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How to find your latitude

How to find your latitude

10:22 pm by Author1 & filed under Uncategorized.

Being a mobile star dome, we travel all over the UK to bring space science to our learners. Luckily, there are sat navs to show us directions and seamlessly guide us through busy traffic, road closures and congestion. But how did people get to their destinations and determined their whereabouts before the sat nav era?

Today’s challenge is to learn to calculate the coordinates the old-fashioned way. Are you ready?

What is a coordinate system?

On Earth we specify one’s position using two coordinates: latitude and longitude. We think of them as a grid made of latitude and longitude lines.

Latitude lines , or parallels, run horizontally and parallel to the equator. Latitude tells us how far North (values 0 to 90 degrees N) or South (values 0 to 90 degrees S) we are from the equator.

Longitude lines , or meridians, run vertically from the North Pole to the South Pole so that they cross the Equator at a 90 degree angle. Longitude is measured relatively to the Prime Meridian that runs through the Greenwich Observatory: West (values 0 to 180 degrees W) and East (values 0 to 180 degrees E).

Every point on Earth lies on the intersection of a specific parallel and meridian – its unique coordinates.

How to find your latitude (Northern Hemisphere only)

A long time ago people have notices that when you move South, the North Star appears closer to the horizon, when you move North, the North Star appears higher in the sky.

In fact, it is easy to show that the height of the North Star above the horizon (or rather the elevation of the Celestial Pole above the horizon, but the two are nearly the same thing) is equal to the observer’s geographic latitude. Therefore to determine our latitude all we have to do is to measure the elevation of Polaris above the horizon! Well, provided you know how to find it first, of course (and here is how ). Alternatively, you can use the elevation of the Sun at noon. But if using this method, remember to never ever look at the Sun directly!

How to find your latitude

Now that you found the North Star, you can determine its elevation using a very simple tool called quadrant (quarter of a circle) or its close relative sextant (sixth of a circle). These instruments have been used for navigation since early times and you can easily make one yourself.

At night, look through your quadrant’s viewer (we made it out of straw) to find the North Star. Then read the number the string with the weight will be pointing at. That’s your latitude!

How to find your longitude

Figuring out your longitude will require a little bit more work. You will need a clock, a phone, a good friend at Greenwich and a sunny day.

The idea behind this method is fairly simple:

In one 24 hour long day the Earth makes one 360 degree turn. That means the Earth rotates at rate 1 degree per 4 minutes (or 15 degrees per hour). Therefore if you find out the time difference between the solar noon at your location and in Greenwich, you will figure out your longitude!

To find the moment of your local solar noon, draw a North-South line on the ground. Then stick a long pole into the ground so that it is in the middle of the line. Remember: the taller the pole and the more accurate its vertical position, the better! The moment the shadow cast by the pole will cross the North-South line is your local noon!

To find the time of the solar noon at Greenwich, ask your Greenwich friend to do the exact same experiment. Alternatively, you can use the Greenwich time signal (the 6 “pips”) on BBC Radio 4 to find out the Greenwich Mean Time.

You want to learn two things from this experiment: whether the Greenwich peeps come before or after your local noon and by how much.

  • The Earth rotates counterclockwise (as seen from the “top”). So if your noon is earlier than Greenwich noon, you are located to the East of the Prime Meridian. Otherwise you are located to the West of the Prime Meridian.
  • The longitude value can be calculated by using a “1 degree longitude for 4 minutes time difference” formula.

Now you know how to find you whereabouts without the sat nav! How cool is that? You will never get lost again!

Still curious?

Read more about Satellite navigation and how it works in our blog. And, as always, feel free to email your questions and comments to our inflatable planetarium team. We would love to hear from you!

To revist this article, visit My Profile, then View saved stories.

How to find your latitude

To revist this article, visit My Profile, then View saved stories.

In a recent episode of MacGyver, Angus (yes, that's his first name) finds his location in the desert using only a string, a protractor, and a watch. Is this actually possible? Basically, yes. (At least that's what I told the show-runners as the technical consultant for the show.)

