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TITLE: MEASURING THE DIAMETER OF THE SUN AUTHOR: JANE RICH, Shawnee High School, Shawnee, OK OVERVIEW: The earth is approximately 150,000,000 km from the sun. This distance varies somewhat with the seasons because of Earth's elliptical orbit. Yet, a simple instrument can be constructed which will provide measurement data that permits a relatively accurate measurement of the sun's diameter. The relationship that will be used is: diameter of sun (km) = diameter of sun's image (mm) -------------------- --------------------------- distance to sun (km) distance between cards (mm) From this relationship we can derive a formula: Dia. of sun (km) = dia. of sun's image X dist. to sun ------------------- dist. between cards MATERIALS/RESOURCES: 2 small cardboard boxes--size not critical but should be ridged enough to hold their shape well 2 pieces stiff cardboard 10 cm X 20 cm (perhaps from a shoebox) meter stick single edged razor blade or sharp knife masking tape small piece of aluminum foil ACTIVITIES AND PROCEDURES: 1. Tape the lids of the boxes shut securely. Cut slits in opposite sides of each box, directly opposite each other. Make each slit in the form of a capitol "I" and of a size that will fit the meter stick snugly when the box is pushed on to the meter stick. If measurements and cuts are made carefully the face of the box will be perpendicular to the meter stick. This is important. Tape one box securely near one end of the meter stick but leave the other box free to slide. 2. Cut a 5 cm X 5 cm hole near one end of one piece of cardboard and cover with the aluminum foil. Tape the foil in place. Punch a very small hole near the center of the foil with a sharpened pencil lead or a pin. 3. Tape this card to the box that has been secured to the meter stick. 4. Draw two parallel lines exactly 8.0 mm apart near the center of the remaining cardboard. 5. Tape the card with the parallel lines to the face of the sliding box. Note: Be certain both cards are as nearly perpendicular to the meter stick as is reasonably possible. The lines are perpendicular to the meter stick. 6. Point the end of the meter stick that holds the foil-covered card toward the sun. CAUTION: Do not look at the sun! Move the meter stick around until the shadow of the foil-covered card falls on the other card. A bright image of the sun will appear on the sliding card. Move the sliding card until the bright image of the sun exactly fills the distance between the parallel lines. Measure the distance between the cards on the meter stick. Distance between the two cards = mm. 7. Use the formula from the theory section to calculate the diameter of the sun. Use 150,000,000 km as the distance from Earth to the sun. Calculation A: 8. Find the percent difference between your measurement of the sun's diameter and the accepted actual diameter of the sun which is 1,391,000 km. CONCLUSIONS: List factors which could account for the difference between your measurement and the accepted diameter of the sun. The calculation you made in step 8 was a test of measurement ACCURACY. What could you do to test the PRECISION of your meter stick instrument? FOR FURTHER STUDY: The actual distance between the earth and sun varies from a minimum of 147,097,000 km to a maximum of 152,086,000 km. 1. Recalculate the diameter of the sun using your distance between cards measurement and the minimum distance between the earth and sun in the formula. Calculation B: 2. Again, recalculate the diameter of the sun using your distance between cards measurement and the maximum distance between the earth and sun in the formula. Calculation C: 3. Does the accepted actual diameter of the sun fall between your calculations B and C? How do calculations B and C affect your estimation of the accuracy of your measurement as opposed to the percent difference you calculated in step B above? EXPANSION: Refer to the relationships described in the theory of this lab and derive a formula for calculation the distance from the earth to the sun. Use the measurements you can obtain from your meter stick instrument to calculate this distance. Obtain an astronomy reference which gives the actual distance between the earth and sun on a given day or week to check the accuracy of your instrument. What changes or refinements would you make in your meter stick instrument if you were to plan to chart the earth-sun distance through the remainder of the school year? How could you present the results of such a charting project in a meaningful way?

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