. '^11 



much too nice to be tlie normal result of the capture 

 of wandering planetoids which must necessarily enter 

 the system in a random fashion, and almost always with 

 relatively high eccentricity, and inclination. Instead, the 

 newly captured planetoid would normally revolve at first 

 in a relatively eccentric and highly inclined orhit not 

 systematically adjusted to the pre-existing system, gener- 

 ally having perigee inside, and apogee far outside of the 

 determinate orbit. Its orbit w^ould resemble that of a 

 comet more nearly than that of a planet or an established 

 satellite. 



6. With the principle of determinate stability in hand, 

 the mechanism of the expansion of the orbit of the pre- 

 viously established satellite falls smoothly into place as 

 an indispensable part of the larger mechanism. We have 

 seen that if the Earth's mass were greater than it is the 

 determinate orbit would be farther out from the Earth 

 than the Moon's present orbit. Hence, any increase of 

 a planet's mass, or any change that produces an equiva- 

 lent eifect, even if only temporary in its action, tends to 

 drive the previously established inner satellite out to a 

 greater distance from its primary. This means that if 

 any planetoid body, say with mass like that of an average 

 satellite, should pass between the Earth and the Moon it 

 would have the effect of temporarily increasing the mass 

 of the Earth, and under the action of the forces which 

 enter into determinate stability, would give the Moon a 

 slight impulse to move out to a greater distance from the 

 Earth. Even if each impulse be very minute and its 

 effect only temporary, yet each such encounter would 

 repeat the impulse, and thousands of successive impulses 

 would cause the Moon to graduall^^ expand its orbit ; and 

 this would continue until the Moon reached a larger orbit 

 in which the impulses of expansion found an exact balance 

 against the normal tendency of the Moon to return to its 

 first position at the determinate orbit. Thus, supposing 

 for the moment that the Earth could hold two satellites 

 in stable revolution, the inner or nearer one, under the 

 law of determinate stability, would revolve in the Moon's 

 present orbit at 240,000 miles, while the outer or second 

 satellite would revolve in a larger orbit situated at a 

 determinate distance outside of the Moon's orbit. At a 

 certain distance from the Moon's orbit, the impulses of 

 expansion would have a continuing value just sufficient 



Am. Jour. Sci. — Fifth Series, Vol. T, No. 4. — April, 1921, 

 21 



