Latitude Longitude North Pole
South Pole PrimeMeridian
The equatorial diameter of the Earth is only about one quarter of a percent longer than the
1
polar diameter, which means that the Earth if very nearly spherical. Also, the top of Mt. Everest is only about one tenth of a percent further from the center of the Earth than is a point at sea level, and the Earth is very nearly smooth.
Definition of Latitude and Longitude for a point on the
Earth’s surface
Coordinates
Definition of terms C Local coordinates
C Geographical
C Latitude - angular measurement of a location on Earth from the equator
C Longitude - angular measurement of a location on Earth from the Prime Meridian C Sky
C Altitude - angle of a celestial point above the horizon C Azimuth - angle of a celestial point from true north
C Zenith - point on the celestial sphere which is directly above your head C Nadir - point on the celestial sphere which is directly below your feet C Celestial coordinates
C Declination - angular measurement of a celestial location from the celestial equator C http://scienceworld.wolfram.com/astronomy/Declination.html
C Right Ascension - angular measurement of a celestial location from the first point in Aries (celestial prime meridian)
C http://condor.stcloudstate.edu/~physcrse/astr106/ra.html
C http://scienceworld.wolfram.com/astronomy/RightAscension.html
Terrestrial Coordinates
To a very good approximation the Earth is a smooth sphere . Any1 point on the surface can then be described in terms of two angles, named the latitude and the longitude.
Latitude
Latitude of a point on the Earth’s surface measures how far that point lies north or south of the equator. It is defined as the angle between two imaginary lines, one connecting the point to the center of the Earth, and the other connecting the nearest point on equator to the center of the Earth. Designations are made to define whether the point is north of the equator or south of it. There are some general statements that can be made.
C Any point on the equator has a latitude of 0 .o
C The North Pole has a latitude of 90 N.o
C Any point in the northern hemisphere has a latitude which lies between 0 and 90 N. For exampleo o
the latitude of London, England is about 51 N.o
C The South Pole has a latitude of 90 S.o
C Any point in the southern hemisphere has a latitude which lies between 0 and 90 S. For exampleo o
the latitude of Cape Town, South Africa is about 33 S.o Longitude
Longitude of a point on the Earth’s surface measures how far that point lies east or west of the Prime Meridian. The Prime Meridian is an imaginary line running along the Earth’s surface from the North Pole to the South Pole, passing through Greenwich, England. (Greenwich is just east of London.) Designations are made to define whether the point is east of the Prime Meridian or west of it. There are some general statements that can be made.
C Any point on the Prime Meridian has a longitude of 0 . Since the Prime Meridian runs througho
Greenwich, it (and London itself) has a longitude of 0 . Other cities with a longitude of 0 includeo o
Accra, Ghana and Bordeaux, France.
C Any point on the Earth’s surface directly opposite the Prime Meridian has a longitude of either 180o
E or 180 Wo
C Since you have to fly west from London to reach any city in the Americas, all locations in the United States have a west longitude. Examples include New York (73 W), Chicago (87 W), and Sano o
Francisco (122 W).o
Sky Coordinates
There are two schemes for defining the location of a point in the sky, one based local on local coordinates, and the other on a universal set of local coordinates.
Local Coordinates
At any one time any observer can see half of the sky, the portion which lies above the horizon. The other half is hidden from view since it lies below the horizon. Note though, that observers at different places on the Earth have different horizons, and therefore see different portions of the sky (although both still see half.) This is not a significant difference for two people standing a few feet from each other, but is a large difference for observers in different cities, sat New York and Chicago. Also, because the Earth rotates on its axis even a fixed observer will see different portions of the sky (although again always half) at different times. This is why some stars appear to rise above the horizon and others to set below it. It is not that the stars that have moved, it is the horizon which has moved as the Earth rotates.
Horizon N E S W 0 90o 180o 270o Azimuth Altitude and Azimuth
Definition of Azimuth, looking down from zenith The altitude measures the position of a point in the sky
above the horizon. It is defined as the angle between two imaginary lines, one from the observer to the point and the other from the observer to the horizon directly below the point. Points below the horizon are sometimes given a negative altitude. There are some general statements that can be made.
C Any point directly on the horizon has an altitude of 0 . That means that the altitude of any objecto
(such as a star) as it rise, or as it sets, is also 0 .o
C The maximum possible altitude is 90 . This corresponds to the point in the sky which is directly aboveo
the observers head, referred to as the zenith. Different observers in different locations have different zeniths, although each one will describe it as the point directly overhead, and each one will give it an altitude of 90 .o
C All other points in the sky which are visible have an altitude between 0 and 90 .o
C Since the Earth rotates on its axis, the altitude of any object in the sky (such as a star) will continuously change. The exception to this is the star Polaris, since it is located at the position of the North Celestial Pole (see below).
