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Definition Celestial Sphere S. celestial pole N. celestial pole N. pole S. pole Celestial equator Equator
Declination Polar zones lie within 23.5º of the poles. Tropics (where Sun is directly overhead at noon at summer solstices) are at latitudes 23.5º and - 23.5º. 1 arcminute, 1’ = 1/60º 1 arcsecond, 1” = 1/3600º Betelgeuse with its small declination can be seen in both the northern and southern hemispheres. 66.5º 23.5º Capella +45º57’ Betelgeuse +7º24’ N. Celestial pole +90º Celestial equator 0º
Declination In London Polaris is 51º above the horizon. From London, a star is circumpolar if its dec is 90 - 51 = 39º or higher. Capella at 45º is circumpolar, Betelgeuse at 7º is not. Stars that have a declination south of -39º will never rise above the London horizon. Celestial equator 0º Capella +51ºN London N+90º Polaris Zenith +51º +39º S. Horizon N. Horizon +51º -39º +39º
Right Ascension Right ascension (RA) on the celestial sphere is similar to longitude on the Earth; it starts from the point where the ecliptic (Sun’s path in the sky over a year) crosses the equator (i.e. the vernal equinox), this point lies in the constellation of Pisces but it is called the First Point of Aries where it used to lie. The RA of a star is the sidereal time between the culmination (highest point - due south) of the First Point of Aries and the culmination of the star. S W Betelgeuse The RA of Betelgeuse is 5h 53m, this is the time difference between the the First Point of Aries crossing the meridian (a circle through both poles and the zenith) and Betelgeuse reaching the meridian. Meridian First Point of Aries E
Right Ascension The RA and declination of a star (those of the Sun, Moon and planets change) is fixed; Betelgeuse always arrives 5h 53m after the First Point of Aries, and its declination is fixed on the celestial sphere. The rotation of the Earth makes its position change relative to the observer. The altitude (N-S) an azimuth (E-W) gives its location of a star at any time in the sky. First Point of Aries crosses the meridian in London 5h 53m later Betelgeuse crosses the meridian in London
Transits A circumpolar star will transit (cross) the meridian twice a day, once when it is above the celestial pole (south of the polar point) and once when it is below the CP (due north). These are called the upper and lower transits of the star respectively. For a non-circumpolar star, the lower transit takes place when the star is below the horizon.
Sidereal time This is the true rotation period of the Earth. At Greenwich 0 hrs is defined as the point when the First Point of Aries is on the meridian. The time for this point to reach the meridian again is 23 hrs 56 min 4 sec . This is the sidereal day . The local sidereal time (LST) at any location is 0 hrs when the First Point of Aries is on the local meridian. The LST is therefore equal to the RA of the star which lies on the meridian, e.g. when Betelgeuse is on the meridian the LST is 5h 53m. The 24 hr day takes into account the 1º progress of the earth in its orbit around the Sun every day; it has to rotate a little more so the Sun is on the meridian at noon i.e the Sun is at its highest point again. Also we use an imaginary mean Sun which moves along the celestial equator at a constant rate when in actual fact the the Sun moves across the sky at a variable rate over a year (the Earth’s orbital velocity varies at different points in its elliptical orbit following Kepler’s laws).
Hour angle A transit instrument points at the meridian and when a known star crosses the meridian you can determine the LST. The hour angle of a star is the difference between the LST and its RA. Meridian LST is 8h 55m E W The hour angle of Betelgeuse is 3h 2m, i.e. it crossed the meridian 3h 2m ago. Betelgeuse RA = 5h 53m
Example Manchester Latitude: 53º14’N, Longitude: 2º18’.4W The star Rigel, RA = 5h 12m, dec = -8º14’ is on the meridian. Using the LST at Manchester, find the Greenwich ST (GST): LST at Manchester = RA of Rigel = 5h 12m. The Earth rotates by 1º every 4 mins, longitude of Manchester is 2º18’.4W of Greenwich so multiply this by 4 and add to LST to get GST (as Earth rotates W to E, Greenwich is ahead in time). So GST is 5h 12m + 9m 13.6s = 5h 21m 13.6s.
Example Rigel’s height above the horizon at Manchester at culmination: 90º - 53º14’ = 36º46’. Rigel is in the southern hemisphere, so 36º46’ - 8º14’ = 28º32’ Capella +53º14’N Polaris Zenith +53º14’ S. Horizon N. Horizon -36º46’ Manchester Latitude: 53º14’N, Longitude: 2º18’.4W The star Rigel, RA = 5h 12m, dec = -8º14’ is on the meridian. -8º14’ -28º32’