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Oceanography >> The World Ocean >> Latitude and Longitude
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1.3 - Latitude, Longitude and Projections
Objectives:
- To understand the concept of latitude and longitude and be able to locate a position on a globe.
- Understand that as the Earth is approximately a sphere, we need to distort it to produce a flat chart.
- To know how projections, such as the Mercator and Mollweide projections, are created and their advantages/disadvantages.
For thousands of years it has been known that the Earth was spherical. Most famously, an Ancient Greek mathematician called Eratosthenes even managed to calculate the radius of the Earth based on some basic observations - although admittedly he did get lucky as the Nile flows in a northerly direction. It was observed that at midsummer the Sun cast no shadow at the Syene (where the modern day Aswan Dam is located), while at the same time at the Great Library of Alexandria it cast a \(7\,^{\circ}\) shadow. As it was known that the distance between the two locations was \(5000\,\text{stadia}\) , which is equal to \(843 \,\text{km}\) according to Google Earth, he achieved a value of a circumference of \(44,000\,\text{km}\). In 1912 this experiment was repeated but using more accurate data and measuring techniques and produced a result of \(40,000\,\text{km}\), which is almost spot on!
(from Wikipedia)
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Eratosthenes made a number of assumptions:
Challenge: can you recreate Eratosthenes' calculation? |
Therefore, he realised that the known world was only a small part of the planet. At the time the Mediterranean literally was the centre of the world, although Alexander had pushed east overland towards the Orient. A modern version of his map is shown below. Note that the gridlines are not evenly spaced, but rather highlight important locations.
On modern maps and charts we see regularly spaced gridlines, which we call LATITUDE and LONGITUDE. With the advent of GPS on smart phones and the myriad of T-shirts on Front Street, every student should know the coordinates of Bermuda! It is important to understand what these numbers mean and how they have been determined.
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Latitude
Latitude is the easiest both to define and measure. The Earth rotates about an axis that runs from the North Pole to the South Pole. The widest part of the sphere from this axis is the equator. The equator was named this as when the Sun is directly over it, the lengths of day and night are exactly equal all over the world. The parallels or circles of latitude are defined by the angle between them and the equator. By a happy coincidence for mariners, there is a star located almost perfectly above the Earth's axis, which is known as the North Star or by its latin name, Polaris. By a quick bit of geometry it is found that the angle between the horizon and the North Star is almost exactly equal to the latitude. So, it was relatively simple to determine the latitude in the northern hemisphere even in the Middle Ages. It can also be calculated based on the angle of the Sun above the horizon at local noon, but this requires knowing how the Sun moves during the year, and takes a lot more mathematics. The navigator has a somewhat harder time in the southern hemisphere as there isn't a conveniently located star above the South Pole. But there are four obvious stars around it, so the 'centre' of this Southern Cross constellation is the 'South Star'. This constellation is found on the flags of both Australia and New Zealand!
Latitude is the easiest both to define and measure. The Earth rotates about an axis that runs from the North Pole to the South Pole. The widest part of the sphere from this axis is the equator. The equator was named this as when the Sun is directly over it, the lengths of day and night are exactly equal all over the world. The parallels or circles of latitude are defined by the angle between them and the equator. By a happy coincidence for mariners, there is a star located almost perfectly above the Earth's axis, which is known as the North Star or by its latin name, Polaris. By a quick bit of geometry it is found that the angle between the horizon and the North Star is almost exactly equal to the latitude. So, it was relatively simple to determine the latitude in the northern hemisphere even in the Middle Ages. It can also be calculated based on the angle of the Sun above the horizon at local noon, but this requires knowing how the Sun moves during the year, and takes a lot more mathematics. The navigator has a somewhat harder time in the southern hemisphere as there isn't a conveniently located star above the South Pole. But there are four obvious stars around it, so the 'centre' of this Southern Cross constellation is the 'South Star'. This constellation is found on the flags of both Australia and New Zealand!
Geometrical sketch to show why the altitude of the North Star equals the latitude of the observer. There are TWO North Stars in the diagram to enable the light rays from the star to be parallel. The distance between the Earth and the North Star is vastly larger than the radius of the Earth, so that the rays are essentially parallel.
