Celestial coordinates

6.1 Constellations

الابراج الشمسية Aries = برج الحمل (March 21 - April 20 ) Taurus = برج الثور (April 21 - May 21) Gemini = برج الجوزاء (May 22 - June 21 ) Cancer = برج السرطان (June 22 - July 22 ) Leo = برج الأسد (July 23 -August 21 ) Vigro = برج العذراء (August 22 - September 23 ) Libra = برج الميزان (September 24 - October 23) Scorpio = برج العقرب (October 24 - November 22 ) Sagittarius = برج القوس (November 23 - December 22) Capricorn = برج الجدي ( December 23 - January 20 ) Aquarius = برج الدلو (January 21 - February 19 ) Pisces = برج الحوت(February 20- March 20) حمل الثور جوزة السرطان وحمى الليث سنبل الميزان ورمى عقربٌ بقوس الجدي وملا دلوٌ بركة الحيتــــــــــان

6.2 Twinkling Is not a property of stars themselves. It is an effect of our Earth’s atmosphere. Stars twinkle. Planets do not usually seem to twinkle.

6.3 Coordinate systems We need to know an object’s direction to observe it. Celestial sphere: large imaginary sphere, on which all astronomical objects hung on its inside surface.

Geographic coordinates Longitudes: half circles run from north pole to south pole. Longitude 0 passes through Greenwich. Dhahran Longitude +49ْ 54’ 33” (East) Latitudes: parallel circles that run around Earth, all parallel to the equator. Latitude 0 is the equator Latitude ±90 the poles Dhahran Latitude +26ْ 24’ 32” (North)

Astronomical coordinates The North Celestial Pole is the point on the celestial sphere directly above the Earth's North Pole. The South Celestial Pole is directly above the Earth's South Pole. The star Polaris, in the constellation Ursa Minor, is located very close to the North Celestial Pole. The celestial equator is directly above the Earth's equator. Right ascention = Longitude (East – West) Declination = Latitude (North South)

The celestial sphere الكرة السماوية

Declination Declination corresponds to latitude and is measured in the same way, but relative to the celestial equator (0° dec). The north celestial pole is at 90° north declination (+90° dec). The south celestial pole is at 90° south declination (-90° dec). Circles of constant declination are all parallel to the celestial equator.

Declination (Zenith) For any position on the surface of the Earth, the point on the celestial sphere that is directly overhead is called the zenith. Since the Earth and the celestial sphere are concentric, simple geometry shows that the zenith will always have a declination equal to the latitude of the observer (such as for Atlanta in the picture).

Right ascension A star's position along a circle of constant declination is described by a second number called right ascension. Right ascension corresponds to longitude, but different units are used. Instead of 360°, a circle is broken into 24 hours of right ascension. So, 360° = 24 h R.A., 15° = 1 h R.A., and 1° = 4 min R.A. Note that hours of right ascension is a unit of angle, not time, although there is an obvious connection due to the daily rotation of the celestial sphere.

Right asention

Right ascension Right ascension is measured from the celestial meridian, chosen to be 0 h R.A. (which is also the same as 24 h R.A.) The celestial meridian is a semicircle connecting the celestial poles and passing through a particular point on the celestial equator called the vernal equinox. Right ascension increases from west to east (note that we are looking at the exterior of the celestial sphere in the above picture).

Motion of the sun

Motion of the sun Although the stars are fixed relative to each other, the Sun moves relative to the stars. Once a year, the Sun traces out a circle on the celestial sphere called the ecliptic. The ecliptic is tilted at an angle of 23.5° with respect to the celestial equator. (The Moon and planets also move near the ecliptic.)  

Motion of the sun The Sun crosses the celestial equator at exactly two points, called equinoxes, from the Latin for "equal nights”. The equinox where the Sun ascends from the southern to the northern hemisphere is called the spring or vernal equinox because the Sun is there on March 21. The vernal equinox is chosen to be 0 h R.A. The Sun again crosses the celestial equator halfway around, at 12 h R.A. This position is called the autumnal equinox because the Sun is there on September 23.

