Figure 1: Courtesy of Peter Dana www.pdana.com
My wife volunteered me to speak to the sixth grade at my son's school. In trying to imagine what I would tell the class, I realized that there are some interesting and relevant resources available in the form of computer programs and websites. For the couple of kids that might be interested in pursuing some of these resources, I wanted to publish some links. These are my links with some added information added. If you find any of this information useful, or you find information that needs to be corrected, feel free to contact me at handheldgps@hotmail.com.
Thanks,
John Bell
Latitude and longitude allow you to use two coordinates to define any point on earth. Needless to say, latitude and longitude has been useful to navigators, geographers, cartographers (people who make maps), and surveyors for a long time. However, even for some of these people, latitude and longitude has not always been used as much as other references. What has made latitude and longitude useful on a daily basis for a great number of people is global positioning system, GPS, and computerized mapping. GPS has reached the point where chain stores such as Target and Wal-Mart sell GPS receivers. The super short explanation of GPS is that a receiver takes the signals from multiple satellites and is able to calculate the latitude and longitude anywhere on earth. Thus, if you have a map with latitude and longitude, you can find your location on the map using GPS. Although some of the more expensive GPS receivers have built in maps and features such as address lookup, latitude and longitude can be used to define any point on earth.
Using latitude and longitude it is possible to calculate all sorts of things. For example, if you want to know how far it is from Orlando, FL to London, England, if you know the latitude and longitude of each point then you can calculate the distance. Not only can you calculate the distances from city to city, but you can calculate the distance from any point on earth to any other point. For example, you could calculate the distance from your house to school. Once you get into high school and take trigonometry, you can run the calculations on a simple scientific calculator. However, in the mean time, there are several calculators available on the Web that will calculate the distance between two latitudes and longitudes.
You can do a Google search for "distance from latitude and longitude" and find numerous examples of distance calculators that use latitude and longitude. I used: http://www.wcrl.ars.usda.gov/cec/java/lat-long.htm.
Example: Distance between Orlando, FL and London, England.
From www.maporama.com, Buckingham Palace is at N51.5016 W 0.1411. A point in downtown Orlando is N28.5466 W-81.3715. If I enter these latitudes and longitudes into a distance calculator, I find that the distance is 6976 km or 4335 miles.
The real point of this page is that there are some easily accessible ways to "play" with latitude and longitude. Although, I am sure that there are many more, here are several useful places that I have found for getting and using latitude and longitude.
Google Maps https://maps.google.com
Google Maps allows you to input a latitude and longitude into the search to see where that location on the maps. For example, one could enter "N28.547914 W81.375394" and find exactly where these coordinates are. Unfortunately, it is more difficult to work the other direction without some technical knowledge to find the coordinates of a point on the map.
There are versions of Google maps for various devices such as cell phones and PDA's at http://www.google.com/gmm.
Microsoft's http://maps.live.com.
From the standpoint of playing with latitude and longitude, Microsoft's Live Search offers the opposite capability from Google Maps. The advantage of Microsoft's Live Search is that it allows you to easily get the coordinates of a point. The trick is to select Share above the map and then View permalink. This link will contain the latitude and longitude for the center of the map. To center the map on the desired point, double click the desired point.
The latitude and longitude is imbedded in the URL, but it is easy to find. For example: http://maps.live.com/default.aspx?v=2&cp=28.547913~-81.375393&style=h&lvl=19&tilt=-90&dir=0&alt=-1000&scene=3887642&encType=1 represents a map with the center at N28.547913W81.375393.
Use Google Maps to find the location for a pair of coordinates and use Live Search to find the coordinates for a location on the map.
Google Earth http://earth.google.com
The previous two sites are quickly accessible and do not require that you install any software. Google Earth requires that you install software, but it is a very impressive program. This allows you to find the location of coordinates or the coordinates for a location. You can even rotate the maps and see things like mountains in 3-D. There are plug-ins and layers for a variety of things such as allowing you to see photos of locations on the maps.