But you can do this, too. So now, for your super basic introduction to navigating the world. And don't worry—this won't be a full blown semester course on navigation, it's just the basics.

If you want to find out where you are on Earth, you need some type of coordinate system. Humans like to use longitude and latitude. You need to understand these in order to actually navigate. Both longitude and latitude can be thought of as circles (but not actual circles). Let me start with a basketball as an example. It already has some lines on it, so I just need to add some extra to make it look like this.

The lines that are already on the basketball are like lines of longitude. They all cross through the top (North pole) and bottom (South pole) of the basketball. This means that all these lines of longitude form circles that have the same radius—the radius of the Earth. Longitude is basically a way of breaking the sphere into 360 degrees. However, we don't measure longitude all the way to 360°. Instead we have 0 to 180° East and 0 to 180° West. The 0° value is in Greenwich, England, and as you move West you would be increasing in longitude West.

OK, but how do you measure longitude? This is where a clock comes in handy. Yes, a clock. To understand this measurement, you need to know two things: The Earth is spherical (mostly spherical, offer not valid in all US States) and the Earth rotates so that it appears the sun travels around the whole sky every 24 hours (again, not exactly true, but close enough).

Now suppose you are in Greenwich (where longitude is 0°). At some time during the day, the sun will be at its highest position in the sky (which will not be directly overhead). We can call this 12:00 noon. If you are in Greenwich, you can set your clock to the sun. Now your clock also says 12:00 noon. Next, you travel westward all the way to New Orleans (since it's close to where I live). You repeat the same experiment by waiting until the sun is at the highest point. But wait. Your clock doesn't say 12:00 noon, it says 6:00 AM since it's still set on Greenwich time. Since the Earth is spherical, the sun is at its highest point in Greenwich, but maybe it hasn't even risen in New Orleans.

In fact, if you know the difference in time between Greenwich noon (what your clock says) and local noon (when the sun is at the highest point), you can find your longitude. This time difference is essentially your longitude. You just need to convert from hours to degrees (which I will skip). But notice how important it is to have a clock to determine your longitude. Really, there is no way around it—that's why the Longitude Act of 1714 was so important. It established a prize for the development of an accurate and portable clock. OK, technically the prize was for a method to determine longitude—but really, a clock of some type is the only practical solution (unless you have GPS).

But wait! What if you want to navigate at night when you can't see the sun? Yes, this method can still work. However, you need to know something extra. If you know the time a star rises (or the moon, or a planet) with respect to the time it would rise in Greenwich then you are all set. It's the same idea as using the sun at noon. Of course. the problem with this method is that most people don't memorize the rise-times of different celestial objects.

The lines of latitude also make circles around the Earth. However, they don't all pass through the same points like the longitude values do. Instead, these are circles that are all parallel to the equator. If you look at my basketball above, the horizontal lines would be lines of latitude. Yes, I had to draw this on the ball.

Latitude is also measured in degrees but it starts at the equator which would be zero degrees latitude. As you move away from the equator (North or South), you increase your latitude degree such that New Orleans would be about 30°N. If you go to Sydney, Australia, you would have a latitude of 33.8°S since it is 33.8° below the equator.

OK, but how do you determine your latitude? This one is pretty straight forward—especially if you are in the Northern hemisphere. In short, you just need to measure the angular height of the North Star (Polaris) above the horizon. This works because the North Star is almost directly in line with the Earth's axis of rotation. So, if you were at the North pole (and hopefully on ice), the North Star would be directly overhead with an angle of 90° above the horizon. If you traveled to the equator, the North Star would be exactly on the horizon and you would be at 0° latitude.

What about the Southern hemisphere? Yeah, that's a small problem. Unlike the Northern hemisphere there isn't a star right on the axis of rotation. Instead you just have to approximate the location of the celestial South pole by looking at other constellations.

Finally, how do you get this angular height of the North Star? That's where the protractor comes in play. Here's what you do. Take a string with a weight to act as a plumb bob. Now hold the protractor upside down and aim the straight part towards the North Star. Boom. That's it. The plumb bob will hang at the angle reading for your latitude. Now you aren't lost.

