Angle d = Latitude. Angle c = Altitude Polaris. Angle c = Angle d ~ 45 deg here

Transcription

1 North Celestial Pole Altitude of Polaris is equal to our Latitude on Earth Proof: Angle Pole Star with the horizon = observer's latitude. Prove: Angle c = Angle d Altitude of Polaris = our latitude on earth Given: The pole and the equator are at right angles, d + a = 90 therefore a = 90 d c = b (AIT Alternate Interior Angles because c b) a + b + 90 = 180 (sum angles of triangle) Therefore: a + b = 90 Substitute for a: (90 d) + b = 90 Angle b = Angle d and angle c = b Therefore Angle c = Angle d Angle d = Latitude We find Polaris at our latitude Roughly 45 degrees north Angle c = Angle d ~ 45 deg here Angle c = Altitude Polaris

2 Star Location: Altitude above Horizon Star altitude depends on the Declination of the Star. The altitude of any star transiting due South on the MERIDIAN Altitude of Star above Horizon = Co-latitude on Earth + Declination of Star Celestial Equator co-latitude Declination ALWAYS measured from celestial equator to star. Due South Local Horizon View: Altitude of Regulus above our horizon = 45(Colatitude) + 11(Declination) = 56 deg

3 Objects on your Meridian North South Line Horizon to Horizon OBJECTS (stars, clusters, galaxies) in the sky - Left(east) of your Meridian RISING - Right(west) of Meridian SETTING, just like the Sun does. Objects ON your Meridian have reached their HIGHEST point in the sky tonight, Best for Viewing = CULMINATION For Northern Hemisphere observers Objects CULMINATE on the Meridian Facing SOUTH. Observers in the Northern Hemisphere orient their observatories Facing 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. Diagram shows more sky looking south for northern observer. Star on Meridian

4 Position of a Celestial Object on our Meridian Range of Celestial Declination of object visible on our meridian Given Altitude of the Pole = Latitude Altitude of Celestial Equator = Colatitude Diagram shows Latitude Northern Horizon Declination = lat = Colat = +50 Zenith: Declination = 90 Colat = Lat = 40 Southern Horizon: Declination = 180 (Lat + 90) = 90 Lat = - 50 Angle is negative because it is measured down from 0 declination in the sky. For 45 degrees, latitude = Colatitiude We see +45 to -45 declination.

5 Example: How high does LMC rise above the horizon of Point Pelee National Park (if at all)? Latitude: Point Pelee N Southernmost point in Canada Large Magellenic Cloud Declination: Visible as a faint "cloud" in the night sky of the southern hemisphere straddling the border between the constellations of Dorado and Mensa. 1. We know altitude of Pole Star = your Latitude. 2. Celestial Equator is thus 90 Latitude = 50. Therefore Maximum Southern declination visible is -50 degrees. No, LMC will never rise above Point Pelee. (and no, we don't see constellations Dorado and Mensa)

6 North Celestial Pole Altitude of Polaris is equal to our Latitude on Earth Proof: Angle Pole Star with the horizon = observer's latitude. Prove: Angle c = Angle d Altitude of Polaris = our latitude on earth Given: The pole and the equator are at right angles, d + a = 90 therefore a = 90 d c = b (AIT Alternate Interior Angles because c b) a + b + 90 = 180 (sum angles of triangle) Therefore: a + b = 90 Substitute for a: (90 d) + b = 90 Angle b = Angle d and angle c = b Therefore Angle c = Angle d Angle d = Latitude We find Polaris at our latitude Roughly 45 degrees north Angle c = Angle d ~ 45 deg here Angle c = Altitude Polaris

7 Star Location: Altitude above Horizon Star altitude depends on the Declination of the Star. The altitude of any star transiting due South on the MERIDIAN Altitude of Star above Horizon = Co-latitude on Earth + Declination of Star Celestial Equator co-latitude Due South Declination ALWAYS measured from celestial equator to star. Local Horizon View: Altitude of Regulus above our horizon = 45(Colatitude) + 11(Declination) = 56 deg 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

8 Objects on your Meridian North South Line Horizon to Horizon OBJECTS (stars, clusters, galaxies) in the sky - Left(east) of your Meridian RISING - Right(west) of Meridian SETTING, just like the Sun does. Objects ON your Meridian have reached their HIGHEST point in the sky tonight, Best for Viewing = CULMINATION For Northern Hemisphere observers Objects CULMINATE on the Meridian Facing SOUTH. Observers in the Northern Hemisphere orient their observatories Facing 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. Diagram shows more sky looking south for northern observer. Star on Meridian

9 Position of a Celestial Object on our Meridian Range of Celestial Declination of object visible on our meridian Given Altitude of the Pole = Latitude Altitude of Celestial Equator = Colatitude Diagram shows Latitude Northern Horizon Declination = lat = Colat = +50 Zenith: Declination = 90 Colat = Lat = 40 Southern Horizon: Declination = 180 (Lat + 90) = 90 Lat = - 50 Angle is negative because it is measured down from 0 declination in the sky. For 45 degrees, latitude = Colatitiude We see +45 to -45 declination.

10 Example: How high does LMC rise above the horizon of Point Pelee National Park (if at all)? Latitude: Point Pelee N Southernmost point in Canada Large Magellenic Cloud Declination: Visible as a faint "cloud" in the night sky of the southern hemisphere straddling the border between the constellations of Dorado and Mensa. 1. We know altitude of Pole Star = your Latitude. 2. Celestial Equator is thus 90 Latitude = 50. Therefore Maximum Southern declination visible is -50 degrees. No, LMC will never rise above Point Pelee. (and no, we don't see constellations Dorado and Mensa)