Motion of the sun The positions where the Sun reaches its highest and lowest points are called solstices, from the Latin for "the Sun stops" as it changes direction. The Sun is highest in the sky (in the northern hemisphere) when it is at 6 h R.A. This position is called the summer solstice because the Sun is there on June 21. The Sun then has a declination of +23.5°. The Sun is lowest in the sky (in the northern hemisphere) when it is at 18 h R.A. This position is called the winter solstice because the Sun is there on December 21. The Sun then has a declination of -23.5°.

Sun Motion Event Date RA Dec VE 21 Mar. 0 h Equator SS 22 Jun. 6 h Equator SS 22 Jun. 6 h +23.5ْ Tropic of cancer AE 23 Sep. 12 h WS 22 Dec. 18 h -23.5ْ Tropic of Capricorn

Horizontal coordinates The altitude of an object is the angle between it and the horizon. The horizon has an altitude of 0° and the zenith has an altitude of 90°. The azimuth of an object is the angle between it and north, measured clockwise along the horizon. North has an azimuth of 0°, east has an azimuth of 90°, south has an azimuth of 180°, and west has an azimuth of 270°.

======================================== Sirius J2000 RA: 6h45m08.90s DE:-16°42'58.0" Date RA: 6h45m38.31s DE:-16°43'41.2“ Dhahran 2010-12-20 2h59m Sideral Time : 9h13m Azimuth :+223°47' Altitude :+33°59‘ Rise : 19h04m Azimuth:+108°27' Culmination : 0h32m Set : 6h00m Azimuth:+251°33‘ ======================================== Date RA: 6h45m38.38s DE:-16°43'41.4“ Dhahran 2010-12-30 2h59m Sideral Time : 9h52m Hour Angle : 3h07m Azimuth :+231°43' Altitude :+27°27‘ Rise : 18h24m Azimuth:+108°27' Culmination : 23h53m Set : 5h21m Azimuth:+251°33‘

Canopus سهيل J2000 RA: 6h23m57.10s DE:-52°41'45.0" Date RA: 6h24m11.70s DE:-52°42'08.0" Dhahran 2010-12-20 2h59m Sideral Time : 9h13m Hour Angle : 2h49m Azimuth :+204°02' Altitude :+03°00' Rise : 20h48m Azimuth:+152°03' Culmination : 0h11m Set : 3h33m Azimuth:+207°57‘

Earth’s axis precession Period of 26000 years. Small correction of celestial positions is needed. Small change (1/60ْ per year). Latest is epoch 2000

Example 6.1 Sep. 22 Autumnal Equinox Sun has Dec. of 0ْ and RA of 12 h Sirius has Dec. of -16ْ 43’ and RA of 6h 45m A) what are the RA and Dec of the Sun on March 21? B) what are the RA and Dec of the Sun on June 22? C) What are the RA and Dec of Sirius on June 22?

Example 6.2 Bernard’s Star has R.A. 17h 57.9m and dec. +4ْ 41’ It crosses the meridian facing south at sidereal time 17h 57.9m

Example 6.3 At what solar time does Bernard’s star cross due south of you on September 22nd? It crosses the meridian facing south at sidereal time 17h 57.9m On Sep. 22nd it corresponds to solar time 17h 58m On Sep. 26th it corresponds to solar time 17h 42m (16 min earlier)

Sun Today The sun Today has RA of approximately 18 h At what sidereal time does the sun cross the Meridian due south, today. Answer: at noon 11:40 am solar time = 18 h sidereal time.

Sirius tonight Sirius has RA 6h45m38.31s It will cross the Meridian due south at 6h45m38.31s (sidereal time) wich is equivalent to 12:08 a.m. In June: it will cross the Meridian at 6h45m38.31s (sidereal time) which is equivalent to 12:23 p.m.