Page:Practical astronomy (1902, John Wiley & Sons).djvu/26

 8 PRACTICAL ASTRONOMY. with its proper sign to the mean longitude of the sun's mean place; the result will be the mean longitude of the sun's true place; hence the Sim's true longitude = Mean longitude of sun's mean place Equation of center Perturbations in longitude Corrections to pass from the mean equinox of date to true equinox of date,. These latter corrections are due to Nutation and constitute the Equation of the Equinoxes in Longitude. 4. Having the true longitude of the sun and the obliquity of the ecliptic, the corresponding Right Ascension and Declination of the sun can be computed for the same instant by the method explained in Art. 180, Astronomy. 5. Earth's Radius Vector. Substituting the values of e and n t, in the second of Eqs. (650), Mechanics, will give the values of the distance of the sun from the earth in terms of the mean distance a: thus / e 2 r = a ( 1 e cos n t + - (1 cos 2 n t) 3e 3 -- (cos 3 n t cos n t )+ etc. j . (14) 6. The Sun's Horizontal Parallax. From astronomical observa- tions the value of a (and hence of r) is found in terms of the earth's equatorial radius, p e . (Young, Chapters XIII and XVI.) The sun's equatorial horizontal parallax, P, at any time is then given by <*) being the number of seconds in a radian = 206264".S, and r being expressed as just stated. At any place where the earth's radius in terms of the equatorial radius is /j, we shall have for the horizontal parallax - = pP. 7. The Sun's Apparent Semi-Diameter. Knowing P, measure- ments of the sun's angular semi-diameter will give its linear semi- diameter s' in terms of p e . Its angular semi-diameter s for any day is then given by