Finding celestial objects in our night sky: Right Ascension Declination Local Time of Day Every star, cluster, nebula, galaxy, radio source, and quasar has a position in the night sky. All the Solar System objects - the Sun, the Moon, the other planets, asteroids, and comets have their own motion across the background of stars, so for all these objects their sky position changes hourly or daily but can be mathematically predicted. All the textbooks, star charts, planispheres and "GOTO" computers refer to sky position coordinates : called Right Ascension and Declination. How can you visualize them on the celestial sphere? Meridian

Your Zenith and Meridian from the Horizon The North South line… Because the sky (celestial sphere) is constantly in motion, due to the Earth's rotation, the stars at your zenith are constantly changing. Regardless, your zenith is always overhead - straight up. Your zenith is a useful point in the sky because it helps to define your meridian. Meridian is the important North/South line through your zenith and also through both celestial poles. We look at our celestial objects while we are oriented along our North/South meridian Notice that both your zenith and meridian are determined by you on your Horizon and not by absolute Right Ascension, Declination Granted, Polaris will always be on your meridian but that is because it happens to be the center of rotation of the celestial sphere.

Celestial Coordinates Right Ascension and Declination We map celestial coordinates  with the aid of the concept of a celestial sphere. This is an imaginary ball larger than the entire visible universe. Imaginary lines are drawn from the Earth through celestial objects, extending beyond them until the lines touch the surface of the celestial sphere. These points mark the apparent positions of those objects given in star charts, catalogs and almanacs. The position of a celestial object is given by its Right Ascension (RA) and Declination (Dec) in the same way as our position on earth is given by our Longitude and Latitude.

Polaris 45 degree up Local Horizon Our Observing Latitude determines what celestial objects are seen above our local horizon For our location at 45 degrees latitude, the pole star is at altitude 45 degrees as shown to the right. We can see that when we look up. This diagram shows that the altitude of Polaris above the horizon is the same as the observer's latitude. Note that the lines drawn to Polaris are parallel because Polaris is very far away. The direction to Polaris from the center of Earth is nearly the same as from the observer's position. Polaris 45 degree up Local Horizon

Our Observing Latitude determines what celestial objects are seen above our local horizon Polaris is always above our horizon and since it is at the pole, it is relatively fixed in the sky during the night. All stars rotate around this axis. Using geometry, it is easy to show that the angle c to the Celestial Pole (Polaris) makes with the horizon is equal to d, the observer's latitude. In the diagram, angle d is observer's latitude. The pole and the equator are at right angles. Altitude Polaris = Latitude of Observer Proof : Angle c = Angle d (Latitude) d + a = 90 c = b (AIT Alternate Interior Angles of || are equal) a = 90 –d a + b + 90 = 180 (sum angles triangle) (1) a + b = 90 substitute for a in (1): 90 – d + b = 90 d = b and… c =b and d = b Therefore c = d pole star altitude = latitude. This fact was used by navigators at sea, who could easily find their latitude by measuring the positions of the stars.

Astronomical Navigation (Latitude) When a star culminates on the navigator’s meridian, the observed altitude plus the of declination the star at the time of meridional crossing gives the navigator’s latitude according to: Latitude = 90 – Altitude + Declination Latitude (but not Longitude) could be found to a fair precision (about 30 miles) by observation of the meridian altitudes of the Sun and certain stars, such as the pole Star above the horizon. Courtesy Man Is Not Lost , D.H. Sadler Her Majesty’s Stationary Office 1968

Stars Culminate on your Meridian Everything in the sky left of your Meridian is RISING and everything right of your Meridian is SETTING, just like the Sun does. (In the southern hemisphere, your large area of sky is facing north, stars rise in the east (on your right) and set in the west (on your left). Everything on your Meridian has therefore reached its HIGHEST point in the sky tonight, and is therefore at its best for viewing since it is as far as it can be away from the (murky) horizons. When the Star crosses the Meridian, it is the single point of highest altitude. Stars are said to CULMINATE on your meridian If the star is off the meridian, there are 2 altitudes for it: east of the meridian west of the meridian. Observers in the northern hemisphere orient their observatories so that the telescope faces South                                               (courtesy http://calgary.rasc.ca/radecl.html ) Side view of Declination lines for an observer at 45° Latitude: 135 degrees of sky from the north pole to the southern horizon Only 45 degrees of sky from north pole to the northern horizon

Star Location: Altitude above Horizon Star altitude depends on the Declination or (Dec) Altitude of Pole Star = Our geographic latitude. The altitude of any other star transiting due South on the MERIDIAN Altitude = Co-latitude + Declination Celestial Equator co-latitude Due South Declination Remember Declination is always measured from the celestial equator to the object. Note: If the star is north of the zenith (i.e. the angle measured from the celestial equator to the zenith > latitude, say 50 deg, then Alt = 90 + (Phi + Dec) rather than (90 – Phi) + Dec Alt = 90 + Our Observing Latitude determines what celestial objects are seen above our local horizon For our location at 45 degrees latitude, the pole star is at altitude 45 degrees . We can see that when we look up. The altitude of Polaris above the horizon is the same as the observer's latitude. I Local Horizon View: Altitude of Regulus = 45 + 11deg Declination = 56 deg Declination ALWAYS measured from celestial equator to star.

Sidereal Rate and Hour Angle Each object is catalogued as being at a certain set of coordinates in (RA,DEC). For objects visible at your latitude at a certain time of year (and night) the object will appear at a certain "hour angle“ east or west or your meridian for a given time. The Right Ascension of the object stays with the object and comes into view at the appointed hour! If you stood outside and looked at the sky for several hours you would see the stars seem to move across your Meridian from East to West at that rate. This is called Sidereal Rate, and it is the rate used in equatorial telescope mounts. Astronomers used to have to know their LST (Local Sidereal Time) to see if it matched up with the Right Ascension of the object for that time of year. …

(Alt,Az) = f(RA,Dec,LST,Latitude) ECU (Earth Centered Universe Computer Program) does the Coordinate Transformations However ECU does the coordinate transformations from an objects (Right Ascension, Declination) to your local (Altitude and Azimuth) For a given latitude, time of year and night ECU calculates all the positions of celestial objects that appear above your horizon (Alt,Az) = f(RA,Dec,LST,Latitude) We can however use the simple cases for objects on our meridian: To check the altitude For objects North of the Celestial Pole and CULMINATING (on the meridian) Altitude = (CoLatitude + Dec) if < 180 else Altitude = 180 - (CoLatitude + Dec) For Circumpolar stars: Lower Culmination: Altitude = (Latitude – CoDec) if < 180 - wrap if > To check Right Ascension – with respect to your Meridian (and Local Sidereal Time) Hour Angle (where the object is East/West of Meridian) = RA – LST If RA = LST, the object is on the meridian

Simple checks for objects near your meridian To check the altitude For objects North of the Celestial Pole and CULMINATING (on the meridian) Altitude = CoLatitude+ Declination if < 180 …else Altitude = 180 - (CoLatitude + Declination) For Circumpolar stars: Lower Culmination: Altitude = Latitude – Dec To check Right Ascension – with respect to your Meridian (and Local Sidereal Time) Hour Angle (where the object is East/West of Meridian) = RA – LST If RA = LST, the object is on the meridian Zenith NP Celestial Equator CoDec Dec CoLat Lat Horizon (Off the meridian, you must use spherical trigonometry)