1. 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

2. 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.

3. 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.

4. 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

5. 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.

6. 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

7. 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 )
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

8. 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.

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. (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 = (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)