Gold Creek School

Noon Day Project  Page

Gold Creek School - Year 8/2002

Our Partner School for this project in March 2002 was:

Ann Arbor Girls' Middle School, Ann Arbor, Michigan, USA

This activity is coordinated by the Center for Improved Engineering and Science Education (CIESE) at the Stevens Institute of Technology in New Jersey, USA. Click here  to visit this site.

Noon Day Web Quest:

By completing the following Web Quest you will learn about Eratosthenes and how he managed to measure the circumference of the Earth about 2200 years ago.  To complete the activity you will need to visit a number of web sites and extract from them various pieces of information.  Your report should be word processed and presented in a plastic sleeve.   If you do not have access to the internet at home the work will need to be completed at school. Not having the internet at home is not an excuse for not completing this activity.

It is essential that questions as well as their answers are included in your work.  Diagrams must also be included  This activity is an important part of your work in Mathematics this term.  Please ensure that an appropriate effort is made.

Our Project

We collected our data on 19 March.  This is one day prior to the official equinox.  However, the error (uncertainty) introduced into our calculations is small.  Data was collected using a metre rule.  The time the Sun was highest in the sky on this particular day was at 1.11 pm (ESDT). This is of course 12.11 (EST).  The shadow cast at this time was found to be 67 cm in length.  The Sun angle is about 34 degrees.  Remember that the Sun angle is NOT the same as the Sun elevation in the sky.

Our partner school for this project was the Ann Arbor Girls' Middle School in Ann Arbor Michigan, USA.  They collected data on 27 March.  This was because they had many days of snow and grey skies prior to this.  The local noon for them  was calculated to be12.40 pm.  The average Sun angle was found to be 41.75 degrees.  Ann Arbor is located at 42.26 degrees North latitude and 83.73 degrees West longitude.  Note that these longitude and latitude values are given as decimals degrees rather degrees:minutes:seconds.  Either format  is completely acceptable, however the decimal degrees allows for easier graphing.

The main Internet site for this project can be found at www.k12science.org/noonday/details.html.  Many of the links shown below can be found on this page.

Task #2: The next activity for you to do is to explain the technique that Eratosthenes used to determine the circumference of the Earth.  To help you do this you will need to visit the site,

http://k12science.org/noonday/noon1.html

1) When and what evidence convinced people, such as Aristotle, that the Earth might be spherical in shape?

2) Eratosthenes worked at a place which assisted his study of the Earth's shape.  Where did he work?

3) Two methods to measure the circumference of the Earth are mentioned at,

http://k12science.org/noonday/options.html

What are these methods.

4) At the page,

http://k12science.org/noonday/option3a.html

you will find the discussion of the technique that Eratosthenes used.  The excerpt from Carl  Sagen's Cosmos that was given out in class should also be read.  A link to Sagen's page can  be found on the page that you are now on.  Outline the approach that Eratosthenes used.  Diagrams will need to be included here.  There is a good diagram at,

http://k12science.stevens-tech.edu/noonday/story.html

http://k12science.stevens-tech.edu/~ihor/sketch/aha8.html

6)  Eratosthenes' technique is based on geometry.  The particular geometry that he used is presented on page 316 of your textbook.  On this particular page look carefully at the section titled Parallel Lines.  Which diagram shown here relates to the picture found on page

http://k12science.stevens-tech.edu/noonday/story.html

Task #3: Now that you have the background theory out of the way it is time to calculate the distance between the two points on the Earth's surface. Eratosthenes found the distance between Alexandria and Syene by having someone pace the distance.  We are unable to do this so we will rely on other methods.  It is essential that the distance between the two places on Earth be the north - south distances between their respective lines of latitude.  That means that at this time of the year the Sun is directly over the Equator.  This represents Eratosthenes' Syene.  Alexandria is represented by Canberra or Ann Arbor.

