## Tuesday, June 3, 2008

### Latitude & Longitude

Any location on Earth is described by two numbers--its latitude and its longitude.

If a pilot or a ship's captain wants to specify position on a map, these are the "coordinates" they would use. Actually, these are two angles, measured in degrees with minutes of arc and seconds of arc. These are denoted by the symbols ( °, ', " ) e.g. 35° 43' 9" means an angle of 35 degrees, 43 minutes and 9 seconds (do not confuse this with the notation (', ") for feet and inches!). A degree contains 60 minutes of arc and a minute contains 60 seconds of arc--and you may omit the words "of arc" where the context makes it absolutely clear that these are not units of time. Calculations often represent angles by small letters of the Greek alphabet, and that way latitude will be represented by λ (lambda, Greek L), and longitude by φ (phi, Greek F).

Imagine the Earth was a transparent sphere (actually the shape is slightly oval; because of the Earth's rotation, its equator bulges out a little). Through the transparent Earth (drawing) we can see its equatorial plane, and its middle the point is O, the center of the Earth. To specify the latitude of some point P on the surface, draw the radius OP to that point. Then the elevation angle of that point above the equator is its latitude λ--northern latitude if north of the equator, southern (or negative) latitude if south of it. [How can one define the angle between a line and a plane, you may well ask? Good question. We must use the angle which completes it to 90 degrees, the one between the given line and one perpendicular to the plane. Here that would be the angle (90°-λ) between OP and the Earth's axis, known as the co-latitude of P.]

On a globe of the Earth, lines of latitude are circles of different size. The longest is the equator, whose latitude is zero, while at the poles--at latitudes 90° north and 90° south (or -90°) the circles shrink to a point. Lines of constant longitude ("meridians") extend from pole to pole, like the segment boundaries on a peeled orange.

Every meridian must cross the equator. Since the equator is a circle, we can divide it--like any circle--into 360 degrees, and the longitude φ of a point is then the marked value of that division where its meridian meets the equator. What that value is depends of course on where we begin to count--on where zero longitude is located. For historical reasons, the meridian passing the old Royal Astronomical Observatory in Greenwich England, is the one chosen as zero longitude. Located at the eastern edge of London, the British capital, the observatory is now a public museum and a brass band stretching across its yard marks the "prime meridian." Tourists often get photographed as they straddle it--one foot in the eastern hemisphere of the Earth, the other in the western hemisphere.

A line of longitude is also called a meridian, derived from the Latin, from meri, a variation of "medius" which denotes "middle", and diem, meaning "day." The word once meant "noon", and times of the day before noon were known as "ante meridian", while times after it were "post meridian." Today's abbreviations a.m.and p.m.come from these terms, and the Sun at noon was said to be "passing meridian". All points on the same line of longitude experienced noon (and any other hour) at the same time and were therefore said to be on the same "meridian line", which became "meridian" for short.

Two important concepts, related to latitude and (especially) longitude are Local time (LT) and Universal time (UT).

Local time is actually a measure of the position of the Sun relative to a locality. At 12 noon local time the Sun passes to the south and is furthest from the horizon (northern hemisphere). Somewhere around 6 am it rises, and around 6 pm it sets. Local time is what you and I use to regulate our lives locally, our work times, meals and sleep-times. But suppose we wanted to time an astronomical event--e.g. the time when the 1987 supernova was first detected. For that we need a single agreed-on clock, marking time world-wide, not tied to our locality. That is universal time (UT), which can be defined (with some slight imprecision, no concern here) as the local time in Greenwich, England, at the zero meridian.

Longitudes are measured from zero to 180° east and 180° west (or -180°), and both 180-degree longitudes share the same line, in the middle of the Pacific Ocean. As the Earth rotates around its axis, at any moment one line of longitude--the noon meridian--faces the Sun, and at that moment, it will be noon everywhere on it. After 24 hours the Earth has undergone a full rotation with respect to the Sun, and the same meridian again faces noon. Thus each hour the Earth rotates by 360/24 = 15 degrees. When at your location the time is 12 noon, 15° to the east the time is 1 p.m., for that is the meridian which faced the Sun an hour ago. On the other hand, 15° to the west the time is 11 a.m., for in an hour's time, that meridian will face the Sun and experience noon.

The Date Line and Universal Time (UT)
Suppose it is noon where you are and you proceed west--and suppose you could travel instantly to wherever you wanted. Fifteen degrees to the west the time is 11 a.m., 30 degrees to the west, 10 a.m., 45 degrees--9 a.m. and so on. Keeping this up, 180 degrees away one should reach midnight, and still further west, it is the previous day. This way, by the time we have covered 360 degrees and have come back to where we are, the time should be noon again--yesterday noon.

Hey--wait a minute! You cannot travel from today to the same time yesterday! We got into trouble because longitude determines only the hour of the day--not the date, which is determined separately. To avoid the sort of problem encountered above, the international date line has been established--most of it following the 180th meridian--where by common agreement, whenever we cross it the date advances one day (going west) or goes back one day (going east). That line passes the Bering Strait between Alaska and Siberia, which thus have different dates, but for most of its course it runs in mid-ocean and does not inconvenience any local time keeping.

Astronomers, astronauts and people dealing with satellite data may need a time schedule which is the same everywhere, not tied to a locality or time zone. The Greenwich mean time, the astronomical time at Greenwich (averaged over the year) is generally used here. It is sometimes called Universal Time (UT).

Right Ascension and Declination
The globe of the heavens resembles the globe of the Earth, and positions on it are marked in a similar way, by a network of meridians stretching from pole to pole and of lines of latitude perpendicular to them, circling the sky. To study some particular galaxy, an astronomer directs the telescope to its coordinates. On Earth, the equator is divided into 360 degrees, with the zero meridian passing Greenwich and with the longitude angle φ measured east or west of Greenwich, depending on where the corresponding meridian meets the equator.

In the sky, the equator is also divided into 360 degrees, but the count begins at one of the two points where the equator cuts the ecliptic--the one which the Sun reaches around March 21. It is called the vernal equinox ("vernal" means related to spring) or sometimes the first point in Aries, because in ancient times, when first observed by the Greeks, it was in the zodiac constellation of Aries, the ram. It has since then moved.

The celestial globe, however, uses terms and notations which differ somewhat from those of the globe of the Earth. Meridians are marked by the angle α (alpha, Greek A), called right ascension, not longitude. It is measured from the vernal equinox, but only eastward, and instead of going from 0 to 360 degrees, it is specified in hours and other divisions of time, each hour equal to 15 degrees. Similarly, where on Earth latitude goes from 90° north to 90° south (or -90°), astronomers prefer the co-latitude, the angle from the polar axis, equal to 0° at the north pole, 90° on the equator, and 180° at the south pole. It is called declination and is denoted by the letter δ (delta, Greek small D). The two angles (α, δ), used in specifying (for instance) the position of a star are jointly called its celestial coordinates.