NASA World Wind, http://worldwind.arc.nasa.gov
Google Earth has stolen some of World Wind's thunder, but World Wind is still an impressive program. You can view mountains in 3-D and zoom in even closer using satellite imagery. However, World Wind requires a fairly up to date and/or powerful computer as well as broadband internet access. The initial download is over 250 MB. As you zoom in World Wind automatically downloads satellite imagery. A tutorial is available at http://ified.ca/IntroToWW/IntroToWW.html.
Degree Confluence Project, http://www.confluence.org/
The idea of this project is to gather photographs of the earth at the intersection of every whole degree increment of latitude and longitude.
Terraserver USA, www.terraserver-usa.com
You can look up an address (U.S. only) and get a latitude and longitude. You can also input a latitude and longitude and get the photo. This site has some nice features, but the the zoom causes a map shift. A nice feature is that you can change the map size and if you select details to the right and above the image, you will get a latitude and longitude grid overlay.
Terraserver, www.terraserver.com
Terraserver and Terraserver- USA were once the same company, but have split. To get more detail than 8 meters per pixel, you will have to subscribe. There is quite a bit of content. One thing that I really like about this site is that as you move the cursor around the image the latitude and longitude shown to the left reflects the cursor position.
Encarta Atlas (online), www.encarta.com and follow the Atlas link or http://encarta.msn.com/encnet/features/mapcenter/map.aspx
This page has an interactive globe. The default size is small, but you can select a bigger size. Clicking on the image re-centers and zooms. You can select the zoom bar above the image to zoom faster, and you can select the north, east, south, and west links along the edge to rotate the globe.
Encarta Atlas (cd-rom or DVD)
There are different versions. The Encarta Reference Library has an interactive globe. I have seen this produce at a relatively inexpensive price after rebate at Costco. The globe is similar to the online version except that it works much faster. In addition to the grids, there is a locator tool that will show the latitude and longitude of the mouse pointer.
Microsoft Streets and Trips (cd-rom)
This is a road mapping program for the U.S. and Canada. If you select TOOLS -> LOCATION SENSOR on the menu bar, the latitude and longitude of the mouse pointer will be displayed. I have also seen this program at Costco for a good price after rebate.
Delorme, www.delorme.com
Delorme sells a variety of mapping products. Most of the Delorme products that I have used have the ability to show latitude and longitude. Most of the Delorme products also allow the printing of a latitude and longitude grid in addition to just displaying the location of the mouse pointer. However, I like the quality of Microsoft Streets and Trips even if it is unable to print with a latitude and longitude grid.
Ordinary Road Maps
Many ordinary road maps now have a latitude and longitude grids. Many do not, so you will have to look at the map to see whether or not it has latitude and longitude. For example, the Rand McNally Orlando Metro street map, the Orlando street atlas, and the Eastern U.S. road maps all have latitude longitude grids. DeLorme has the Atlas and Gazetteer series for each state which has a latitude and longitude grid. These maps are available from a wide variety of ordinary retailers such as Walmart and Target.
A trip to the travel section of your local Borders or Barnes and Noble will turn up several maps from around the world that have latitude and longitude grids.
GPS and the manufacturers' mapping software
Needless to say, a mapping GPS and the associated manufactures' software is an excellent tool for finding latitude and longitude. My preference is Garmin.
Photomaps USA, www.jdmcox.com
This is a program that downloads free aerial photographs and tiles them together. It is then possible to create waypoints to upload to a GPS receiver and download tracks from a GPS receiver to display on the aerial photographs. As you move the mouse pointer around the screen, the latitude and longitude of the cursor will be displayed
Mulitmap, www.multimap.com
The latitude and longitude is shown below the map in the "Information" block.
Maporama, www.maporama.com
Maporama has worldwide coverage. The latitude and longitude is shown to the left and below the map under the Information heading.