Fortunately for us we are able to use the Internet to do our calculations.  Firstly visit the page,

http://kencole.org/calcdist.htm

Once you are on this page click the link How Far Is It.  Read carefully once at this site to determine how the data should be entered.  Firstly find the distance between Canberra and the Equator and then find the distance between the Equator and Ann Arbor.  Make sure you record the kilometres rather than the miles. Record this information carefully on the world map that you have already used.

Task #4: Now that you know the distance between Canberra and Ann Arbor you need to determine the central angle.  Remember that it was this remarkable association that Eratosthenes made between Sun angle and central angle that allowed this particular technique to work. Before you do this you will need to construct a scale diagram showing a metre rule creating a shadow of 67 cm.  The angle of elevation of the Sun and the Sun angle can then be measured using a protractor.  Use a piece of graph paper for this scale diagram.  Make sure that the diagram is very carefully labelled and has an appropriate title.

To calculate the central angle you will need to check out the information on the page.

You will also need to check out Case 2 on page

http://k12science.stevens-tech.edu/noonday/proof2.html

so that you can use information on Sun angles in Canberra and Ann Arbor.  Make sure you include the diagram on this page to show how you are going to calculate the appropriate central angle.

Show the details of your calculations.

Task #5: Now that we know the distance between line of latitude of Canberra and and Ann Arbor and we know the central angle it is now time to calculate the circumference of the Earth.  To help you with this task you should visit the page,

http://k12science.stevens-tech.edu/noonday/example2.html

The example used here assumes that both cities are in the same hemisphere of Earth, in this case the Northern hemisphere.  Nevertheless the discussion of how to convert the measurement of the central angle of the Earth and the vertical north - south distance between two places to a measurement of the Earth's circumference is still relevant.

In your report you will be expected to show all necessary calculations as well as the final value for the Earth's circumference.  The actual circumference of the Earth is given on the page immediately above.

Visit the site,

http://www.spaceref.com/directory/Astronomy/Planets/Earth/

and record at least ten other facts about the Earth.

Task #6: The value that you obtained for the circumference of the Earth may not be in agreement with value that is now accepted as the correct value.  Discuss which factors could account for this difference.  Here you will need to do some calculations.  For example if the central angle was one degree in error, what effect would this have on the determination of the circumference?  What effect does 1, 10 or 100 km error in distance measurements between the two cities have on the calculation of the circumference?

Task #7: The table below show data lodged on the main web site as at 30 March.  You will notice that Gold Creek School is the last entry.  If you visit the site,

http://k12science.org/noonday/asp/viewdata.asp

the most recent data can be viewed.  You will notice that the data below has been modified slightly to allow for easier analysis.  For instance north and south latitude is changed to + and - respectively.  Likewise east and west longitude has been changed to + and - respectively.  A number of non essential columns have also been deleted.

The data for Alice Deal Junior High School is not correct.

1) What corrections need to be made with this.data?

Also the data for Bayside High School is in a non consistent format.

2) What change needs to be made to this data?

3) What relationship appears to exist between Sun angle and latitude?  Briefly discuss.

Last Friday I received notification from the Noon Day coordinator asking about the relationship mentioned in Q3.  If you have time check out the following page and see if you can come up with an answer to the question that is posed there.

http://www.k12science.org/noonday/viewsundata.html

Data Table as at 30 March 2002

School Name City State Country Date Latitude

N = +

S = -

Longitude

E = +

W = -

Device Used Date of Measurement Length of Device

(cm)

(cm)

Angle of Sun

(deg)