Note that with my DIY sextant (and most others), the string would point to a value on the protractor that is not the angle above the horizon. Actually, you would have to take your angle measurement and subtract from 90° to get your latitude. Also, there is a straw on top of my protractor to assist with the aiming—and it looks cool.

Of course both of these methods work, but the key is precision. For latitude, just a 1° difference in measurement means a distance of 69.1 miles or 60 nautical miles. In fact, the nautical mile is defined by the size of 1 minute of a latitude (where there are 60 minutes in 1 degree). This means that the better your angle measurement, the better you will know your actual location. Sure, a protractor works, but a sextant does this even better. A sextant is essentially just a much better protractor.

That's it. That's the basics of finding out where you are on Earth. But there are many other cool and fun details; if you want to learn more, I can recommend this nice online course from Vanderbilt University—AstroNavigation (it's free).

If you have adequate reception at your site, you can use your phone to determine your latitude and longitude.

  • iPhone: Use your iPhone’s built-in GPS device
  • Android: Open Google Maps; it will zoom to your approximate location. Press and hold on the screen to drop a pin marker. Click on the dropped pin; latitude and longitude will be displayed below the map. If you don’t have Google Maps, you can install a free GPS app before heading to your site.

Off-Site Using a Computer

If you don’t have adequate cellular reception at your site to use the methods above, you can determine your site’s latitude and longitude when you get back to your computer.

Via Monitor My Watershed

If you are sharing your data on the Monitor My Watershed data portal, during the site registration process you can zoom in on the map, click to place a pin at your deployment location, and the lat/long will be auto-generated. See step-by-step instructions on WikiWatershed.org.

Via Google Maps

If you are not sharing your data on Monitor My Watershed (please do!), you can use Google Maps to determine your site’s latitude and longitude. Go to maps.google.com and follow the instructions in this video.

Explore WikiWatershed

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Leaf Pack Network Simulation

If you can’t get to a stream to perform a study, you now have a virtual option! The Leaf Pack Network® Simulation is a web-based virtual stream study in a field notebook format.

Introducing the Rock Pack Experiment!

How to find your latitude

The Rock Pack Experiment combines STEM topics of engineering, ecology, geomorphology, and mathematics in stream ecosystems through the world of the net-spinning caddisfly.

Dive Into the Water Quality App

Enhance stream study and monitoring activities for students and citizen scientists with this mobile app for Apple and Android devices.

With some simple math is it possible to measure your latitude directly at night time.

Full instructions are available at the EAAE Astronomy On-Line final event 1996

During 24 hours, the sky above us performs one full rotation.

If you record (by drawing or photographing) the northern sky several times during one night, you will see something like this :

The constellations Cassiopeia (that looks like an "M" or a "W"), the Big Dipper, and the Polar Star "P".

Note that nearly all stars appear to move due to the rotation of the Earth. Only one star seems to be fixed – the Polar Star "P" ; it is also known as the "North Star".

The Polar Star – the only northern star which stays fixed in the sky during all night hours – has a constant altitude above the horizon.

By a bit of simple math, it is possible to show that this altitude is very nearly equal to your own geographical latitude. For instance, if you live at latitude 50° North, then the North Star will be placed at an altitude of 50° above your horizon.

Exercises:

1. Imagine that you stand on the geographical north pole. Where in the sky would you see the Polar Star?

2. Measure your own geographical latitude by means of the Polar Star. This may be done by means of simple homemade equipment, for instance a Jacobean Cross Staff (a quadrant) or an oriental Kamal as shown on this Portuguese stamp.

3. Repeat the old Bishop Nicholas "Right Hand Latitude method" that was described in EAAE Astronomy On-Line final event 1996.

How to find your latitude

Do you know how to determine your latitude — your position on Earth relative to the equator — without using the internet?

Would you like to learn? You never know when a skill like this could come in handy.

DON’T MISS: Math Trick: Find Any Square Root in 3 Seconds Flat

It’s really simple — all you need is a bit of basic spherical geometry and the stars. In the Northern Hemisphere, you need to find Polaris, aka, the “North Star.” You can find Polaris by locating the Big Dipper, or Ursa Major. Then, imagine a line connecting the two front stars of the Big Dipper continuing off to the upper right. The first bright star you come across is Polaris.

