Week 6 (Sep. 29 Oct. 1, 3)
Read: From Astronomy to Cartography (Chap. 9) and Climates and Continents (Chap. 10).
Quiz: Monday. Covers Bede's The reckoning of time.
Homework exercises: Latitudes (Ex. 9.1), Waldseemuller's worldview (Ex. 9.2).
Laboratory exercises: Latitude and longitude observations (Ex. 9.3). How can you determine the latitude at your present location? For the latitude exercise this week, you should find and measure the altitude of Polaris using your cross staff during any evening this week. Don't look up your latitude before going out to observe! After your observation, check your latitude. How far off is your measurement? If you were a sailor, how many (nautical) miles off would you be?
Next, how can you determine your longitude? This is precisely the problem that sea-farers have faced for centuries. Answer: based on your measurements of the time of local noon. Consider how this works. If the sun passes the prime meridian in Greenwich, England, at noon, then a quarter of the way around the globe toward the Americas (at, say, 90 degrees west longitude), the sun will pass the local meridian 6 hours later than it crossed the local meridian in Greenwich. So, if one has (correctly) calibrated his wristwatch to Greenwich time, then he can determine his longitude by measuring the time of local noon at his location on the earth.
For our longitude exercise, then, you must go out on a sunny day around noon, set up a small vertical stick (gnomon), and use a sheet of paper to measure the length of the shadow every five minutes between 12:15 and 1:15 pm. Draw a line from your gnomon to the end of the shadow for each measurement. Be sure to collect enough data both before -and- after local noon so that you can clearly identify the time of the shortest shadow. Make a data table that lists the time on your clock and the length of the shadow at that time. Then, for analysis, make a clearly labelled plot (using a graphing program such as Logger Pro) that shows your shadow length (vertical axis) versus the time of day (horizontal axis). Use a fitting function to pick out the time at which the shadow is shortest. At what (clock) time is local solar noon? Put all of this data and analysis in your lab notebook.
There is one additional complication. On the day of your measurements, the sun probably did not pass the local meridian in Greenwich at exactly 12pm (local Greenwich time). At the website timeanddate.com, you can look up the exact (local) time at which the sun passed through the meridian in Greenwich on the date of your measurements. If you know how many hours and minutes later the sun passed through your local meridian (say, in Milwaukee, Wisconsin), then you can determine your longitude.
Be sure to make a scan of your lab book that includes your data, sketches, and calculations of latitude and longitude.
From astronomy to cosmography (3 videos):
Climates and continents (no videos yet…):
Homework exercises: Latitudes (Ex. 9.1), Waldseemuller's worldview (Ex. 9.2).
Laboratory exercises: Latitude and longitude observations (Ex. 9.3). How can you determine the latitude at your present location? For the latitude exercise this week, you should find and measure the altitude of Polaris using your cross staff during any evening this week. Don't look up your latitude before going out to observe! After your observation, check your latitude. How far off is your measurement? If you were a sailor, how many (nautical) miles off would you be?
Next, how can you determine your longitude? This is precisely the problem that sea-farers have faced for centuries. Answer: based on your measurements of the time of local noon. Consider how this works. If the sun passes the prime meridian in Greenwich, England, at noon, then a quarter of the way around the globe toward the Americas (at, say, 90 degrees west longitude), the sun will pass the local meridian 6 hours later than it crossed the local meridian in Greenwich. So, if one has (correctly) calibrated his wristwatch to Greenwich time, then he can determine his longitude by measuring the time of local noon at his location on the earth.
For our longitude exercise, then, you must go out on a sunny day around noon, set up a small vertical stick (gnomon), and use a sheet of paper to measure the length of the shadow every five minutes between 12:15 and 1:15 pm. Draw a line from your gnomon to the end of the shadow for each measurement. Be sure to collect enough data both before -and- after local noon so that you can clearly identify the time of the shortest shadow. Make a data table that lists the time on your clock and the length of the shadow at that time. Then, for analysis, make a clearly labelled plot (using a graphing program such as Logger Pro) that shows your shadow length (vertical axis) versus the time of day (horizontal axis). Use a fitting function to pick out the time at which the shadow is shortest. At what (clock) time is local solar noon? Put all of this data and analysis in your lab notebook.
There is one additional complication. On the day of your measurements, the sun probably did not pass the local meridian in Greenwich at exactly 12pm (local Greenwich time). At the website timeanddate.com, you can look up the exact (local) time at which the sun passed through the meridian in Greenwich on the date of your measurements. If you know how many hours and minutes later the sun passed through your local meridian (say, in Milwaukee, Wisconsin), then you can determine your longitude.
Be sure to make a scan of your lab book that includes your data, sketches, and calculations of latitude and longitude.
From astronomy to cosmography (3 videos):
Climates and continents (no videos yet…):