Earth 201 lab1 question PDF

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Summary

Great circles mark the shortest path between two points along the surface of any sphere or planet.
More specifically, a great circle is any circle made at the surface of the Earth by a flat plane that goes through the
center point of Earth, and bisects the planet into two equal halves. T...

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EARTH201 Lab 1 - The Globe, Maps, and Isolines Part A: Spherical Geometry and the Globe Lines of latitude and longitude are used to locate and describe the position of any place on the surface of the Earth. The Greek geographer, mathematician, and astronomer Ptolemy (c. AD 100) produced the first known maps where lines representing latitude were recorded. Because the surface of the Earth is very close to a sphere, he divided it into 360 degrees (360˚), each degree having 60 minutes (60'), and each minute 60 seconds (60"). Today we basically continue to use the same coordinate system. From a couple of reference lines (Equator and Prime Meridian), we use degrees, minutes, and seconds, of arc to fully describe the position of any point on the globe. For Example: latitude 34˚ 12' 31" N

longitude 77˚ 03' 41" W

This notation is used by navigators in ships and planes. Some scientists convert minutes and seconds to the decimal system, so that the above coordinates become: 34.2086˚N

77.0614˚W

They do this by making a ratio of the number of minutes given divided by the number of minutes in a degree and adding this to the degrees given. The same procedure works for seconds of arc. For the above latitude, for example: or: add 12/60 to 31/3600 = 0.2086 + 34 = 34.2086 degrees 1. Using the above example, convert the following latitude and longitude from degrees, minutes, and seconds to degrees (four decimal places please) a) 19˚ 35' 14" N

_____________

b) 65˚ 39' 26" E

_____________

2. One degree of latitude is the same distance of 110.58 km (68.71 miles) everywhere on Earth. What is the length of one minute of latitude? Of one second of latitude? Show your work. (Four decimal places please)

a) length of 1 min.: ____________ km

______________ mi

b) length of 1 sec.: ____________ km

_______________ mi

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3. The latitude of the UM’s Central Campus is 42° 16' 36" N. If you were to drive from there to Old Mission Point (Grand Traverse Bay) in western Michigan, which is located on the 45th parallel, what is the exact north-south distance that you will have covered? https://www.mnmuseumofthems.org/45th/OldMission.html Please give your answer to 2 decimal places in both kilometers and miles, and show your work! (hint: first convert UM’s latitude to decimal units, then take the difference to find the answer)

4. This one is a bit tricky, but give it a try. First, some background: we can all agree that the Earth makes one full rotation on its axis each 24 hour day. That means that as you sit here doing this lab, you are being whirled around prey quickly in space. But the velocity at which you are spinning varies with latitude, with a minimum at the poles (velocity=0), and a maximum at the equator (approximately 1,038 miles/hour). You get that value by dividing the circumference of the Earth at the Equator (24,900 miles) by 24 hours. Later in the semester, we will see that this variation in rotational velocities by latitude creates a “Coriolis effect“ which affects both oceanic and atmospheric circulation paerns. So the question is, what is your linear velocity in miles per hour based on your location on Earth? Assume a) that you are in Ann Arbor at 42˚ N latitude, b) that the radius of the earth is 3963 miles, and that c) the Earth turns exactly 360˚ in 24 hours. (Hint: Find radius of the small circle on which you travel, then calculate the circumference {2π r = Circumference}, and finally calculate the rate { Rate = Distance/Time}.) Show all work! (Hint #2: it is possible to do this using just the cosine function on your calculator and the latitude)

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Part B: Position on a Map (substitute the world maps in lab for the web link) 1.