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The altitude angle is the latitude. This can be measured by a sextant, or an astrolabe - even a straw, protractor and a weighted string! A minor correction needs to be made to account for the height of the observer above the water, but this is almost negligible.
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Longitude
Longitude is defined as the segmentation of the Earth from north to south, this lines are NOT parallel and are known as MERIDIANS. However, there is no obvious starting point like the equator. So one was defined... Until 1884 each major country defined their own based on where they had an observatory located that could take measurements of the motion of the Sun and stars as the Earth spun on its axis and moved around the Sun. As Britain was the dominant sea power at the time, it was universally agreed that the Prime Meridian be set through the Royal Observatory at Greenwich, London. This is known as the Greenwich Meridian. To measure the longitude requires an accurate clock. As the apparent motion of the Sun was \(360^{\circ}\) over a \(24\,\text{hr}\) period, it equates to \(15^{\circ}\) longitude every hour. If the navigator could accurately measure the TIME between when the Sun was overhead the Greenwich Meridian and his location, he could do a quick bit of maths and determine his longitude. So until the advent of GPS all navigators ensured that they had an accurate clock (chronometer) that was set to Greenwich Mean Time (GMT) and checked regularly against signals from a radio. Local noon is determined by measuring the time at the Sun reaches its highest angle above the horizon. It took a very long time to invent a chronometer that was accurate enough for reliable navigation. Harrison's famous chronometer is displayed at the Royal Observatory.
For example: a sailor near Bermuda measures that local noon is at 1600 hrs GMT. That is 4 hours after noon in Greenwich. So the longitude is \(4\times15^{\circ}=60^{\circ}\text{W}\).
The story behind the invention of the chronometer is fascinating and detailed in Dava Sobel's highly readable book, Longitude. Actually became a movie due to the political skulduggery and machinations involved! An essential read for an ocean-going sailor.
Longitude is defined as the segmentation of the Earth from north to south, this lines are NOT parallel and are known as MERIDIANS. However, there is no obvious starting point like the equator. So one was defined... Until 1884 each major country defined their own based on where they had an observatory located that could take measurements of the motion of the Sun and stars as the Earth spun on its axis and moved around the Sun. As Britain was the dominant sea power at the time, it was universally agreed that the Prime Meridian be set through the Royal Observatory at Greenwich, London. This is known as the Greenwich Meridian. To measure the longitude requires an accurate clock. As the apparent motion of the Sun was \(360^{\circ}\) over a \(24\,\text{hr}\) period, it equates to \(15^{\circ}\) longitude every hour. If the navigator could accurately measure the TIME between when the Sun was overhead the Greenwich Meridian and his location, he could do a quick bit of maths and determine his longitude. So until the advent of GPS all navigators ensured that they had an accurate clock (chronometer) that was set to Greenwich Mean Time (GMT) and checked regularly against signals from a radio. Local noon is determined by measuring the time at the Sun reaches its highest angle above the horizon. It took a very long time to invent a chronometer that was accurate enough for reliable navigation. Harrison's famous chronometer is displayed at the Royal Observatory.
For example: a sailor near Bermuda measures that local noon is at 1600 hrs GMT. That is 4 hours after noon in Greenwich. So the longitude is \(4\times15^{\circ}=60^{\circ}\text{W}\).
The story behind the invention of the chronometer is fascinating and detailed in Dava Sobel's highly readable book, Longitude. Actually became a movie due to the political skulduggery and machinations involved! An essential read for an ocean-going sailor.
Harrison's chronometer. In the list of inventions that 'changed the world'.
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Using Latitude and Longitude as Coordinates
Latitude is always stated first. It is written as an angle followed by a capital N or S to establish whether the latitude is north or south of the equator. The degree symbol can be left off if it is clear. Latitude goes from \(90^{\circ}\text{N}\) to \(90^{\circ}\text{S}\). Longitude is written in a similar manner but ranges from \(180^{\circ}\text{W}\) to \(180^{\circ}\text{E}\). Sometimes longitude eastwards of the Greenwich Meridian is written as a negative number.
However, as with many things there are complications. There are many ways to write an angle. The old-school approach is to use degrees, minutes and seconds. This sounds confusing as minutes and seconds are intervals of time. Just like with time, there are \(60\,\text{minutes}\) in a degree and \(60\,\text{seconds}\) in a minute. There is a complicated reason that angles are measured in the same way as time - can you guess what it is?
