1. 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

2. 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

3. 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

4. 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.

5. 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.
                                             
Side view of Declination lines for an observer at 45° Latitude: - they are all parallel - the circles get smaller towards the Celestial Poles

6. 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.

7. 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 = deg Declination = 56 deg
Declination ALWAYS measured from celestial equator to star.

8. 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.

9. 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. …

10. 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 = (CoLatitude + Dec)
For Circumpolar stars:
Lower Culmination:
Altitude = (Latitude – CoDec) if < 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

11. 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 = (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)