Chapter 4: Rising & Setting Stars © BRIEF 20141

2 Rising & Setting Stars Overview: Coordinate Systems Celestial Sphere Local Sky Ecliptic Equatorial Coordinate System 3 Classes of Stars Local Sky Examples Measuring Angles

© BRIEF Rising & Setting Stars Rising & Stetting Stars: Coordinate systems Observer based – azimuth and altitude Earth based – latitude and longitude Celestial – declination and right ascension (or sidereal hour angle) All three are basically ways of describing locations on a sphere – inherently two dimensional Requires two parameters (e.g. latitude and longitude) What you see in the sky depends on Date of year Time Latitude Longitude Which is how we can use the stars to navigate!!

© BRIEF Rising & Setting Stars Celestial Sphere: Points on the Sphere North and south celestial poles Celestial equator REMEMBER: These are points /lines on the celestial sphere and NOT on the Earth

© BRIEF Rising & Setting Stars Your Local Sky: Zenith: Imaginary point directly above your head on the celestial sphere Nadir: Imaginary point directly below your feet Horizon: The apparent line that separates the earth from the sky Meridian: Imaginary great circle passing through the celestial north and south pole and the zenith Transit: When a celestial body crosses the meridian due to the Earth’s rotation

© BRIEF Rising & Setting Stars Your Local Sky: Horizontal Coordinate System Coordinates are measured with respect to horizon Change with time and depend on observer Azimuth: 0 to 360 degrees around horizon from north towards east 0° = North, 90 ° = East, 180 ° = South, 270 °= West Altitude: 0 to 90 degrees up from horizon 0 ° = Horizon, 90 ° = Zenith DEMO:

© BRIEF Rising & Setting Stars Ecliptic: Ecliptic: The Sun's apparent annual path among the constellations Plane containing the Sun and planets Ecliptic is tilted 23.5° with respect to the Equator

© BRIEF Rising & Setting Stars Ecliptic:

© BRIEF Rising & Setting Stars Ecliptic: Cardinal Points Vernal Equinox Sun rises due East and sets due West Length of day = length of night = 12 hours Summer Solstice Sun is highest in the sky Autumnal Equinox Sun rises due East and sets due West Length of day = night = 12 hours Winter Solstice Sun is lowest in the sky This is REVERSED for the Southern Hemisphere

© BRIEF Rising & Setting Stars Celestial Sphere: Tilted 23 ½ degrees We live on the side of the Earth. Sky appears tilted at an angle equal to our latitude. Stars appear to move in arcs across the sky that are not perpendicular to horizon.

© BRIEF Rising & Setting Stars Basic Motion of the Celestial Sphere (Demo with TheSky) The sky appears to rotate around NCP. Altitude of NCP from the horizon is always equal to your latitude on Earth's surface Stars move in arcs that parallel the celestial equator Star move across the sky at 15 o per hour (4 minutes per degree) Each day star positions move 1 o west (difference between Sidereal vs. Solar Time) Some stars are “circumpolar” – never set Practical Application with TheSky X

© BRIEF Rising & Setting Stars Equatorial Coordinate System: Coordinates fixed on the celestial sphere Time and observer independent (unlike Alt/Az) Declination (dec)‏: Analogous to latitude, but on the celestial sphere North-south distance between celestial equator and a location on the celestial sphere. Measured in degrees: +90 ° to 0 ° – north from celestial equator 0 ° to -90 ° – south from celestial equator Right Ascension (RA)‏: Analogous to longitude, but on the celestial sphere Measured in units of time: hours, minutes, seconds (See next slide) 0 h – 24 h from Vernal Equinox towards east Ex. Sirius has RA = 6 h 45 m OR 6:45 Don’t confuse RA with time on your watch! DEMO: decdemo.html decdemo.html

© BRIEF

© BRIEF Rising & Setting Stars Equatorial Coordinate System: Latitude and longitude vs. Declination and Right Ascension DEMO:

© BRIEF Rising & Setting Stars RA and Dec of the Cardinal Points on the Ecliptic: Vernal Equinox Sun appears on March 21 RA = 0h Dec = 0˚ Summer Solstice Sun appears on June 21 RA = 6h Dec = 23.5˚ Autumnal Equinox Sun appears on Sept. 21 RA = 12h Dec = 0˚ Winter Solstice Sun appears on Dec. 21 RA = 18h Dec = -23.5˚

© BRIEF Rising & Setting Stars RA and Dec of the Cardinal Points on the Ecliptic: Vernal Equinox – Sun appears on March 21 – RA = 0h Dec = 0˚ Summer Solstice – Sun appears on June 21 – RA = 6h Dec = 23.5˚ Autumnal Equinox – Sun appears on Sept. 21 – RA = 12h Dec = 0˚ Winter Solstice – Sun appears on Dec. 21 – RA = 18h Dec = -23.5˚ Declination 0 h Ecliptic Equator 6 h12 h18 h24 h 23.5° -23.5°

© BRIEF Rising & Setting Stars Equatorial Coordinate System: Practical Example - Vega Declination tells us that it is 38°44′ north of the celestial equator. We can interpret its right ascension in two ways: As an angle, it means Vega is about 279° east of the vernal equinox As a time, it means Vega crosses the meridian about 18 hours 35 minutes after the spring equinox.

© BRIEF Rising & Setting Stars Constellations of the Zodiac: The constellations on the celestial sphere through which the ecliptic passes Origin of Astrology (Zodiac Sign)

© BRIEF Rising & Setting Stars Local Skies: 3 Classes of Stars Circumpolar North Always visible Never Set Rotate Around the NCP Circumpolar South Never visible for northern observers Rising and setting Stars Lie between Circumpolar North & South DEMO:

© BRIEF Rising & Setting Stars Local Skies: How to determine your Latitude The altitude of the celestial pole in your sky is equal to your latitude.

© BRIEF Rising & Setting Stars Local Skies: Equator

© BRIEF Rising & Setting Stars Local Skies: 30 degrees South Latitude

© BRIEF Rising & Setting Stars Local Skies: 40 degrees North Latitude

© BRIEF Rising & Setting Stars Local Skies: North Pole

© BRIEF Rising & Setting Stars Measuring Angles on the Sky: Full circle = 360º 1º = 60 (arcminutes) 1 = 60  (arcseconds)

© BRIEF Rising & Setting Stars Measuring Angles on the Sky:

© BRIEF Rising & Setting Stars Declination Angles: Seasons Simulator: Alt/Az Simulator: Lat/Long Demonstrator: RA/Dec Demonstrator: Sun Motions Simulator: Motions of Sun Simulator: Sun Rays Simulator: Sun’s Position on Horizon: Season’s Simulator: Rotating Sky Coordinate Systems Comparer:

© BRIEF Rising & Setting Stars Sidereal Time and Hour Angle Demonstrator: html html Celestial and Horizon Systems Comparison: Sidereal and Solar Time Simulator:

© BRIEF Rising & Setting Stars Questions?

© BRIEF Rising & Setting Stars Celestial Sphere: Our lack of depth perception when we look into space creates the illusion that Earth is surrounded by a celestial sphere In reality, stars that appear very close together in our sky may actually lie at very different distances from Earth.

© BRIEF Rising & Setting Stars Celestial Sphere: Our lack of depth perception when we look into space creates the illusion that Earth is surrounded by a celestial sphere In reality, stars that appear very close together in our sky may actually lie at very different distances from Earth.

© BRIEF Rising & Setting Stars The Celestial Sphere: Pasachoff_Fig © Cambridge University Press 2013

© BRIEF Rising & Setting Stars Precession: Precession: rotation of Earth’s axis itself; makes one complete circle in about 26,000 years This is due to the gravitational tug of BOTH the Sun and Moon. Earth’s axis currently points nearly toward the star Polaris. About 12,000 years from now—almost halfway through one cycle of precession—Earth’s axis will point toward a star called Vega, which will then be the “North Star.” Five thousand years ago, the North Star was a star named Thuban in the constellation Draco.