Extra Credit Assignment

Due Friday, Feb. 20

A.

1.ааааааа Find Polaris, the north star, and measure its elevation in degrees from the horizon using your sextant. (See below) This elevation gives your latitude.

2.ааааааа Explain why the elevation of the north star is equal to your latitude. You may want to use a diagram.

3.ааааааа Calculate the circumference of the earth from your measurement of our latitude and using the fact that we are about 3000 miles from the equator. Show how you got your result.

 

B.

1. Make a gnomon about 6 to 10 inches long and use it to determine local noon. Make measurements of the length and direction of the shadow from about 11:45 to 12:15. Measure about every 5 minutes and mark each point on a piece of paper. Hand in the paper.

2. What is the length of the shadow at noon? What is the angle at which the sun's rays hit the stick? This equals the angle made by the gnomon and the hypotenuse of the triangle made by the base of the stick, its top, and the end of the shadow. The complement of this angle is the elevation of the sun off the horizon, or the angle between the ground and the hypotenuse.

3. Use your sextant to measure the angle of the sun in the sky as close to noon as you can. Don't look directly at the sun with your sextant move it from below till you start to see the bottom of the sun, then move it down from above to get the top of the suns disk and take the average of these. What is the diameter in degree's of the disc of the sun?

4. Add 0.26 degreesа to your reading of the altitude of the sun from the gnomon for every day that your reading was before the spring equinox. This will give what the altitude would be at the equinox since the altitude changes .26 degrees a day.а Altitude = Measured Altitude + (days before equinox x 0.26) The complement of this angle is your latitude. Latitude = 90- Altitude.

5. Repeat the calculation with the altitude measured from the sextant to get another latitude measurement.

6. Repeat your calculations of the circumference of the earth with these two measurements of your latitude. Which is most accurate?

 

Optional :а What is the diameter in degrees of the disc of the sun?а Draw an isosceles triangle whose smallest angle is this same angle. Use this angle to estimate how far the sun would be from the earth if it was the same size as the earth. You should use Thales's method of similar triangles.

How big would the sun be if it was 1000 miles away? 1,000,000?а 90,000,000?а Can you think of any way to tell which of these is closest to being correct just from the information available from earth with the naked eye? (Hint: Aristarchus of Samos could.)

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To make a sextant take a piece ofа cardboard and trace a protractor to it marking the angles along the left side of the curve. Attach a straw to the top edge of the cardboard as in the diagram to serve as a sight. Attach a string with a weight to the center of the traced protractor as in the diagram. When the sight is horizontal the string will hang straight down onto the 0 degree mark. as you raise the sextant to sight through the straw the string will move. When you sight the target hold the string where it is and read the degrees of elevation from the position of the string.