How to measure the diameter of the sun

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?