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Academy Curricular Exchange
Columbia Education Center
Science


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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John Kurilecjmk@ofcn.org




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