Theory of the Motion of the Heavenly Bodies Moving about the Sun in Conic Sections
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1857 edition. Excerpt: ... most important in this work, and, for this reason, will be treated with the greatest care in this section. 21 (161) But in the special case, in which, the plane of the orbit coincides with the ecliptic, and thus both the heliocentric and geocentric latitudes, from their nature, vanish, the three vanishing geocentric latitudes cannot any longer be considered as three data independent of each other: then, therefore, this problem would remain indeterminate, and the three geocentric places might be satisfied by an infinite number of orbits. Accordingly, in such a case, four geocentric longitudes must, necessarily, be given, in order that the four remaining unknown elements (the inclination of the orbit and the longitude of the node being omitted) may be determined. But although, from an indiscernible principle, it is not to be expected that such a case would ever actually present itself in nature, nevertheless, it is easily imagined that the problem, which, in an orbit exactly coinciding with the plane of the ecliptic, is absolutely indeterminate, must, on account of the limited accuracy of the observations, remain nearly indeterminate in orbits very little inclined to the ecliptic, where the very slightest errors of the observations are sufficient altogether to confound the determination of the unknown quantities. Wherefore, in order to examine this case, it will be necessary to select six data: for which purpose we will show in section second, how to determine an unknown orbit from four observations, of which two are complete, but the other two incomplete, the latitudes or declinations being deficient. Finally, as all our observations, on account of the imperfection of the instruments and of the senses, are only approximations to the truth, an...
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- 28 Jun 2012
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- Illustrations, black and white