How to find your latitude

Here’s how to find your latitude. First, imagine you are standing right at Earth’s north pole. Where is Polaris? Directly overhead, and it will always be directly overhead with the whole sky appearing to rotate around it once every 24 hours.

How to find your latitude

Star trail photograph showing the apparent motion of stars around Polaris — the bright star near the center, just above the jet trail. Photo credit: TedQuackenbush/Wikipedia (CC BY-SA 3.0)

Next, imagine walking south towards the equator — which is technically any direction. As you walk towards the equator, Polaris will start to move away from the point directly overhead towards the horizon. Once you make it all the way to the Equator, where is Polaris now? At the horizon.

To figure out your latitude, all you have to do is estimate the angle between Polaris and the horizon due north from where you are standing. For example, at Earth’s north pole, Polaris is directly overhead, which is 90 degrees above the horizon. This is also your latitude. At Earth’s equator, Polaris is on the horizon, or 0 degrees above it. Your latitude is 0 degrees.

SEE ALSO: How to Fairly Cut a Cake, According to Math

If you are located in Boston, Massachusetts, Polaris is located roughly 42 degrees above the horizon, so your latitude is approximately 42 degrees north. It’s that simple!

But what if you are in the Southern Hemisphere where Polaris is not visible? You have to use the Southern Cross, or Crux. The Southern Cross is a constellation with many stars, but five are clearly visible. Mimosa is the bright star that forms the left-hand point of the Crux, Hip 59747 forms the right-hand point, Gacrux the top, Crux in the middle, and Acrux the bottom point.

How to find your latitude

Photo credit: Till Credner/Wikipedia (CC BY-SA 3.0)

The Southern Cross can be used for navigation since the longer bar of the Cross points almost exactly toward the South Pole of the sky, which unfortunately has the nickname the “south solar pit” because it is not marked by any bright star.

How to find your latitude

‘Ships, Clocks & Stars: The Quest for Longitude’ traces the history of finding reliable methods for determining your longitude at sea. Image: ANMM.

Ships, Clocks and Stars: the Quest for Longitude tells the amazing story of how the problem of determining longitude at sea was solved. The exhibition explains the rival methods and shows the incredible craftsmanship and ingenuity of clockmaker John Harrison, whose timepieces finally gave sailors a practical means to calculate their longitude in a simple manner.

Why was it so hard to sort out a means of finding longitude, when it seems finding latitude had been a relatively simple process?

The short answer is that latitude had reference points easily available and they were also easy enough to measure and use for guidance, even without fancy instruments. However, the references for longitude were much less obvious and needed very accurate tools and tables of information for their measurement to be usable.

Reference points are a key to either being lost or knowing where you are. If you are lost, there is nothing familiar around you as a reference to guide you on your journey or locate where you might be and get you back to where you came from.

In contemporary terms, latitude is your location north or south of the equator and longitude is your location east or west of the prime meridian, 0 degrees. Both are imaginary lines circling the earth and on a modern chart they establish a grid of lines at right angles to each other that enable you to locate your position. These terms, and their associated method of mapping with a geometric grid, are relatively recent within human history.

How to find your latitude

A Terrestrial hand globe made by Newton & Son, 1851-1857. ANMM Collection: 00045821.

However, latitude, or the same thing by another name, has been widely used by humans since they took to exploring the oceans and maybe even earlier, perhaps as people moved to new places on land, leaving a locality with known landmarks. This is because latitude has an obvious reference in the sky – a map or chart featuring the sun during the day and the stars, moon and planets at night. As you move north and south, the map in the sky changes.

You could ‘measure’ where you were in relation to the changes in the location of celestial bodies. Their relative position as they rose and set was simple enough to observe, but also their height above the horizon changed as you moved north and south, and this could be estimated or even measured with quite reasonable accuracy by different methods.