Azimuth
The azimuth measures the position of a point in the sky relative to the north. It is defined as the angle between to two imaginary lines, one from the observer to the horizon directly north of the observer, and the other one from the observer to the horizon directly below the point. It is always measured from the north towards the east, from 0 to 360 .o
There are some general statements that can be made.
C Any point due north of the observer has an azimuth of 0 .o
C Any point due east of the observer has an azimuth of 90 .o
C Any point due south of the observer has an azimuth of 180 .o
C Any point due west of the observer has an azimuth of 270 .o
C Since the Earth rotates on its axis, the azimuth of any object in the sky (such as a star) will continuously change. The exception to this is the star Polaris, since it is located at the position of the North Celestial Pole (see below) it always has an azimuth of 0 .o
Celestial Coordinates
As we saw above, the local coordinates are specific to a particular observer, at a particular time. Whereas they are easy to use, communicating information about a particular location to a different observer, or one which is looking at the sky at some other time, is fraught with difficulties. The different observers have
Right Ascension Declination
Celestial Equator First point in Aries
North Celestial Pole
South Celestial Pole
Right Ascension and Declination different local coordinates. To overcome this difficulty astronomers have developed a set of celestial coordinates which everyone can agree on, regardless of their individual locations on the Earth’s surface, or on when they are looking at the sky. The disadvantage is that celestial coordinates are relatively difficult to use, unless your telescope has previously been aligned with stars whose celestial coordinates are known. The starting point of the Celestial Coordinates is to imagine that all of the stars in the sky (including those which are below the horizon) are the same very large distance from us. In this model all of the stars are positioned on the Celestial Sphere, with the Earth at the center of the sphere.
If we take the axis of rotation of the Earth, which runs through its north and south poles, and extend this line outwards until it reaches the Celestial Sphere, then the points where it reaches the Celestial Sphere are known as the Celestial Poles. The North Celestial Pole lies directly above the Earth’s north pole. It is the zenith for an observer standing at the Earth’s north pole. Similarly, the South Celestial Pole is the zenith for an observer standing at the Earth’s south pole.
Just as the Earth is divided into two hemispheres by the equator, the Celestial Sphere is also divided into two by the Celestial Equator. It is an imaginary line which runs around the Celestial Sphere directly above the Earth’s equator. For an observer standing on the Earth’s equator the zenith would be a point on the Celestial Equator.
Declination
The declination plays the same role on the Celestial Sphere as latitude does on the Earth’s surface. It is a measurement of how far, north or south, a point is from the Celestial Equator. It is defined as the angle between two imaginary lines, one connecting the point to the Earth, and the other
connecting the nearest point on equator to the center of the Earth. Designations are made to define whether the point is north of the equator or south of it. On the Celestial Sphere points which are north of the Celestial Equator has a positive declination. Those which are south of the Celestial Equator have a negative declination. There are some general statements that can be made.
C Any point on the Celestial Equator has a declination of 0 .o
C The North Celestial Pole has a declination of 90 .o
C Any point in the northern half of the Celestial Sphere has a declination which lies between 0 and 90 .o o
C The South Celestial Pole has a declination of -90 .o
C Any point in the southern half of the Celestial Sphere has a declination which lies between 0 and -o
90 .o Right Ascension
Just as the declination is the equivalent of latitude, on the Celestial Sphere the right ascension is the equivalent of longitude. It measures how far that point lies east of a reference point known as the first point in Aries. The first point in Aries is an imaginary point in the sky corresponding to the position of the Sun at the time of the Vernal equinox. All measurements are made in a direction east of this point. For a point which is just to the west of the first point in Aries the right ascension is measured almost around the Celestial Sphere.
Although the Right Ascension can be defined as an angle equivalent to that for longitude, it is normally expressed not as an angle but as a time. Remember that the stars (and other objects) appear to move across our sky because the Earth rotates on its axis through 360 once every 24 hours, that is 15 per hour.o o
C What is a declination of 3 h expressed in degrees? C 3 h * 15 per h = 45o o
C What is a declination of 120 expressed in hours?o
C 120 / 15 per h = 8 ho o
C What is a declination of 4 h 24 m expressed in degrees? C 4 h 24 m = 4 h + 24/60 h = 4.4 h
C 4.4 h * 15 per h = 66o o
C What is a declination of 275 expressed in hours?o
C 275 / 15 per h = 18.33 ho o