Antilles High School  Guaynabo  Puerto Rico  Puerto Rico  3/21/02  18.4  - 66.1 Meter Stick  March 20,2002.  100  31.7 18
Edison Middle School  West Orange  New Jersey  USA  3/21/02  40:47:34  - 74:15:49  meter stick  3/21/02  100 78 38
Forest Lake Homeschool  Montrose  PA  USA  3/23/02  41.8  - 75.9  Meter Stick  March 21, 2002  100 87.31  41
Home School  Norfolk  VA  USA  3/24/02  36:55:00  - 76:14:00  Meter stick  03/22/02  100 72.0  35.8
MacKinnon Middle School  Wharton  New Jersey  USA  3/25/02  40.9  - 74.6  Meter Stick  March 21, 2002  100 87.04  43
Georgetown-Ridge Farm High School  Georgetown  IL  USA  3/25/02  39:59:00   - 87:38:00  meter stick  3-22-02  100 81.17 39.07
Alice Deal Junior High School  Washington  DC  USA  3/25/02  38:57:09   - 77:04:32   Steel pipe  3-22-02  56  69  39
Bayside High School  Virginia Beach  VA  USA  3/26/02  36:51:00  - 76:06:00  half meter stick  3/22/02  50  35.3  35.22
University High School  Newark  New Jersey  USA  3/27/02  40.7  - 74.2  meter stick  3/21/02  100  72.4  35.9
Georgetown-Ridge Farm High School  Georgetown  IL  USA  3/27/02  40.0  -  87.6  meter stick  3-22-02  100 90.39 39.64
Paddock Elementary School  Palatine  Illinois  USA  3/27/02  42:06:30  - 88:02:56  meter stick  March 20, 2002  100 87.9 40
Gladys Hillman Jones  Newark  NJ  USA  3/28/02  40:44  - 74:11  meter stick  March 21, 2002  100   78  39
Gold Creek School  Canberra  ACT  AUSTRALIA  3/29/02   - 35.28  + 149.22  Metre stick  19 March   100  67  34

Noon Day Project - September 2002

WebQuest: Completion of the following material will form part of your homework over the next few weeks.  You will need to have access to the Internet to complete the work.  This can occur on Mondays and Fridays in our specific computer time or at other times in the classroom during the week.  You are expected to create a word processing document.  You will then cut and paste appropriate material into this document.  All questions that are asked need to be answered in your word processing document as well.  Your work when completed is then printed and pasted into your homework book.  The original word processing document will remain in your folder.  Remember to name your document appropriately.  Check the material below to revise naming conventions.

For the computer activities you may work with a partner.  You will need to print two copies of any material produced, however.

File Names - A reminder: When you are saving any files that you create it is important to use the standard naming convention, i.e.,

[your first name] [brief descriptive title] [date]

for example

sophienoonday14_10

Saving your work - Another reminder:  It is also important to save your material to the correct folder.  This is especially the case when you are working in the technology lab.  When you save in the tech lab you need to go to the Users folder.  You will need to find your folder.  It will have the same name as your  log in user name.  This will be the only folder that you have access to.  Other folders will not allow you access.

Homework Due 21 October:

If you were in my maths group at the beginning of the year then the Noon Day Project will be familiar to you.  This internet project is always done at the time of the autumn and spring equinoxes.  Although it can in theory be done at any time of the year.  Our data was collected in the last week of term 3.

What this project aims to do is to calculate the diameter of the Earth using a technique that was used by a Greek scientist called Eratosthenes about 2200 year ago.  The technique used is based upon determining the length of a shadow cast at noon by vertical sticks placed in the ground at different points on the Earth's surface.

Read the material written by Karl Sagan by clicking on the following link

http://k12science.org/noonday/cosmos.html

Copy and paste this material into your word document.  Make sure that the text is formatted differently from the answers to your questions.  The following questions need to be copied and pasted prior to being answered  in your word document.

Q1) In which city did Eratosthenes live?

Q2) He was a director of one of the great institutions in this city.  What was its name?

Q3) What did he read that was of great interest to him?

Q4) What experiment did he then carry out?  What were the results of this experiment?

Q5) How did Eratosthenes explain the information he had read in the book and the results of his experiment?

Q6) What other pieces of information did Eratosthenes need to know before he could calculate the circumference of the Earth.

The data that was collected in March is shown in the table above.  You will now need visit the Noon Day site to view the data collected in September.  The following link will take you to the data.

http://k12science.org/../noonday/asp/viewdata.asp

Once you have the data you will need to copy and paste this to a new word processing document.  Because the data is very wide you will need to format you page in landscape format before you paste. From the File menu in Word choose the Page Setup command.  Select Landscape.  Part of the dialog box is shown below.

