Latitude and longitude You get a great circle when you cut through the centre The equator is defined in terms of the poles, which is defined in terms of the rotation of the Earth Same latitude: circles of latitude (or parallels of latitude) – small circles Same longitude: meridians – great semi-circles Prime meridian: meridian through Greenwich Latitude defined by nature, longitude by politics (in 1884)

Angles Distances on a sphere are measured in degrees and minutes and seconds of arc 1 degree = 60 min. of arc, 1° = 60’ 1 min. of arc = 60 sec. of arc, 1’ = 60’’ 1° 30’ = 1.5 ° Two great circles intersect at two antipodal points, and halfway between those two points the circles are maximally apart with distance equal to the angle between them

Different parts of the Earth North Pole, lat = 90°N Arctic region lat > 66.5°N, midnight sun Arctic circle, lat = 66.5°N North temperate zone, 23.5°N < lat < 66.5°N Tropic of Cancer, lat = 23.5°N Northern part of the tropics, 0°N< lat < 23.5°N, Sun can be in zenith (directly overhead) Equator, lat = 0

Different parts of the Earth 2 Southern part of the tropics, 0°S< lat < 23.5°S, Sun can be in zenith (directly overhead) Tropic of Capricorn, lat = 23.5°S South temperate zone, 23.5°S < lat < 66.5°S Antarctic circle, lat = 66.5°S Antarctic region lat > 66.5°S, midnight sun South Pole, lat = 90°S The tropics is the region between the Tropics

The Celestial Sphere Horizon: great circle that separates the visible part of the celestial sphere from the invisible (local) Can also think of it as the tangent plane of the observer The horizon circle is the intersection of the horizon plane with the celestial sphere

Celestial Sphere 2 North celestial pole (NCP): point directly above the north pole (global) North point: point on the horizon straight north (local) Zenith: point directly above (local) Nadir: point directly below; invisible (local)

Celestial Sphere 3 Celestial equator: great circle above the earth’s equator (global) Declination: distance from the celestial equator (Celestial) meridian: great circle through the north point, zenith and the south point (local)

Celestial Sphere 4

Celestial Sphere 5 Infinitely many meridians on the Earth – only one in the Sky a.m. = ante meridiem, p.m. = post meridiem

Celestial Sphere 6 Vertical circle: great circle perpendicular to the horizon Prime vertical: vertical circle through the west point, zenith and the east point Notice that the prime vertical and the meridian intersect perpendicularly at the zenith

The Celestial Sphere 7 The altitude (distance from the horizon) of the NCP = the latitude of the observer If we use negative latitude for the southern hemisphere, this formula holds there, too

The Celestial Sphere 8 The angle between the celestial equator and the southern part of the horizon = 90 - the latitude of the observer, which is called the colatitude This also holds for the southern hemisphere, where the colatitude is larger than 90

The Celestial Sphere 9 The altitude of the intersection between the celestial equator and the meridian = colatitude If we measure the altitude from the south point and interpret an altitude of x > 90 as an altitude of 180 – x from the north, this will also holds for the southern hemisphere

Motion of the Stars Stars move westward (across the visible part of the celestial sphere) The daily (diurnal) path of the stars are parallel to the celestial equator The stars cross the horizon at an angle equal to the colatitude of the observer

Circumpolar Stars Circumpolar stars are stars that are so close to the pole that they never set In Singapore there are no circumpolar stars On the north pole, all stars are circumpolar A star is circumpolar if the distance from the pole is less than the latitude

Circumpolar Stars 2 For an observer on the northern hemisphere, stars inside a disc around the NCP with radius equal to the observer’s latitude will never set Stars inside a disc around the SCP with radius equal to the observer’s latitude will never rise Stars in the middle will rise and set Circumpolar does not mean visible all the time; a star is only visible if the Sky is dark and it is above the horizon