Longitude and Latitude
When the GPS on your cell phone shows where you are on the map, it is really giving you two numbers: your latitude and your longitude. With them, any point on Earth can be located, just as the coordinates $(x, y)$ locate a point on the plane. The difference is that here the "sheet of paper" is a sphere, and the coordinates are angles.
Meridians and Parallels
We imagine Earth as a sphere that rotates on an axis passing through the North and South Poles.
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Meridians: semicircles that run from pole to pole. The reference one is the Greenwich meridian (London), the 0° meridian.
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Parallels: circles perpendicular to the axis. The largest is the equator (the 0° parallel), which divides Earth into the Northern and Southern Hemispheres.
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Imagine you are a beginner cartographer. On your first map, you must locate the most important reference lines on Earth. Look at the diagram and match each letter with…
Imagine you are a beginner cartographer. On your first map, you must locate the most important reference lines on Earth. Look at the diagram and match each letter with its corresponding name:
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Equator.
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Greenwich Meridian.
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North Pole.
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Any parallel.
Geographic Coordinates
State which hemisphere (Northern or Southern for latitude, Eastern or Western for longitude) the following geographical points are located in: Point A: $34^\circ$ N,…
State which hemisphere (Northern or Southern for latitude, Eastern or Western for longitude) the following geographical points are located in:
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Point A: $34^\circ$ N, $120^\circ$ E
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Point B: $12^\circ$ S, $45^\circ$ W
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Point C: $89^\circ$ N, $5^\circ$ W
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Point D: $40^\circ$ S, $170^\circ$ E
An explorer has mistakenly written down the following coordinates in his diary. Explain why these coordinates are geographically impossible: a) Latitude: $105^\circ$ S,…
An explorer has mistakenly written down the following coordinates in his diary. Explain why these coordinates are geographically impossible:
- a) Latitude: $105^\circ$ S, Longitude: $20^\circ$ E.
- b) Latitude: $45^\circ$ N, Longitude: $210^\circ$ W.
Two ships, Alfa and Beta, are sailing across the Atlantic Ocean. Their coordinates are: Ship Alfa: $20^\circ$ N, $30^\circ$ W Ship Beta: $20^\circ$ N, $60^\circ$ W…
Two ships, Alfa and Beta, are sailing across the Atlantic Ocean. Their coordinates are:
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Ship Alfa: $20^\circ$ N, $30^\circ$ W
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Ship Beta: $20^\circ$ N, $60^\circ$ W
Answer giving reasons:
- a) Are they located on the same parallel or on the same meridian?
- b) Which of the two ships is closer to the Greenwich Meridian?
Distances Along a Meridian
Two cities on the same meridian are separated by an arc of a great circle. Earth's radius is about 6 371 km, so the length of a full meridian (one complete turn) is $2\pi \times 6\,371 \approx 40\,000$ km.
Two towns, Villa Sol and Villa Luna, are located on the same meridian. If Villa Sol has a latitude of $45^\circ$ N and Villa Luna has a latitude of $20^\circ$ S, how…
Two towns, Villa Sol and Villa Luna, are located on the same meridian. If Villa Sol has a latitude of $45^\circ$ N and Villa Luna has a latitude of $20^\circ$ S, how many degrees of meridian arc separate them?
Two cities, P and Q, are situated on the same meridian. City P is at $42^\circ$ N and city Q is at $15^\circ$ N. Another city, R, is situated on the same parallel as Q,…
Two cities, P and Q, are situated on the same meridian. City P is at $42^\circ$ N and city Q is at $15^\circ$ N. Another city, R, is situated on the same parallel as Q, but at a distance of $20^\circ$ longitude to the East.
Calculate, using $R = 6\,371$ km:
- a) The distance between P and Q along the meridian.
- b) The distance between Q and R along the parallel.
Which of the two distances is greater?
In navigation, the "nautical mile" is used, defined as the arc length of a meridian of $1'$ (one minute of arc). a) Calculate how many kilometers one nautical mile is…
In navigation, the "nautical mile" is used, defined as the arc length of a meridian of $1'$ (one minute of arc).
- a) Calculate how many kilometers one nautical mile is equivalent to (Radius of the Earth = $6{,}371$ km).
- b) If a sailboat has sailed along a meridian from a latitude of $30^\circ$ N to $35^\circ$ N, how many nautical miles has it traveled?
Time Zones
Earth makes a 360° turn in 24 hours, so it rotates $360° : 24 = 15°$ every hour. That is why it is divided into 24 time zones, each 15° of longitude wide. Toward the east it is later; toward the west, earlier.
We know that the Earth takes 24 hours to complete a rotation of $360^\circ$ on its axis. a) How many degrees of longitude correspond to a time difference of one hour? b)…
We know that the Earth takes 24 hours to complete a rotation of $360^\circ$ on its axis.
- a) How many degrees of longitude correspond to a time difference of one hour?
- b) If it is 12:00 noon in a city located at $0^\circ$ longitude (Greenwich), what time will it be in a city located at $30^\circ$ E?
A group of friends in Mérida, Yucatán (longitude $89^\circ$ $37'$ W) wants to watch the live launch of a rocket from Cape Canaveral (longitude $80^\circ$ $36'$ W). If…
A group of friends in Mérida, Yucatán (longitude $89^\circ$ $37'$ W) wants to watch the live launch of a rocket from Cape Canaveral (longitude $80^\circ$ $36'$ W). If the launch is scheduled for 14:30 Florida local time, and each $15^\circ$ time zone corresponds to one hour of theoretical time difference, at what time should they tune in to the live broadcast in Mérida? Use the diagram of theoretical time zones to do the calculation.
An aircraft takes off from Tokyo ($35^\circ$ N, $139^\circ$ E) at 08:00 on Monday bound for San Francisco ($37^\circ$ N, $122^\circ$ W). If the flight lasts 10 hours,…
An aircraft takes off from Tokyo ($35^\circ$ N, $139^\circ$ E) at 08:00 on Monday bound for San Francisco ($37^\circ$ N, $122^\circ$ W). If the flight lasts 10 hours, what time and day will it be in San Francisco when the aircraft lands? Take into account the date change when crossing the Greenwich antimeridian ($180^\circ$).