Latitude and longitude

1
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)

2
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
• The angle between two great circles is equal to
  the maximal distance between them

3
Different parts of the Earth

• North Pole, lat 90N
• Arctic region lat gt 66.5N, midnight sun
• Arctic circle, lat 66.5N
• North temperate zone, 23.5N lt lat lt 66.5N
• Tropic of Cancer, lat 23.5N
• Northern part of the tropics, 0Nlt lat lt 23.5N,
  Sun can be in zenith (directly overhead)
• Equator, lat 0

4
Different parts of the Earth 2

• Southern part of the tropics, 0Slt lat lt 23.5S,
  Sun can be in zenith (directly overhead)
• Tropic of Capricorn, lat 23.5S
• South temperate zone, 23.5S lt lat lt 66.5S
• Antarctic circle, lat 66.5S
• Antarctic region lat gt 66.5S, midnight sun
• South Pole, lat 90S
• The tropics is the region between the Tropics

5
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

6
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)

7
Celestial Sphere 3

• Celestial equator great circle above the earths
  equator (global)
• (Celestial) meridian great circle through the
  north point, zenith and the south point (local)

8
Celestial Sphere 4
9
Celestial Sphere 5

• Infinitely many meridians on the Earth only one
  in the Sky
• a.m. ante meridiem, p.m. post meridiem

10
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

11
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

12
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

13
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

14
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

15
Circumpolar Stars 2

• For an observer on the northern hemisphere, stars
  inside a disc around the NCP with radius equal to
  the observers latitude will never set
• Stars inside a disc around the SCP with radius
  equal to the observers 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