Basic GPS Navigation, www.cockpitgps.com or www.smallboatgps.com
If you want to learn to navigate with GPS, this my downloadable book on the subject. If you are a teacher or Saint James student or parent, ignore the beg for payment -- heck, everyone does anyway.
Celestial Navigation and compact disk sextant, http://www.tecepe.com.br/nav/
It is possible to find your position using the position of the stars and planets. This is not a skill that I have mastered, but it has always intrigued me. This site has an explanation of celestial navigation as well as plans to build a sextant with a compact disk and some mirrors. While learning celestial navigation and building a sextant is probably beyond sixth grade level, it is might be of interest for high school. For that matter, it is a project on my to do list. Thanks to Ron McConnell for sending this link.
The earth is almost a sphere, but not quite. The radius along the axis is 3949.9 miles (6,356.7 km) and the radius of the equator is it is 3963.2 miles (6,378.1 km). This is a difference of 13.3 miles (42.8 km). This is still very round, the difference is only 1/298 of the equatorial radius. If you are looking at a piece of paper with the cross section, you would probably never notice it and swear that it was a circle. The mathematical model for the earth with the fattened equator is referred to as a spheroid. I should add that the earth varies slightly from this spheroid, but that is another discussion.
The equator and the equatorial plane is pretty easy to visualize. The equatorial plane is the slice of earth that divides the earth in half and is perpendicular to the earth's axis. Before we move on to latitude and longitude, if you split the earth in two along the equatorial plane, you divide the world into two hemispheres -- the northern and southern.
The concept of the equatorial plane is important, because latitude is measured relative it. Latitude is the angle that a perpendicular line from the surface of the spheroid intersects the equatorial plane. If the earth were a perfect sphere, then the line would intersect at the center of the earth. Due to the slight fattening of the earth at the equator, the perpendicular line misses the center of the earth slightly. The distance that the line in Figure 1 misses the center is exaggerated to show the concept. If this were drawn to scale, you would probably not even notice that the line did not pass through the center.
Figure 1: Courtesy of Peter Dana
www.pdana.com
If you divide the earth into latitudes, lines of equal latitude are parallel to each other and are often referred to as parallels.
http://www.hammondmap.com/sites/hammond/geography/latlong1.html
Due to the tilt of the earth's axis, the orientation of the sun changes with the seasons. This creates some special parallels.
Tropic of Cancer and Capricorn: The farthest north that the sun is directly overhead is known as the Tropic of Cancer. The farthest south that the sun is directly overhead is known as the Tropic of Capricorn. These latitudes are approximately 23.5 degrees north and south respectively. The sun is above the Tropic of Cancer at the summer solstice which is the longest day in the year in the northern hemisphere. The sun is above the tropic of Capricorn at the winter solstice, which is the shortest day of the year in the northern hemisphere. Although the days may differ slightly, the summer solstice is approximately June 22 and the winter solstice is approximately December 22.
Arctic and Antarctic circles: The further north or south that you go, the more the time of year has an effect on the length of the day. If you go far enough north, there is at least one day in the winter where the sun never rises and one day in the summer that the sun never sets. Likewise, the same thing happens towards the southern pole, except at opposite times from the north pole. These circles are known as the Arctic circle in the north and the Antarctic circle in the south. The latitude of these parallels is approximately 66 degrees. The north and south poles are at 90 degrees.
One of the best ways to visualize longitude is to peel an orange. The surface of these slices are referred to as meridians.
http://www.hammondmap.com/sites/hammond/geography/latlong1.html
The 0 degree meridian is referred to as the prime meridian. The prime meridian could be placed anywhere as long as everybody used the same reference. The standard chosen by the International Meridian Conference in 1884 is to use the meridian that passes through the Royal Observatory in Greenwich, England as zero longitude. Longitudes are measured west or east of the prime meridian.