Some applications prefer to use decimals. So \(12^{\circ}\, 30^\prime\,45^{\prime\prime}=12.5125^{\circ}\)
Navigators prefers a mixed approach, using degrees, minutes and decimals of minutes. So \(12^{\circ}\, 30^\prime\,45^{\prime\prime}=12^{\circ}\,30.75^\prime\). The reason for this is that the nautical mile is defined as a minute of a great circle of longitude.
Latitude is always stated first. It is written as an angle followed by a capital N or S to establish whether the latitude is north or south of the equator. The degree symbol can be left off if it is clear. Latitude goes from \(90^{\circ}\text{N}\) to \(90^{\circ}\text{S}\). Longitude is written in a similar manner but ranges from \(180^{\circ}\text{W}\) to \(180^{\circ}\text{E}\). Sometimes longitude eastwards of the Greenwich Meridian is written as a negative number.
However, as with many things there are complications. There are many ways to write an angle. The old-school approach is to use degrees, minutes and seconds. This sounds confusing as minutes and seconds are intervals of time. Just like with time, there are \(60\,\text{minutes}\) in a degree and \(60\,\text{seconds}\) in a minute. There is a complicated reason that angles are measured in the same way as time - can you guess what it is?
Some applications prefer to use decimals. So \(12^{\circ}\, 30^\prime\,45^{\prime\prime}=12.5125^{\circ}\)
Navigators prefers a mixed approach, using degrees, minutes and decimals of minutes. So \(12^{\circ}\, 30^\prime\,45^{\prime\prime}=12^{\circ}\,30.75^\prime\). The reason for this is that the nautical mile is defined as a minute of a great circle of longitude.
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Activity
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Projections
A major problem for cartographers is that the Earth is almost spherical. This is great is we can use a globe, not so great if we want to portray the surface on a flat piece of paper. A map of the sea is known as a chart. The curvature of the Earth is not a problem on a small scale - even including the Mediterrean, but as we get to oceanic scales it becomes a major issue. There are many different methods of 'flattening' the Earth onto paper, which are called projections. Two of the most common are the Mercator and the Mollweide Projections.
A major problem for cartographers is that the Earth is almost spherical. This is great is we can use a globe, not so great if we want to portray the surface on a flat piece of paper. A map of the sea is known as a chart. The curvature of the Earth is not a problem on a small scale - even including the Mediterrean, but as we get to oceanic scales it becomes a major issue. There are many different methods of 'flattening' the Earth onto paper, which are called projections. Two of the most common are the Mercator and the Mollweide Projections.
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Mollweide Projection
Advantage - equal area Disadvantage - awkward shape and bearings are inconsistent. |
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Mercator Projection
Advantage - bearings remain constant, useful for navigation Disadvantage - distortion of area, especially towards the polar regions. Polar regions are often cut off to make chart look better. Other issues with putting the surface of a sphere onto a flat plane, is where you put the boundaries. The meridians of the world have no start and finish. The most common solution is to make the Greenwich Meridian run through the centre and show "east and west", but this cuts the Pacific Ocean in half. Other charts put the Americas in the centre, which cuts Russia/Asia in half. There is no easy solution. Weird sliced or conical projections don't help either. |
Have fun distorting the Earth using the different projections available in the Nullschool.net simulation of the Earth. Clicking the image will take you to the site.
Activities:
- Lat/long scavenger hunt using a variety of charts and Google Earth
- Making a chart of the world using different projections. See: https://manoa.hawaii.edu/exploringourfluidearth/physical/world-ocean/locating-points-globe/activity-mapping-globe
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Other Resources
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This website has a huge array of various projections that you can superimpose and compare. Kind of cool!
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This website compares the distortions as you scan through them.
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7 Things About Map projections - geeky geographer has fun with projections.
TO DO
origin of lat and long - especially north star
converting minutes to decimal
worksheet of lat long plotting and measuing
definition of nautical mile
worksheet of making projections
origin of lat and long - especially north star
converting minutes to decimal
worksheet of lat long plotting and measuing
definition of nautical mile
worksheet of making projections