Theory of the motion of the heavenly bodies moving about the sun in conic sections; a translation of Gauss's "Theoria motus." With an appendix

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 Excerpt: ...INVESTIGATION OF THE ORBITS OF HEAVENLY BODIES FROM GEOCENTRIC OBSERVATIONS. FIRST SECTION. DETERMINATION OP AN ORBIT FROM THREE COMPLETE OBSERVATIONS. 115. Seven elements are required for the complete determination of the motion of a heavenly body in its orbit, the number of which, however, may be diminished by one, if the mass of the heavenly body is either known or neglected; neglecting the mass can scarcely be avoided in the determination of an orbit wholly unknown, where all the quantities of the order of the perturbations must be omitted, until the masses on which they depend become otherwise known. Wherefore, in the present inquiry, the mass of the body being neglected, we reduce the number of the elements to six, and, therefore, it is evident, that as many quantities depending on the elements, but independent of each other, are required for the determination of the unknown orbit. These quantities are necessarily the places of the heavenly body observed from the earth; since each one of which furnishes two data, that is, the longitude and latitude, or the right ascension and declination, it will certainly be the most simple to adopt three geocentric places which will, in general, be sufficient for determining the six unknown elements. This problem is to be regarded as the 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 plac...