You will need to adjust the column widths so that the table will fit across an A4 page.  The following columns can be deleted.  Teacher Name, State, Date, Device Used, Partner City, Partner State/Country.  Once these columns are deleted then the data will fit easily across the page.  In fact you may find now that you can change your page to portrait orientation.

Once your table is completed in Word it will now be copied and pasted into an Excel spreadsheet so that it can be manipulated further.  From Word select the entire table.  Open Excel and choose paste from the Edit menu.  Save your Excel document as

Our first task will be to determine the average circumference of the Earth from the data as calculated by many of the schools.  To do this all the data in the Circumference column must be numerical.  This means that you will need to remove the symbol km and the word miles from some of the data.  Also you will need to convert the miles to kilometres so that we have consistent units.  The conversion can be determined using the following formula

Kilometres = 8/5 x miles

Insert two rows above the top line of the table.  To do this highlight rows 1 and 2.  Then from the Insert menu choose Rows.  In the top row provide a title for your table - Table of Noon Day Data from September 2002.  Now highlight row 5 and insert a new row below the titles.  Into cell I5 type the word Average. Into cell J5 create the formula for calculating this average.  To do this type

= average(

Once you have created the first ( drag your mouse down the Circumference column.  When you have reached the end create the other bracket as shown below

If your formula works you should now have a number in cell J5.  Once you have completed creating this value print a copy of your Word and Excel tables.  Finally answer Q7.

Q7) What was the average circumference of the Earth as calculated by Excel.

You have now reached the end of the material that will be due 21 October.

Noon Day Project  - Part 2

The following material will need to be completed by Monday

So far we have extracted the table of data from the Noon Day web site and we have created an Excel spreadsheet.  We have also written a formula to calculate an average value for the circumference of the Earth.

We will now continue to modify the spreadsheet so that we are able to analyse the data in more detail.

The first four rows of the table are shown below.

 School Name City Country Latitude Longitude Date of Measure Length of Device Length of Shadow Angle of Sun Circum- ference Average 38764.99 Mission Viejo High School Mission Viejo USA 33:35:59.75 N 117:40:17.05 W 9/20/02 1 meter 0.609 meter 31.34 42887.78 Elmira High School Elmira USA 44 03.57 N 123 21.15 W 9-23-02 100 cm 109 cm 47.5 37071

Task #1:  Consistent Data:  When you look down any one column in the table you will notice that different units or different ways have been used to display the data.  In  the Length of Shadow column centimetre, metre and inch data has been used.  The date column uses both the American abbreviation for dates and other systems have been used.  In the longitude and latitude columns both decimal degrees and hours minutes seconds have been used.  Your task now is to make all of the data consistent

a) Length of Device and Length of Shadow.  In the cell directly below the column titles type the word "metre". Working down each column convert each measurement to metres.  You will need to remove any letters or words from each cell.  Each cell should only contain a number.  If the measurement is in inches use the calculator found in Accessories to carry out the conversion. The conversion factor is 1 inch equals 2.54 cm.

b) Longitude and Latitude: All data here needs to be changed to decimal degrees.  If the longitude is E a positive value is entered if it is W a negative value is entered.  If the latitude is N a positive value is entered, if it is S a negative value is entered.  If the longitude or latitude looks something like the following 45:35:56, then it is in hours:minutes:seconds format.  To change this to decimal format ignore the seconds, ie the 56 in the example, take the 35 and divide this by 60.   The value for this example is 0.58.  The decimal degrees are then expressed as 45.58.  In the cell directly beneath the column title type the word degrees. Also include the following key, for longitude, + = E, - = W and for latitude - = S, + = N

c) Sun Angle:  In this column the data needs to be changed to a number only by removing any text elements, i.e., words or letters.  In the cell directly below the column titles type the word degrees.