Local noon is the time that the sun reaches its highest point during the day. Due to the rotation of the earth, this occurs at different times for different longitudes. Using this noon reference the time changes about one hour per each 15 degrees of longitude or 4 minutes per each degree of longitude. Tampa is a little more than 1 degree of longitude west of Orlando. This means that Tampa would be 4 minutes behind Orlando if we based time on the sun being noon. With the invention of railroads, using local time became very inconvenient. In 1884 the world was divided up into time zones. Everywhere within the same time zone will use the same time. Instead of being 4 minutes apart, Orlando and Tampa use the same time because they are in the same time zone.
http://worldatlas.com/aatlas/infopage/timezonz.htm
Just as longitude is referenced to the prime meridian, time zones are referenced to the time in Greenwich, England which is referred to as Greenwich Mean Time, GMT. Generally, the time zones are aligned by longitude with some adjustments so that the breaks in the time zone occurs at a state or national border instead of a specific meridian. One notable exception is China where the whole country is GMT + 8 hours.
Another interesting aspect of longitude is that measuring longitude has been harder than measuring latitude. It is possible to measure latitude by referencing stars. For example, if you measure the angle of Polaris, the North Star, above the horizon this will give you a good approximation of latitude. Since the earth rotates, measuring longitude has been much more difficult. Many lives were lost at sea due to the lack of ability to measure longitude. In the late 1700's, John Harrison developed an accurate marine chronometer (clock) that allowed longitude to be measured from the angle of stars as well as taking the time into account. This is a fascinating story worth further reading. A good synopsis is available at http://en.wikipedia.org/wiki/John_Harrison.
If you know a latitude and longitude you can pinpoint a location anywhere on earth:
http://www.hammondmap.com/sites/hammond/geography/latlong1.html
It's easy to mix up latitude and longitude. Here are two tricks for remembering which is which.
If you mispronounce latitude in your mind as laddertude, you can think of the rungs on a ladder which are aligned the same direction as rungs on a ladder.
Jimmy Buffet has a song with the lyrics, "changes in latitude - changes in attitude." The point of this is that your attitude is going to be much better in the warmth of Florida than in the cold dark winter of Maine.
Latitudes and longitudes are expressed in degrees. However, the increments of less than one degree can be expressed as a decimal, minutes, or minutes and seconds. Minutes and seconds work like they do with time. There are 60 minutes in a degree and 60 seconds in a minute. The math is relatively easy. Additionally, there are online calculators and many scientific calculators that have a conversion button. The calculator button may be labeled hours, minutes, seconds instead of degrees, minutes, and seconds. However, it should not make any difference in the functioning of the conversion.
Longitudes can be written with an E or W for east or west. Latitudes have N or S for north or south. Optionally, a negative sign is usually used for west longitudes if there is not E or W and south latitudes if there is not a N or S.
Example:
Lets take a latitude of 28.54623 degrees.
If we multiply the .54623 by 60, then we can write this latitude as 28 degrees 32.7738 minutes. We can further take the minutes and express them as seconds. Multiplying .7738 by 60, then we have 28 degrees 32 minutes and 46.428 seconds. This is often expressed as 28 32' 46.428". If we had a number with degrees, minutes, and seconds, we would divide the seconds by 60 and add that to the minutes and divide the minutes by 60 to get the decimal portion of the number.
In our example: 28.54623, 28 32.7738', and 28 32' 46.428" are different ways of expressing the same value.
A nice online converter is available at http://www.terraserver.com/tools/degrees_converter.asp.
Geocaching is basically a high tech scavenger hunt. Often the cache is hidden in a water tight container such as Tupperware. The idea is that you use a GPS to find something that is hidden. Depending on the type of cache, you sign a logbook, exchange something in the cache for something else, or some other variation. Often the location for the cache is given as a latitude and longitude. One of the original sites, if not the original, is www.geocaching.com. You can also Google on "geocache" or "geocaching."