How to find your latitude

The Bleu celestial globe represents the first full publication of the Southern Hemisphere’s constellations, including the Southern Cross. Willem Blaeu is renowned for the quality of his charts and cartography which represent some of the most accurate work of the 17th century. ANMM Collection: 00005756.

This whole reference in the sky formed a chart of its own, and although it changed through the night and through the seasons, and even presented a different view of the bodies depending on your location, the changes were all gradual and formed a pattern which many communities and civilisations were able to observe and record, often in stunning detail and insight. This accumulated knowledge and understanding was passed on and people were able to determine anything from a broad indication through to a reasonably precise location of where they were in a north-to-south direction, either relative to another known point or, in later times, relative to the equator.

The quest for determining longitude developed a number of possible methods, three of which were potentially quite accurate. Observations of Jupiter’s moons could be used and worked well on land, and observations of the moon through the lunar distance method presented a very precise answer, too. Also, the concept of using the difference in time between a known location and your location as a means of calculating your longitude was also widely known. However, all of these needed very precise observations of the different celestial bodies, and in the case of the first two, very detailed recordings of their patterns of movement, and tedious calculations to arrive at an answer. The time of day was also needed, and needed very accurately. The instruments required – telescopes, sextants, timepieces and so forth – were gradually improving in accuracy, but did not begin to meet the requirements needed until the 1700s and into the 1800s.

The difference in time or timekeeping method that eventually gave practical access to longitude at sea used a specific reference as a datum for time that was within the east-to-west moving chart in the sky. Lying within this east-to-west movement was a north-to-south oscillation. All of the bodies were rising in the sky to a high point above the horizon and then setting again in the west. This change in height above the horizon could be seen on earth as a north/south vector, or drift, within the east/west motion. The highest point was due north or south in the sky and always occurred at the midpoint between when a body rose and set, and this midpoint was a constant reference as it occurred at the same time each day.

It was one of these midpoints, along with Harrison solving the technical problem of creating a clock that kept time accurately for days on end, which helped provide a practical solution to the longitude problem. The point is called local noon, the point at which the sun was highest in the sky. Whereas sunrise and sunset change time each day, local noon was always the same time and thus a precise reference point for checking time each day wherever you were. If you could then just check your time against the time at another known location, you could calculate your longitude relative to the known location.

How to find your latitude

The sun’s motion across the sky looking north – local noon (1.09 pm EDST) at the museum on 10 February 2016. Images: David Payne / ANMM.

In fact the high point of other bodies could do this as well, but the sun was an obvious one. Local noon at the prime meridian of 0 degrees, which passes through the Royal Observatory at Greenwich in London, eventually became the accepted datum for longitude and time, leading to the well-known term Greenwich Mean Time. GMT is actually an average or ‘mean’ for local noon at the Greenwich Meridian because there are some minor fluctuations in local noon that need to be allowed for. You can read more about that, along with some other intriguing issues that had to be resolved, and explore some wide-ranging background to time, distance and speed in the digital story Longitude – A story comes full circle.

Ships, Clocks & Stars: The Quest for Longitude has been produced by the National Maritime Museum, part of Royal Museums Greenwich, London.

How to find your latitude

Sailors and travelers have used Polaris, also known as the North Star, for centuries to locate their position on the surface of the Earth. Polaris is the brightest star in the constellation Ursa Minor, whose seven brightest stars form the Little Dipper. Polaris is the brightest star at the end of the tail of the Little Dipper and is useful because it is the only star that does not appear to move in relation to a specific location on Earth. Polaris cannot be seen from south of the equator.

The altitude of a star is the measurement in degrees of the angle of the star above the horizon. Flat out on the horizon is 0° and straight up in the sky is at 90°, which has a special name, the zenith.

How to find your latitude

Materials

  • Drafting compass with degree measurements
  • Clear, starry night

Procedure

  1. Go outside on a dark, clear, starry night.
  2. Locate Polaris. It is the last star in the tail of the Little Dipper.
  3. Hold the compass out in front of you.
  4. Align the 0° edge of the compass with the horizon.
  5. Keeping the 0° edge flat against the horizon, lift one arm of the compass until it points directly at Polaris.
  6. Read off the angle. This is the altitude of Polaris from your location on Earth. This corresponds to your latitude. What would be the altitude of Polaris if you were standing at the North Pole? What would be the altitude of Polaris if you were standing at the Equator?

