On the left, the many GPS satellites in geosynchronous orbit above the planet. At right, the North Star (Polaris) sits above the North Pole.
A sextant allows you to measure exact angles of celestial objects like the North Star. Two mirrors inside the telescope allow you to turn a calibrated knob that moves one of the mirrors until the star appears to touch the horizon. A gauge connected to the knob then gives you your latitude.
The Prime Meridian is the anchor point for determining longitude. Greenwich Mean Time (GMT) is the local time on the Prime Meridian. By calculating the difference in hours between your time and the GMT (or UTC), then multiplying that number by 15 degrees, you'll get an approximate longitude.
A chronometer is used on ships to exactly measure longitude based on Coordinated Universal Time, or UTC.
During the course of a year, Earth's slightly changing axis rotation across the seasons creates variations in the apparent length of a day. The UTC approximates the mean solar day, which averages out all those variations. So using the sun to establish local time can produce a gap with UTC time of up to 16.5 minutes, or 4 degrees of longitude. The graph above gives you the amount of adjustment needed for a more accurate measurement.
Time zones start at the Prime Meridian. The difference in hours increases the farther you are away from it.
Latitudes and longitudes of the continents and oceans. Before traveling across an ocean, you may want to memorize a few pairs of coordinates between where you start your journey, and where you hope it ends without incident.
A handmade sundial with the gnomon tipped North.To make reading it easier, create a gnomon in the shape of a right triangle, with the pointed end at the top.
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With the introduction of GPS technology for public use in the 1990s, navigators added a powerful tool to their arsenal. GPS stands for Global Positioning System, which takes advantage of more than two dozen satellites managed by the U.S. Department of Defense. GPS units on the ground pick up the satellite signals from space, then triangulate a location to within a few meters of accuracy. With the coordinates provided, you can look up your position on a map or simply use the onboard features of your GPS unit to take you to your destination.
In order to understand the numbers in GPS mapping, it helps to step back for a moment and appreciate the evolution of navigation systems. Latitude and longitude coordinates have been used by travelers for centuries to pinpoint where they stood on the planet. In fact, long before Columbus set off on his famous voyage, mariners from Polynesia sailing to Africa were already more or less able to deduce their horizontal position on Earth. They estimated the angle between the horizon (where the sun sets on the ocean), and either the North Star or Southern Cross, depending on which side of the Equator they were sailing.
Including their perspective from the boat, these three locations created a triangle. (See graphic in the right column.) And the angle they measured told them how far to the north or south of the Equator they were. Measured in degrees, this angle translates into a latitude between 0 (at the Equator) and 90 degrees (at either pole).
Even longitude can be figured out without a GPS unit. All you need is either radio that gets the BBC News, a telephone/internet connection which can give you the time in the U.K., (or an onboard chronometer). While latitude is gauged by measuring an angle, lines of longitude are a function of time, as you'll see in a minute (so to speak).
If you look up at the North Star (also known as Polaris), your viewing angle from the continental United States would be between 30 and 50 degrees. You can estimate your exact latitude by going outside on a clear night and pointing one arm at the horizon (or straight ahead if you're standing on level ground), the other at Polaris.
In 1731, the sextant was invented to allow mariners to measure latitudes more precisely than previous devices (or using their arms).. Like a compass, no batteries or electronics are required for this device to operate. As such, it's an important backup tool to bring along on an ocean voyage. Sextants traditionally measure an angle in degrees. (See photo on the right.) However, a common unit of measurement used by survey instruments and some sextants these days is the mil. A slope conversion chart allows you to translate mils into degrees, so you may need to bring that along on your trip as well.
Lines of latitude are also known as parallels. As already mentioned, the parallel at the Equator is 0 degrees. The latitude at both poles is 90 degrees. Above the Equator lies the northern hemisphere, so parallels here are identified with the designation "North". Below the Equator lies the southern hemisphere, so parallels there are designated "South".
Unlike latitudes, identifying your vertical position on Earth presents a greater challenge, since the planet is constantly turning. To calculate a longitude, mariners work with the 24-hour day and an agreed-upon starting point to count the hours, minutes and seconds of distance from that point. Lines of longitude are known as meridians. And the agreed-upon starting point is known as the Prime Meridian.
Like the Equator at the center of the earth, the Prime Meridian is an imaginary line that runs all the way around the planet, specifically down through the United Kingdom, the western coast of Europe and western Africa. It's designation is 0 degrees of longitude. The Prime Meridian is a purely arbitrary designation, established by Great Britain at its planetary observatory in Greenwich in the late 19th century. The time along the Prime Meridian was traditionally known as Greenwich Mean Time, abbreviated GMT.
Turn a globe around eastward, toward Asia, and you'll see 12 eastern lines of longitude, each separated by one hour, or 15 degrees. Why 15 degrees, you ask? It takes one hour for the sun to move 15 degrees.
Now turn the globe towards the United States and you find 12 lines of western longitude. The two sets of 12 combine for 24 hours and converge half away around the world, at 180 degrees of longitude, along the International Date Line. The Date Line runs across the Pacific Ocean, close to New Zealand and the islands of Fiji, Somoa and Tonga. A longitude, therefore, must be number between 0 and 180 degrees.
Together, the Prime Meridian and International Date Line also separate the western hemisphere from the eastern hemisphere. As a result, longitude coordinates are designated as either "West" or "East".
Nowadays, Coordinated Universal Time, or UTC, has taken the place of GMT as the starting point for determining longitude. UTC is based on another standard known as International Atomic Time (TAI), which calibrates our 24-hour clock much more precisely than solar time. Since the Earth's angular rotation causes the Sun's path to vary somewhat, there's really no such thing as an exact 24-hour solar day.
