Coordinate Systems

Purpose To locate stars/galaxies/other objects To locate an object in the space, how many quantities do we need? x, y, z Direction (2 quantities), distance

How do we locate a spot on the earth? Maps, mapquest, Google Map, GPS If we ignore how high it is above the sea To describe a spot on the surface of the earth, we use a set of numbers (degrees), called Coordinates Longitude Latitude 0º

Position in Degrees 0º 90º N Amherst 42°22′49″N, 72°31′25″W 0º 90º S Longitude – connecting the poles, 360 degree, or 180 degree east + 180 degree West Latitude – parallel to the equator, 0 – 90 N and 0 – 90 S A location is the intersect of a (virtue) longitude line and a latitude line 0º 0º 90º N 90º S Amherst 42°22′49″N, 72°31′25″W

Same idea when we describe the position of a celestial object Celestial Sphere An imaginary giant sphere, centered on the earth All objects seem to be on the surface of this imaginary sphere Earth’s poles extends and intersect with the celestial sphere as the North Celestial Pole and the South Celestial Pole Earth’s equator extends and intersects with the celestial sphere as Celestial Equator To locate an object, two numbers (in degrees) like the longitude and latitude are enough!

The horizon coordinate system Altitude Angle above the horizon 0° - 90° The altitude of the north celestial pole equals the observer’s latitude on the earth Azimuth Angle measured eastward along the horizon, starting from the north 0° - 360° Zenith The extended vertical line intersects with the celestial sphere Meridian The great circle passing through the celestial poles and the zenith Meridian Horizon The great circle whose pole is the zenith

Pros and Cons of the horizon system Easy to tell and understand Cons At different position on the earth, the same object has different coordinates At different time, the same object has different coordinates The Coordinates of an object Change in the horizon system!

Equatorial Coordinate System A system in which the coordinates of an object does not change Like the longitude and latitude on the earth, we have Right Ascension and Declination in the Equatorial system The equatorial coordinate system rotates with stars and galaxies

Equatorial Coordinate System Declination (DEC) A set of imaginary lines parallel to the Celestial Equator 0 ° at the celestial equator, increases from south to north negative in the southern hemisphere Dec of the north celestial pole is 90 ° Dec of the south celestial pole is -90 ° 0 ° 90 ° -90 °

Equatorial Coordinate System 0 ° 90 ° -90 ° Right Ascension (RA) imaginary lines that connect the celestial poles The origin of the longitude of the earth is the Greenwich Observatory The origin of the RA is Vernal Equinox What is Vernal Equinox?

The equatorial system Ecliptic The earth revolves annually around the Sun The Sun appears to moves from west to east on the celestial sphere The path of the sun is called ecliptic

The equatorial system The earth’s axis is titled – line through the celestial poles is NOT perpendicular to the plane of ecliptic 23.5 degree angle between the celestial equator and the ecliptic The ecliptic and the celestial equator intersect at vernal equinox and autumnal equinox

The equatorial system RA 360 degrees Historically, use HOURS:MINS:SECS as unit – 24 hours Starts from Vernal equinox (0 h) increases from west to east Stars w/ larger RA rise later 0 h 6 h Andromeda: RA: 00h 42m 44.3s DEC: +41° 16′ 9″

Vernal Equinox: RA: 0h DEC: 0º Summer Solstice: RA: 6h DEC: 23.5º Autumnal Equinox: RA: 12h DEC: 0º Winter Solstice: RA: 18h DEC: -23.5º Vernal Equinox: RA DEC Summer Solstice: RA DEC Autumnal Equinox: RA DEC Winter Solstice: RA DEC

Seasons

Why do we have seasons? The path of the earth moves around the sun is not a circle, but an eclipse The distance of the earth to the sun is not fixed Summer is hot, winter is cold, is it because we are closer to the sun in the summer time, and more distant from the sun in the winter time?

The axis of the earth is tilted! 23.5 degree angle between the earth’s axis and line that perpendicular to the earth’s orbit plane

Seasons More hours of daylight in the summer than in the winter Angle of sunlight: Earth’s tilt constant at 23.5 degrees, in the summer time of the Northern Hemisphere, the sun light falls more directly on the Northern Hemisphere

Seasons Vernal Equinox, around March 21, day hour = night hour at any place on the earth Summer Solstice, around June 22, for the northern hemisphere, day hour > night hour; longest day; opposite in the southern hemisphere Winter Equinox, around Sept. 23, day hour = night hour at any place on the earth Winter Solstice, around Dec 22, for the northern hemisphere, day hour < night hour; longest night; opposite in the southern hemisphere

Vernal Equinox: RA: 0h DEC: 0º Summer Solstice: RA DEC: 23.5º Autumnal Equinox: RA DEC: 0º Winter Solstice: RA DEC: -23.5º