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Astronomy 305 Exam Topics Exam I – Star Charts Exam II –Coordinate Systems and Telescopes Exam III – Planets, Comets and Asteroids Exam IV – Stars and Deep Sky Objects Coordinate Systems 17 - Horizontal Coordinates 18 - Equatorial Coordinates 19 - Ecliptic Coordinates 20 - Galactic Coordinates 21 - Converting decimal degrees to °, ’, ” 22 - Converting Degrees to Hours 23 - Converting between Coordinate Systems 24 - Converting Right Ascension to Hour Angle 25 – Equatorial to Horizontal Coordinate Conversation Celestial Coordinate Systems These are coordinate systems with two angular measurements: • Geographical • Horizontal • Equatorial • Ecliptic • Galactic Geographical System Latitude (f) – the angle of a city above the equator Longitude (L) – the angle around the equator from the Prime Meridian 17 - Horizontal System Altitude (a) – the angle of a star above the horizon Azimuth (A) – the angle around the horizon from the north point; measured eastward 18 - Equatorial System Declination (d) Right Ascension (a) Hour Angle (H) – the difference between the right ascension of your meridian and the right ascension an object 24 – Converting between a and H LST = Local Sidereal Time – LST is the same as the right ascension of the meridian on your star charts H = LST – a Examples: – What is the hour angle of Regulus at 11:00 PM tonight? – What is the hour angle of Sirius at 8:00PM tonight? Celestial Meridian d H Celestial Equator 90°- f S HORIZON Celestial Meridian d Celestial Equator a 90°- f S HORIZON 19 - Ecliptic System Ecliptic Latitude (b) – the angle of a star above the ecliptic Ecliptic Longitude (l) – the angle around the ecliptic from the vernal equinox – measured eastward – labeled along the ecliptic on the star charts Obliquity (e) – the angle between the ecliptic and the celestial equator and is approximately 23.5 degrees 20 - Galactic System Galactic Latitude (b) – the angle of a star above the galactic plane Galactic Longitude (l) – the angle around the galactic plane – measured eastward from the galactic center Examples Problem For all of the planets find… – their ecliptic longitudes – the host constellation – their equatorial coordinates Hint: Use Appendix 11 Planet Positions Planet Mercury Venus Mars Jupiter Saturn Uranus l a d Constellation Planet Positions Planet Mercury Venus Mars Jupiter Saturn Uranus l Visible? Rise Time Set Time Example Problems Calculate the altitude and azimuth of Capella for 11:00PM tonight. 25 - Equatorial to Horizontal Step 1 Find a, LST and H is decimal hours. Step 2 Convert H to degrees. Step 3 Convert d to decimal degrees. Step 4 Find sin a = sin d sin f + cos d cos f cos H Step 5 Find a Step 6 sin d sin f sin a Find cos A cos f cos a Step 7 Find A’ Step 8 sin d sin f sin a cos A cos f cos a If sin H is negative, A = A’ If sin H is positive, A = 360° – A’ Step 9 Find a and A in degrees, minutes and seconds. More Examples What are the coordinates of Jupiter on May 5, 2005 at 8:00PM? b l a d LST H a A Reading Assignment Chapter 2 – A Tour of the Sky Chapter 3 – The Monthly Sky Maps Chapter 16 – Telescopes and Binoculars More Examples What are the coordinates of Venus tonight at 7:00pm? b l a d LST H a A 25 - Equatorial to Horizontal Step 1 Find a, LST and H is decimal hours. Step 2 Convert H to degrees. Step 3 Convert d to decimal degrees. Step 4 Find sin a = sin d sin f + cos d cos f cos H Step 5 Find a Step 6 sin d sin f sin a Find cos A cos f cos a Step 7 Find A’ Step 8 sin d sin f sin a cos A cos f cos a If sin H is negative, A = A’ If sin H is positive, A = 360° – A’ Step 9 Find a and A in degrees, minutes and seconds. More Examples Suppose that the Moon occults the star Antares on Feb 6th. Find the following for the Moon: a d b l Ecliptic Coordinates Step 1 Find a and d. Step 2 Find a and d in decimal degrees. Step 3 Find sinb = sind cose – cosd sine sina Step 4 Find b. Step 5 Find y = sina cose + tand sine Step 6 Find x = cosa Step 7 Find l. y l' tan x 1 More Examples On what day does Vega cross the meridian at 8:00 PM? What is the maximum altitude of the Sun for today in Nacogdoches? At approximately what time does the Sun cross the meridian today? What is the maximum altitude of the Sun over one year?