To find out their longitude, ships began using a clock called a chronometer in 1761. The chronometer is a special kind of clock built with precision gears to keep accurate time at sea. Formally set to the GMT, chronometers nowadays follow the UTC (although GMT is only a fraction of one second off UTC). As mentioned before, to calculate your longitude anywhere on earth, you would need to know two things: the current time at the Prime Meridian, as well as the local time. The chronometer automatically tells you the difference between the two. You can then multiply that number by the rate of 15 degrees per hour. For example, if you were sailing west of London, and the local time is 12:00 (noon), while the UTC time is 16:00 (4 p.m.), the difference of 4 hours X 15 degrees per hour gives you a longitude of 60 degrees west. (Note that the hour unit on both the sides of the equation cancels out.)
Without a chronometer or internet/phone service, gauging local time generally means using the reference point of the Sun reaching its zenith at noon. Once you estimate that, you calculate the difference between it (i.e. local time) and the time you hear on the BBC broadcast, assuming you have a radio. It's not as exact a measurement, however, because solar time is a fluctuating thing as a result of a phenomenon called analemma, a figure-8 that the sun makes in the noon sky when you chart its position through the four seasons.
As we all know, in the physical world, a solar day varies according to the Earth's rotation and the seasons. So your high noon on any given day may be out of sync with UTC by up to 16 minutes. So the measurement you take at sea (or wherever you are) is known as "apparent solar time".
To line up with UTC for more accurate measuring, navigators turn to the equation of time in order to factor in the necessary adjustment needed to nail down the exact time difference. (See graph at right.) If, for example, the date is January 15th, noontime, according to the equation, the Sun will be lagging 15 minutes behind the noon of the UTC. For this reason, you'll want to add 3 degrees and 45 minutes of longitude to compensate for that margin of error. So if it's mid-January and your local zenith time while sailing the Atlantic is noon, and the BBC says it's 4 p.m. GMT, then your location is 63 degrees, 45' W. (Be sure to download an equation of time chart for future reference.)
One other caviat to remember: the 60 minutes of an hour are not the same as the 60 minutes that make up one degree. Instead, 4 minutes on a clock translate to one degree (or 60 minutes) of longitude. And a half hour equals 7 degrees 30 minutes, not 30 degrees.
Computing latitude and longitude without any instruments
To make domestic timekeeping easier, time zones were instituted in the 19th century, eliminating the problem of every town and village scattered around the planet following the solar time directly over their heads. With time zones, it’s relatively easy to identify the line of longitude that runs through a location, so long as you have access to a local clock. For example, for New York state, just subtract the current time there from the time in the U.K.and you’ll get a difference of five hours. (Note: UTC doesn't observe Daylight Savings Time.) Now you can multiply the five-hour time zone difference between London and New York by 15 degrees to get 75 degrees of longitude. So cities in New England, the Mid-Atlantic states and Florida will lie between 70 and 80 degrees of longitude west. Manhattan resides almost exactly at 74 degrees west.
Incidentally, west and south coordinates are often expressed as negative numbers, instead of mentioning cardinal directions. You'll also find that decimals are commonly used in place of minutes and/or seconds. For example -143.98 is a western longitude, while - 40.77 is either a southern latitude or a western longitude. If a number is higher than 90 degrees, it will always be a longitude, since latitude never goes beyond 90 degrees.
Now for a real life example. Let's say you’re on a long flight abroad and happen to crash in a storm. Washing up on an uncharted island, you can estimate your latitude by measuring the angle between the North Star (or Southern Cross, if you're in the southern hemisphere) and the horizon. You can estimate your longitude if you can determine both local time and the time in the U.K. For the latter, you would need a radio that can pick up the live broadcast of the BBC World Service. The news show airs around the planet on public radio stations, so it's not as hard to find as you might think. Just remember to listen carefully for the standard when the announcer gives the time. It should be UTC, but GMT is also acceptable. (Another standard in the U.K. is BST, or British Summer Time, which is the same as Daylight Savings Time in the United States.)
In order to figure out your local time on a deserted island outside (rather than just knowing when it's high noon), consider building a makeshift sundial on your deserted island. Start by placing a stick straight up in the sand, watching the direction its shadow moves in. When the shadow cast by the stick disappears completely, that's your noon refernce point. Tip the stick towards due North (or due South in the southern hemisphere).
Next, begin setting up a clockface. The stick or whatever else you use to cast the shadow is called a gnomon. In the northern hemisphere, the gnomon must be pointed towards the geographic North Pole to make it parallel to the Earth's north-south axis. In the southern hemisphere, tip it towards the South Pole.
Mark the top of the shadow as 12 o'clock and watch where the shadow turns. Your "clockface" will be semi-circle. (See photos above right.) Hours 1 to 6 p.m. will be plotted on the right side, with 6 pointed due East at 90 degrees. Hours 11 to 6 a.m. will run down the left. (Needless to say, you can't keep track of time between sunset and sunrise using a sundial.) Always read the bottom edge of the shadow for the time. If you don't have a watch or timer to help you set up the position for the hours, you'll have to use trial and error until the hours are proportionally set up. Notice in the photos, the space between numbers is uneven - tighter around the noon hour, with increasing space as you head out towards the 6. Such is the modus operandi of a solar clock.
Of course, determining latitude and longitude is only as useful as your knowledge of geography. Any trip on a plane or ocean-going vessel should be preceded by careful study of your travel perimeter, perhaps even memorizing major latitude-longitude coordinates for different countries and populated island chains. In-flight magazines usually include a map of your theatre of travel with the flight path charted across it. Rip the map out and stuff it in your pocket, just in case. Based on the time the plane crashed, and the total travel time between departure and arrival points, you should be able to deduce your approximate location. And when it's time to escape the island on a raft, if it comes to that, you'll also know in which direction to paddle.
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