Results

Use a map or the internet to determine the latitude of your hometown and see if your measurement is correct.

Polaris is so far away (about 434 lightyears) that the rays of light approach the Earth in a parallel manner. This allows us to look at the angle between us and the star (which is the same as the angle between the horizon and the star) to locate our latitude on the Earth. Polaris is about 0.7° from the exact North Pole, so with the rotation of the Earth it makes its own tiny circle in the sky at night as well, but it is the only star that appears fixed in the sky to us.

Polaris is also a multiple star, which is why it is so bright. It consists of alpha-Polaris, the main, brightest star, and two tiny stars very close to it, so to the naked eye they appear as one star.

Earth moves in a motion called precession. This means our axis shifts in a circle over the span of about 26,000 years. This means Polaris hasn't always been above our North Pole as it is right now. In ancient Egyptian times, the North Star was Thuban, from the constellation Draco, and in about 12,000 years, it will be Vega, from the Lyra constellation, which will appear to be an even brighter beacon than Polaris.

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Have you ever wondered how people figured out their latitude back in the days before the Internet? Did you know you can use the same math trick they used to pinpoint your latitude today? Keep on reading to find out how it works

  • By Math Dude Jason Marshall on May 25, 2016

How to find your latitude

Greetings, Secret Agent Math! Your mission, should you choose to accept it, is to figure out where you are on Earth relative to the equator. Why might you need to be able to figure this out? Who knows! But a secret agent like yourself is always curious to learn new things, right? After all, you never know when one of these skills is going to come in handy.

Perhaps it’ll be when you’re on that super secret mathematically-oriented spy mission to crack the code used to encrypt that really important message. Or perhaps it’ll be when you’re deploying your particularly well-honed set of mathematical skills to solve that riddle that’s going to help you save those people from that thing. Or … whatever.

The point is, you never know when figuring out where you are on Earth relative to the equator—by which I mean figuring out your latitude—is going to come in handy. So, as every good secret agent skilled in the fine and beautiful art of mathematics has done before, today we’re going to add this trick to our repertoire. Stay tuned to find out how it works!

Recap: What Is Latitude?

Before we rejoin Secret Agent Math and the quest to pinpoint your latitude on Earth, we’d first better recap what we mean by latitude. Those of you who have stared at a globe long enough to notice the grid of horizontal and vertical lines already know pretty much everything you need to understand latitude (as well as its close cousin longitude).

ABOUT THE AUTHOR(S)

Jason Marshall, PhD, is a research scientist, author of The Math Dude’s Quick and Dirty Guide to Algebra, and host of the Math Dude podcast on Quick and Dirty Tips.

Any point on Earth can be defined by the intersection of its lines of latitude and longitude. Latitude is measured as the angle from the equator, to the Earth’s center, to your position on the Earth’s surface (Figure2.1.1). It is expressed as degrees north or south of the equator (0 o ), with the poles at a latitude of 90 o . Thus the poles are referred to as high latitude, while the equatorial region is considered low latitude. Lines of equal latitude are always the same distance apart, and so they are called parallels of latitude; they never converge. However, the circles created by the parallels of latitude do get smaller as they approach the poles.

Figure 2.1.1 The latitude of a point on the Earth’s surface is determined by the angle (ø) between the point and the equator, passing through Earth’s center (Peter Mercator [Public domain], via Wikimedia Commons).

One degree of latitude is divided into 60 minutes (‘). One minute of latitude equals one nautical mile , which is equal to 1.15 land miles (1.85 km). Each minute of latitude is further divided into 60 seconds (“). So traditionally, positions have been expressed as degrees/minutes/seconds, e.g. 36 o 15′ 32″ N. However, with modern digital technology, positions are increasingly expressed as decimals, such as 36 o 15.53′ N, or 36.2589 o N. (A useful tool for converting coordinates between these formats can be found at: https://www.fcc.gov/media/radio/dms-decimal).

