Name
_______________________________
The
Astrolabe
Ptolemy designed the astrolabe (c. 150 AD)
as an armillary ring, held vertically, on which was fit a diametrical cord with
one sight at each of its ends. Arabic craftsmen (9th-11th centuries) improved
the astrolabe to determine time from stellar or solar observations without use
of tables, though it was limited to one century and one
latitude. English poet Geoffrey Chaucer describes an astrolabe in detail
in his Treatise on the Astrolabe (1381).
The Astrolabe is useful in determining the
altitude of objects in the sky. The astronomical term altitude means
angle from the horizon and should not be confused with the aviation term
meaning height above the ground.
You will need a soda straw, a pin or needle,
string or thread, a weight, a file folder or poster board, and glue. Follow the
procedure below to construct the astrolabe.
- Glue the Quadrant below to the file folder or poster board.
- Carefully cut out the quadrant.
- Using the pin or needle push a hole through the quadrant at the
center of the quadrant circle.
- Push the string or thread through this hole, knot it, and glue the
knot in place so that the string will not slip out of the hole. Tie the
weight on the other side of the string.
- Glue a length of soda straw onto the quadrant along and parallel
to the side marked top.
- You may wish to put an eye shield over the straw as indicated in
the drawing.
Experiment:
Use the astrolabe to find the altitude of Polaris (the North Star). Recall that
you can find the North Star using the "pointer stars" at the end of
the bowl of the Big Dipper. Extend the line between the pointer stars, going
about five times their separation and you end up at Polaris.
The size of the patch of sky (angular field
of view) seen through the straw can be calculated by
Record:
A. Length of straw in cm.
__________.
B. Radius of straw in cm.
__________.
C. (Radius of straw)/(Length of straw) _____________.
D. Take
the inverse tangent of the result in C.
I will use the calculator in Windows to demonstrate how this calculation
is done. The calculator is found
under Programs/Accessories in Windows.
The default display in the program is the standard calculator, but we
want the scientific calculator.
Click on the View tab on the menu bar and select scientific. The calculator now looks like…
Notice
that the radio buttons just under the entry region show us that the calculator
has been set for Dec (decimal) output and Degrees display. Enter the number from part C above, press the “Inv” square at upper left and
then the “tan” function at lower left. Now multiply the result by two. Your result will be in degrees and
should be close to 1.8 deg. ______________
If repeated attempts to find Polaris through
your straw fail, shorten the straw. The field of view is now bigger. Calculate
the new field of view. As you sight through the straw at Polaris, the weighted
string will hang over the altitude on the quadrant circle. Measure the altitude
of Polaris five separate times and take and average.
Altitude of Polaris
1.
_____________
2.
_____________
3.
_____________
4.
_____________
5.
_____________
Average ________
The altitude of Polaris is close to your
latitude. Please bring in your astrolabe with this page to receive credit for
the exercise.
Use this template to build your astrolabe.