Using the world map link provided here, find the latitude and longitude to the nearest degree (no decimal places necessary, but use E-W and N-S) of these small nations: hps://www.mapsofworld.com/world-maps/world-map-with-latitude-and-longitude.html (hint: use the latitude-longitude search engine “By Country”)

Albania Andorra Aruba Belize Malta Burundi Quatar Rwanda

Latitude (˚) ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________

Longitude (˚) ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________

2. Give the approximate latitude and longitude (as above) of the University of Michigan - Ann Arbor.

3. Where is your hometown and what is its approximate latitude and longitude? Place: ________________________

Lat & Long: ________________________

Part C: Great-Circle Routes and Rhumb Lines Great circles mark the shortest path between two points along the surface of any sphere or planet. More specifically, a great circle is any circle made at the surface of the Earth by a flat plane that goes through the center point of Earth, and bisects the planet into two equal halves. The equator and all meridians are great circles. The fact that great circles represent the shortest path between two points on the surface of the Earth is not always apparent from maps which are flat, 2-dimensional representations of the Earth’s curved surface. Only a globe will show this fact clearly and without distortion. Rhumb lines are lines of constant direction on a flat map projection of the Earth. On a navigational chart, a great circle route is first laid out between the origin and destination (since this is the shortest distance between two points). This route is then divided up into a series of straight legs (tangents), each one being a rhumb line. At the end of each leg, a change of course is made in order to follow the great circle path. Commercial airline pilots still use this technique to navigate the globe.

Remember: Lines of latitude are called parallels. Lines of longitude are called meridians. Which parallel is also a great circle (one word answer)? _______________

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Use the Mercator map above to answer the following 5 questions: 1. If a pilot follows the great circle course ploed above from Portland, Oregon to Cairo, Egypt, at what point would you be flying due east? Locate this point on the Mercator map. Give the location (in lat. and long.) of that point. (Hint: what latitude line, or parallel, is represented by a rhumb line at this point?)

2. When you’re departing Portland, in what general compass direction are you headed (N, NW, W, SW, S, SE, E, NE)?

3. As you pass over Europe, what is your compass direction?

4. Examine the alternate routes from Rio de Janeiro to Capetown. Explain why the rhumb line is only slightly longer than the great circle, as compared with the two lines/arcs for Portland - Cairo.

5. In view of your explanation in question 4, can you predict where on the globe the great circle route and the rhumb line are the same line? (There could be two answers.)

Part D: Using graphic scales to measure distances (substitute maps in the lab for this) For this exercise we will be using the Ann Arbor East Quadrangle 7.5’ Topographic Map, produced by the U.S. Geological Survey (USGS) in 1973. Please answer the following questions, using the pdf version of the map your computer screen (you can assume that the answers are the same as if you had the full size map version to work with).

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1. a. What is the fractional scale given on this map?

b.

How many ‘feet on the ground’ are represented by an inch on the map? (hint: 12 inches = 1 foot)

c. How many kilometers on the ground are equivalent to a centimeter on the map? (100,000 cm = 1 km).

2.

At the boom of the map, the elevation contour interval (i.e., height above sea level) is given as 10 ft. Please answer the following questions: a) On the west side of the map along the Huron River, what is the elevation of the Huron River in feet above sea level (near Fairview Cemetery)? b) On UM Central Campus (west side of the map), there is a benchmark labeled BM879, which is a geodetic survey marker recording feet above sea level. How high above the Huron River is this point on UM’s campus (you can use your answer in part A to answer this)?

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Part E: The basics of topographic maps Throughout the rest of the semester you will be looking at a number of different maps, and asked to interpret them. The maps you are probably used to seeing are ones that give you the location of roads, buildings, and landmarks relative to each other, with a scale to translate the map distances to real distances as you navigate the Earth’s surface. These kinds of maps are called planimetric maps. However, a map can be constructed to give more information than just location. We can make maps that show us topography ("the lay of the land"), temperature variation, pollution, or rainfall - a sort of "third dimension" overlaid on the topographic map. We do this by constructing isolines, or lines connecting points of equal value. Isolines are also called contour lines. In the example of a topographic map, this means a line connecting all points of equal elevation above mean sea level (i.e., an elevation contour). Not all lines connecting all elevations are drawn, just one line for every e.g., 20 feet change in elevation etc. This vertical distance change between contour lines is called the contour interval, and their paerns allow the viewer to ascertain the shape of the land at a single glance.

