Theoretical astronomy relating to the motions of the heavenly bodies revolving around the sun in accordance with the law of universal gravitation, ... of the geocentric and heliocentric
James Craig Watson
Paperback
(RareBooksClub.com, March 6, 2012)
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. 1885 Excerpt: ...n, n", n', and n'" are obtained, to compute from these and the data furnished directly by observation the curtate distances for the extreme places. The corresponding heliocentric places may then be found, and hence the position of the plane of the orbit as determined by the first and fourth observations. Thus, by means of the equations (37) and (38), we obtain log P = 0.0256953, log p'" = 0.4492542. With these values of p and p'", the following heliocentric places are obtained: I = 716'51".54, log tan b =8.4289064, logr =0.3083732, f" = 91 37 40.96, logtan6"' = 8.8638549„, logr"'= 0.3172678. Then from tan t sin (i. (?" + I)--SI) = £ (tan V" + tan b) sec (f--1), tan i cos (i (1" + 1)--Si) = £ (tan b'"--tan 6) cosec--I), we get SI = 206 42' 45".23, i = 4 36' 49".76. For the arguments of the latitude the results are u = 16030' 35".99, u" = 244 59' 12".53.;Ecliptic and Mean Equinox 1864.0. The equations tan b'--tan isin (J--& ), tan b" = tan i sin (i"--Q ), give log tan 6' = 8.1827129., log tan b" = 8.6342104., and the comparison of these results with those derived directly from p' and p" exhibits a difference of + 1".04 in b', and of--0".06 in h". Hence, the position of the plane of the orbit as determined from the extreme places very nearly satisfies the intermediate latitudes. If we compute the remaining elements by means of these values of r, r'", and «, u'", the separate results are: It appears, therefore, that the principal effect of neglecting tne extreme latitudes in the determination of an orbit from four observations is on the inclination of the orbit and on the longitude of the ascending node, the ...