Finding celestial objects in our night sky … … requires knowing celestial coordinates, based on the time of night, and our location 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 andDeclination. How can you visualize them on the night sky?. Meridian

Meridian http://www.synapses.co.uk/astro/earthmot.html Your Zenith and Meridian – Looking up and towards your meridian – The North South line… Zenith Zenith: 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 your meridian are determined by you and not by things like Right Ascension or the stars. Granted, Polaris will always be on your meridian but that is because it happens to be the center of rotation of the celestial sphere. Meridian http://www.synapses.co.uk/astro/earthmot.html

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 very 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 Polaris or the celestial pole makes with the horizon is equal to the observer's latitude. In the diagram, the angle   is the observer's latitude. The pole and the equator are at right angles, or   Since the angles in a triangle add to 180°, we know that 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 = d pole star altitude = latitude. which means that the angle between the pole and the horizon (c) is the same as the observer's latitude. This fact was used by navigators at sea, who could easily find their latitude by measuring the positions of the stars.

Objects 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. Observers in the northern hemisphere orient their observatories so that the telescope faces south because there is a larger surface area of celestial sphere ( i.e the band of sky ) from the north pole to the southern horizon then from the north pole to the northern horizon. Stars are said to CULMINATE on your meridian.                                               http://calgary.rasc.ca/radecl.htm#ra Side view of Declination lines for an observer at 45° Latitude: - they are all parallel - the circles get smaller towards the Celestial Poles

highest overhead in the SOUTH for northern observers. Looking South Northern observers face south to observe star and planets culminate in the south along their North/South meridian Here the orange line of the planets (and many comets and asteroids) is the ecliptic. The ecliptic rises highest overhead in the SOUTH for northern observers.

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.

Right Ascension If Declination is the "up-down" coordinate, then what is the "left-right" coordinate? The answer is Right Ascension. Each of these curved lines is like a N-S longitude line on the Earth - they all meet at the poles and they all cross the Equator at a 90° angle. But how to label them? They are not nearly as fixed in the sky as Declination, since the Earth is constantly rotating bringing new grid lines up from the East, and loosing those low in the West. So a fixed degree system based on the Pole and the Equator just won't work. They need to be tied into the fact that Earth rotates every 24 hours and this is an amount of time.

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. …

ECU 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)