A few things to remember about contour lines: 1. Contour lines never cross (although they may overlap). 2. Contour lines never end abruptly. They always close on themselves, though they may run off a particular map before they do so. 3. Contour intervals are constant over the entire map. 4. Contour lines that are very closely spaced = an abrupt change in elevation (steep slope); widely spaced = gradual change or flat (gentle slope). 5. Contour lines crossing a stream or river will bend (or kink) to form a "V" pointing upstream, with the tip of the "V" on the stream. This is called the Rule of V’s. 6. Hachured, closed contours (with short ‘whiskers’ pointing down slope), indicate a hole or a depression in the land, sometimes filled with water (e.g., a pond). 7. Elevations of specific places are given. These are usually labeled BM (bench mark, used for surveying) as in the above example on the Ann Arbor East Quadrangle Map.

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1. You are camped with your friend, an energetic hiker, and her 2 hiking partners on the shores of Lake Longbegone. Your only map of the area is Map 1, above. After studying the map, you find the contour interval to be ________ feet. You can make the map easier to read by labeling each of the contour lines. 2. Your hiker friend wants to climb to the highest point on the map. Which leer best represents the highest point? ________ How high is it?__________ 3. She also wants to climb the steepest slope in the area. Where is this slope? ____________________ How steep is it? (give a ratio of number of vertical feet to horizontal foot, or “rise over run”) ____________________ 4. Her hiking partners are siing by the lake at point D and decide to climb to point C to enjoy the view. Describe the route that would have the least vertical climb (i.e. would be easiest)? What is the elevation of point C? ________________ 5. During the hike they take a wrong turn and end up at point B. What is the elevation at point B? (Careful!)

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6. Somehow, they manage to make it to point A. What is the elevation? ___________ 7. They finally see her waving to them from point C, and since she has the pack with the lunches, they decide to join her. What is the easiest route you can choose for them (the least amount of up and down, or least elevation gain)?

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Part F: Topographical Cross-section This exercise will help you to visualize what information a topographic map gives you. You will be constructing a topographic profile across the map, as if you took the landform the map shows and cut it along the line, then looked at the profile from the side. Aached is a sample topographic map, Map 2, and a line A B, called a section line, which cuts across it. A graph is given below the map. A brief set of instructions is given below. Step #1. Determine the lowest and highest points along the section line A - B. Step #2. Label the left vertical axis of the graph below the map with an appropriate range of elevations. Step #3. For every point along the section line A - B where a contour line crosses the section line, draw a vertical line down to the graph below which crosses the entire graph. Step #4. On the graph, make a mark where the vertical line from a contour line crosses the same elevation line on the graph. Step #5. After marking all of the spots on the cross section, draw a smoothly curving line which connects the marks. This should give you your cross-section!

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Part G: Drawing an Isoline map (can do this in lab with the students using projector) Now that you have used contour lines, you can apply your knowledge to other isolines, such as temperature, rainfall, or pollution. In order to complete this map, you will have to interpolate where the isolines go, as there are few data points. Interpolation is an educated guess, done by dividing the distance between two known points into equally spaced divisions, and then running the isoline through the appropriate division. For example:

Your interpolated isolines should be as accurate as possible by using a ruler. You need not interpolate between all points, only the ones that adequately define the isoline. Remember, lines can go off the map without closing! 1. Complete the isoline map of average annual precipitation for the state of Nebraska. Interpolate and draw in the isolines for 15, 18, 21, 23, 24, 27, 30, 33, and 36 inches of annual precipitation, and neatly label the lines. 2. Where is the region of most precipitation? (ex: NE corner of map)

_________

3. Across which region does the average annual precipitation change most? (ex: NE corner of map). __________ 4. Describe in two sentences how the precipitation varies from west to east across your map of Nebraska.

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