On Hansen's theory of the physical constitution of the Moon

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1868
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Abstract
On Hansen's Theory of the physical Oonstitution of the Moon; by SmoN NEWCOMB.THE great reputation of the author has given extensive currency to the hypothesis put forth by Pro! Hansen some years since, that the center of gravity of the moon is considerably farther removed from us than the center of figure.The consequences of this hypothesis are developed in an elaborate mathematical memoir to be found in the twenty-fourth volume of the Memoirs of the Royal Astronomical Society.But the reception of the doctrine seems to have been based rather on faith in its author, than on any critical examination of its logical foundation.!) Such an examination it is proposed to give it.An indispensable preliminary to this examination is a clear understanding of what the basis of the doctrine is.Let ns then consider these three propositions:1.The moon revolves on her axis with a uniform motion equal to her mean motion around the earth.2. Her motion around the earth is not uniform, but she is sometimes ahead of and sometimes behind her mean place, owing both to the elliptic inequality of her motions and to perturbations.3. Suppose her center of gravity to be farther removed from us than her center of :figure, and so placed that when the moon is in her mean position in her orbit, the line joining these centers passes through the center of the earth.Let us also conceive that these two centers are visible to an observer on the earth.Then a consideration of the geometrical arrangements of the problem will make it clear that when the moon is ahead of her mean place, the observer will see the two centers separated, the one nearest him being farther advanced in the orbit, while, when the moon is behind her mean place, the nearest center will be behind the other.This apparent oscillation of the two centers is, indeed, an immediate effect of the moon's libration in longitude.Now the inequalities in the moon's motion, computed from the theory of gravitation, are those of a supposed center of gravity.But the inequalities given by observation are those of the center of figure.Hence, in the case supposed, the inequalities of observation will be greater than those of theory.* In this connection it is curious to notioe that on page 83 of his memoir Hansen appears as the first of the independent modern discoverers of Cagnoli's theorem of spherical trigonometry: cos a cos 11 cos C+sin a sin 1I=oos A cos B cos c+sin A sin B. This was about three years before the above formula was published as new by :Mr.Cayley, and geometrically demoustrated
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Authors Sally Newcomb
Journal american journal of science
Year 1868
DOI
10.2475/ajs.s2-46.138.376
URL
https://doi.org/10.2475/ajs.s2-46.138.376
Keywords Keywords not found

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