Finding celestial objects in our night sky:Right AscensionDeclinationLocal Time of Day

Every star, cluster, nebula, galaxy,radio source, and quasar has a

positionin the night sky. All the Solar Systemobjects - the Sun, the Moon, the

other planets, asteroids, and comets have

theirown motion across the background

of stars, so for all these objects their

sky position changes hourly or daily but

canbe mathematically predicted.

All the textbooks, star charts,planispheres and "GOTO" computersrefer to sky position coordinates :called Right Ascension and

Declination.

How can you visualize them on thecelestial sphere?

Meridian

Your Zenith and Meridian from the Horizon

The North South line…

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 linethrough your zenith and also throughboth celestial poles. We look at our celestial objects while we are oriented along our North/South meridian

Notice that both your zenith and meridianare determined by you on your Horizon andnot by absolute Right Ascension, Declination

Granted, Polaris will always be on yourmeridian 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.

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 Polarisabove the horizon is the same as the observer'slatitude. Note that the lines drawn to Polaris areparallel because Polaris is very far away. The direction to Polaris from the center of Earth isnearly 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 tothe Celestial Pole (Polaris) makes with the horizon

isequal 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 ObserverProof : Angle c = Angle d (Latitude)

d + a = 90c = b (AIT Alternate Interior Angles of || are

equal)a = 90 –da + b + 90 = 180 (sum angles triangle)(1) a + b = 90substitute for a in (1): 90 – d + b = 90 d = band…c =b and d = bTherefore c = dpole 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 starat the time of meridional crossing gives thenavigator’s latitude according to:

Latitude = 90 – Altitude + Declination

Latitude (but not Longitude) could be found to a fair precision (about 30 miles) byobservation of the meridian altitudes of theSun and certain stars, such as the pole Starabove 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 isRISING and everything right of yourMeridian 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 yourleft).

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 orienttheir 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 horizonOnly 45 degrees of sky from north pole to the northern horizon

Star Location: Altitude above Horizon

Star altitude depends on theDeclination 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

Local Horizon View:Altitude of Regulus = 45 + 11deg Declination = 56 deg

Declination ALWAYS measured from celestial equator to star.

Due Southco-latitude

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 (Earth Centered Universe Computer Program) does the Coordinate Transformations

However ECU does the coordinatetransformations 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 aboveyour horizon

(Alt,Az) = f(RA,Dec,LST,Latitude)

Simple checks for objects near your meridian

NP

Celestial Equator

Zenith

Horizon

To check the altitude For objects North of the Celestial Pole and CULMINATING (on the meridian)Altitude = CoLatitude+ Declination if < 180…elseAltitude = 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

CoLat

Dec

Lat

CoDec

(Off the meridian, you must use spherical trigonometry)