Hence its mean place for Jan. 1, 1840, is R9h 19m 43.568 tang. 9.14584" 0.25651" D= 7° 58' 4".83. To calculate the effects of nutation, we have S=339° 40′, D=242° 30', O=281° 15' -0.3448 sin. = 0.1205, 9".25 cos. 8".673 0.00415 sin.2 -0.0027,-0.0903 cos. 2=-0.068 -0.00413 sin. 2D-0.0034, 0".0900 cos.2D-0".032 -0.02502 sin. 20= 0.0096, 0.5447 cos.20-0.504 C=t' 0.1240, 8 0 1 = 8".049 20".0426 × 0.1240 cos. R = c' t' — 15′′.335 × 0.1240 — c' t' — 1′′.901 Cc ct+0.1240 X 2.948 ct' +0.365 -swd=8".049 cos. R tang. D=-0.861 —— 0.058, Nutation in right ascension and declination. whence the variations arising from nutation are D=3".28, R = 0.30, and the true places are D7° 58' 1".55, R9 19 43.87. 3. Find the mean obliquity of the ecliptic for the year 1950, and reduce the formulas for finding the variations of mean right ascension and declination to the beginning of that year. Ans. "1 = 23°26′ 36′′.18. & R = 46".1059 t'+ 19.8903 t' sin. R tang. D. 4. Find the annual variations in the right ascension and declination of Ursa Minoris for the year 1839, and its true place for mean midnight at Greenwich, Aug. 9, 1839; its mean right ascension for Jan. 1, 1839, being 14" 51" 14.943, its declination 74° 48′ 48.89 N., the longitude of the moon's ascending node for Aug. 9, 1839, being 347° 17', that of the moon 144° 2′, and that of the sun 136° 30′, and using the constants of the Nautical Almanac, which give for Aug. 9, 1839, f=32.33, g=16′′.70, G = 327° 30'. Ans. Var. in R. A. —— - 0.277 ; var. in Dec. =14′′.71; and for Aug. 9, 1839, R 14h 51m 16.36 D74° 48' 32".46. Tables XL and XLIII. 5. Calculate the values of f, g, and G for April 1, 1839, mean midnight at Greenwich, when 354° 10', 11° 34, and D is neglected. = = Ans. f 12.53, g=11".05, G299° 34'. In Table XL of the Navigator, the decimal is neglected, and 20 used instead of 20.0562. Table XLIII is calculated from the formulas of Bessel, which differ a little from those of Bailly used in the Nautical Almanac. The construction of these two tables is sufficiently simple from the calculations already given. 26* Sideral and solar day. CHAPTER VII. TIME. 86. The intervals between the successive returns of the mean place of a star to the meridian are precisely equal, and the mean daily motion of the star is perfectly uniform; so that sideral time is adapted to all the wants of astronomy. The instant, which has been adopted as the commencement of the sideral day, is the upper transit of the vernal equinox. The length of the sideral day, which is thus adopted, differs therefore from the true sideral or star day by the daily change in the right ascension of the vernal equinox. But this change is annually about 50′′ or 3.3, so that the daily change is less than 0.01, and is altogether insensible. 87. Corollary. The difference between the sideral time of different places is exactly equal to the difference of the longitude of the places. 88. The interval between two successive upper transits of the sun over the meridian, is called a solar day; and the hour angle of the sun is called solar time. This is the measure of time best fitted to the common purposes of life. Perigee. Apogee. The intervals between the successive returns of the sun to the meridian, are not exactly equal, but depend upon the variable motion of the sun in right ascension, and can only be determined by an accurate knowledge of this motion. 89. The want of uniformity in the sun's motion in right ascension arises from two different causes. I. The sun does not move in the equator, but in the ecliptic. II. The sun's motion in the ecliptic is not uniform. The variable motion of the sun along the ecliptic, and its deviations from the plane of the mean ecliptic, cannot be distinctly represented, without reference to the variations of its distance from the earth, and to the nature of the curve which it describes. This portion of the subject, therefore, which involves the determination of the sun's exact daily position, that is, the calculation of its ephemeris, must be reserved for the Physical Astronomy. It is sufficient, for our present purpose, to know that the sun moves with the greatest velocity when it is nearest the earth, that is, in its perigee; and that it moves most slowly when it is farthest from the earth, that is, in its apogee. 90. The sun arrives at its perigee about 8 days after the winter solstice, and at its apogee about 8 days after the summer solstice. The mean longitude of the perigee at the beginning of the year 1800, was 279° 30′ 5′′, and it is advancing towards the eastward at the annual rate of about 11".8; so that, by adding the precession of the equinoxes, the annual increase of its longitude is about 62". |