In the Northern Hemisphere, latitude can be determined by the angle of the North Star (Polaris) from the horizon. The North Star always sits over the North Pole. Here, if a person looks straight ahead towards the horizon, the star would be directly overhead, creating a 90 o angle; thus the latitude at the North Pole is 90 o N. At the equator looking north, the star is in the same direction as the horizon, so the angle between them is 0 o , and thus the equatorial latitude is also 0 o . At any other point in the Northern Hemisphere, the angle between the horizon and the star will give the latitude.

Early mariners used an instrument called an astrolabe to calculate this angle. Later the sextant was developed, which allowed more accurate measurements (Fig. 2.1.2).

How to find your latitude

Figure 2.1.2 An astrolabe (left) and sextant (right) (Public domain via Wikimedia Commons).

There is no direct analogue to the North Star in the Southern Hemisphere that is useful for determining latitude. However, the Southern Cross and Centaurus constellations can be used to find the south celestial pole. If a line is drawn through the long axis of the Southern Cross, and another line is drawn between the two brightest stars in Centaurus, the two lines will intersect at the south celestial pole.

Longitude measures the distance east or west of an imaginary reference point, the prime meridian (0 o ), which is now defined as the line passing through Greenwich, England (although throughout history the prime meridian has also been located in Rome, Copenhagen, Paris, Philadelphia, the Canary Islands, and Jerusalem; unlike the equator, the prime meridian’s location is fairly arbitrary ). Your longitude represents the angle east or west between your location, the center of the Earth, and the prime meridian (Fig. 2.1.3).

Figure 2.1.3 Longitude is determined as the angle (λ) between the prime meridian and your position (Peter Mercator [Public domain], via Wikimedia Commons).

As you move east and west from the prime meridian, eventually you reach 180 o E and W on the opposite side of the globe from Greenwich. This point is the International Date Line. Lines of longitude are called meridians of longitude, or great circles. All circles of longitude are the same length, and are not parallel like lines of latitude; they converge as they near the poles. Therefore, while one minute of latitude always equals one nautical mile , the length of one minute of longitude will decline from the equator to to poles, where it will ultimately decline to zero.

Measuring longitude requires accurate time at your current location, and also the time at some distant point like a home port at the same instant. The time difference can be used to calculate longitude. This is because the Earth takes 24 hours for a complete 360 o rotation. So in one hour, the Earth rotates through 1/24 of 360 o , or 15 o . Therefore, for each hour of time difference between two locations, there is a 15 o difference in longitude.

Accurate measurements of latitude using the North Star have been made since at least the third century B.C.E. Because longitude measurements required accurate timekeeping, it wasn’t until the mid-18th century that longitude was easily and precisely measured at sea. Before then, sailors would often sail north or south to get to the desired latitude, then just head east or west until they reached the target longitude. Solving the longitude problem was so important that the British government passed the Longitude Act in 1714, offering a £20,000 prize to anyone who could devise a method of measuring longitude at sea to within half a degree. Many unsuccessful solutions were proposed, including astronomical observations, but it was a clock maker, John Harrison, who developed a series of clocks that eventually satisfied the criteria. The first version (the H1) weighed over 80 lbs, but his final timepieces, the H4 and H5, could be held in the palm of one hand. Ironically, even though his clocks satisfied the criteria, Harrison was never named as the winner of the longitude prize, and in fact no winner was ever officially determined. With accurate timepieces now available, a ship could have one clock set for Greenwich time (or some other home location), and another clock set to local time, which could be reset each day by observing the sun. The time difference between the two clocks could be used to calculate longitude.

Today we use GPS (Global Positioning System) technology to determine latitude and longitude, and even the smallest smart phones and smart watches can use GPS to calculate position. GPS works through a system of orbiting satellites that constantly emit signals containing the time and their position. A GPS receiver receives these signals from multiple satellites, and triangulates the signals to calculate position. The system needs 24 satellites to be functional at one time; as of 2015, the system consisted of about 32 operational satellites, able to give a position with an accuracy of 9 meters (30 feet) or less.