Changing the origin of light in the diurnal motion

When the light comes and goes, its z = 90 °, h = 0e, and the azimuths of the points of sunrise and sunset depend on the declination and the latitude of the place lights up. At the time of upper culmination zenith distance of the light of the minimum, maximum altitude and the azimuth A = 0 (if the star culminates south of the zenith), or A = 180e (unless it culminates from the zenith to the north). At the time of the lower culmination of the zenith distance of lights reaches its maximum value, the height - the minimum, and the azimuth A = 180e, or A = 0e (if the lower culmination of the nadir occurs between Z 'and the south pole of the world P'). Hence, from the lower to the upper culmination zenith distance of the light decreases, and the height increases, from the upper to the lower peak, by contrast, the zenith distance increases, the height decreases. At the same azimuth lights will also vary within certain limits. Thus, the horizontal coordinates of luminaries (z, h and A) are continually changing as a result of the rotation of the celestial sphere, and if the light has always connected with the sphere (ie, its declination d and a right ascension remain constant), then its horizontal coordinates take their previous values ​​when the sphere will make one revolution. Since the daily parallel bodies at all latitudes of the Earth (except the poles) are inclined to the horizon, the horizontal coordinates vary unevenly, even for a uniform daily rotation of the celestial sphere. Altitude h, and its zenith distance z more slowly varying near the meridian, ie, at the upper or lower culmination. Azimuth is shining A, on the contrary, in these moments varies most rapidly. Local luminaries angle t (in the first equatorial coordinate system), like the azimuth A, is constantly changing. At the time of upper culmination of his lights t = 0. At the time of the lower peak hour angle of the lights t = 180e, or 12h. But, in contrast to the azimuth, hour angle luminaries (if the declination d and a direct ascent remain constant) change uniformly because they counted on the celestial equator, and the uniform rotation of the celestial sphere angles are proportional to changes in hourly time intervals, ie increment of time equal to the angle of rotation angle of the celestial sphere. The uniformity of the angles change time is very important in the measurement of time. Altitude h, or the zenith distance z at the climax depends on the declination shone d and latitude of the observer j. Drawing directly from (7): 1) If the declination shone M1 d <j, then it culminates to the south of the zenith at the zenith distance z = j - d, (1.6) or the height h = 90 ° - j + d; (1.7 ) 2) if d = j, then the star culminates at the zenith, and then z = 0 (1.8) and h = + 90 °, (1.9) 3) if d> j, then the star of M2 in the upper peak is located to the north of the zenith to the zenith distance z = d - j, (1.10) or the height h = 90 ° + j - d. (1.11) 4) Finally, at the time of the lower culmination of the zenith distance z = M3 lights 180e - j - d, (1.12) a height h = d - (90 ° - j) = j + d - 90 °. (1.13) is known from observations (see § 8) that at a given latitude j each star always rises (or sets) at the same point of the horizon, the height it is also always the same meridian. We can therefore conclude that the declination of stars do not vary over time (at least visibly). The point of sunrise and sunset, moon and planets, as well as their height in the meridian at different days of the year - are different. Consequently, the declination of these stars are continuously changing over time.