**Document ID**: 07_31_97_1

**Date Received**: 1997-07-31 **Date Revised**: 10/27/97 **Date
Accepted**: 10/30/97

**Curriculum Topic Benchmarks**: S3.4.5, S14.3.2, S14.4.2, S15.3.2,
S15.4.4, M4.3.7, M4.3.20, M4.4.5, M4.4.6

**Grade Level**: \[9-12\] High School

**Subject Keywords**: day, solar day, sidereal day, star day, Earth\'s
orbit, astronomy, analemma, seasons

**Rating**: Advanced

**Length of the Day**

**By**: Stephen J Edberg, Jet Propulsion Laboratory, 4800 Oak Grove
Drive, M/S 183-501, Pasadena CA 91011 e-mail: sedberg@jpl.nasa.gov

**From**: The PUMAS Collection http://pumas.jpl.nasa.gov

©1997, S.J. Edberg. ALL RIGHTS RESERVED.

The length of the day is something we take for granted. Yet, much can be
learned about the day \-- and the way the Earth moves \-- from careful
observations of the Sun and a more distant star, over as little as 24
hours, with a home-made viewer and a good clock.

**OBJECTIVES**: Measure the length of the day using the rotation of the
Earth, with the Sun and a star as celestial landmarks; work at refining
the measurement process. Discover that the Sun is not exactly in the
same place at the same clock time every day. Understand that the changes
are due to motions of the Earth, and lead to differences in solar, star,
and sidereal time.

**WARNING**: Observing the Sun can be EXTREMELY HAZARDOUS TO EYESIGHT.
Shadows may be safely observed without protection (though regular
sunglasses may increase comfort), but OBSERVING THE SUN DIRECTLY
REQUIRES SAFE SOLAR FILTERS (e.g. Welder\'s Glass No. 14). DO NOT LOOK
DIRECTLY AT THE SUN WITHOUT A SAFE SOLAR FILTER. OTHERWISE, BLINDNESS
CAN RESULT.

**APPARATUS**: (1) One or more **alignment devices** to view stars. The
devices may be home made **sighting tubes**, frontsight/rearsight
devices, telescopes, etc. Sighting tubes can be made from toilet paper
and paper towel roll cores, plastic or galvanized pipe, soda straws, or
virtually anything that is tubular and straight. The length and internal
diameter will affect the precision of the time determination: it may be
easier to find the star, but harder to judge centering, when a larger
radius surrounds the target before the tube walls are reached. A
light-weight sighting tube is easier to use, but it should be strong
enough not to bend under its own weight.

\(2\) A setup for measuring the **position of the** **Sun**. Create an
image of the Sun by putting a pin hole, thumbtack hole, or larger hole
in a piece of cardboard, and projecting the Sun\'s image on the ground.
The smaller the hole and the longer the projection distance, the sharper
and fainter is the image of the Sun. Note the direction of motion of the
Sun\'s image on the ground and draw a line perpendicular to the
direction of motion for use as a time mark. Make the length of the line
three or four times the image diameter to allow for the Sun\'s slow
seasonal motion.

\(3\) A wall **clock** or wrist watch, accurate to at least few seconds
per day. Instead of the clock, you can use a **stop watch** that, in
advance of its expected use, has been synchronized with the hourly time
tone from the local CBS radio network affiliate. The stop watch acts as
a portable source of accurate time. Or, if a short wave radio is
available, you can tune to short wave stations WWV or WWVH at 5, 10, and
15 MHz, that provide time tones on the minute, accurate to milliseconds.

\(4\) An experiment notebook.

The **sighting tubes must be mounted** in fixed positions for the
duration of the experiment. Sight on the desired star the night before
you plan to begin taking data, to determine the star\'s transit point.
The star sighting tube should be taped to a pole, tree limb, fence post,
etc. in a fixed position, so it can view the star on subsequent nights.

For greater precision, you may drill the sighting tube and mount it
permanently to a tripod or other support. Or make a frontsight/rearsight
device, by partially driving nails (so the heads are above the surface,
by as much as an inch) into a yardstick or similar light weight, long,
sturdy material. It, too, can be attached to a pole, tree limb, fence
post, etc. in a fixed position, once the transit point of the desired
star is known. The Sun motion setup must also be in exactly the same
position every time it is used.

**PROCEDURE**: During class hours, use the clock to check the **clock**
**time of the Sun\'s passage** by the ground mark for several days in a
row. Also measure the exact position of the sun\'s image at that time.
Watch the Sun\'s disk slowly move across the ground. When its leading
edge is tangent to the reference mark the clock time should be recorded.
The clock time can also be recorded when the trailing edge of the disk
is tangent to the mark. The moment of tangency is easier to note than
the time when the Sun is centered on the marker.

At home during the evening hours, have the students measure the clock
time when a star of their choice falls into alignment. Repeat these
measurements on subsequent days, being prepared to note the respective
transit times starting 23 hours 50 minutes after the first measurements.
Remember that the alignment devices must not be moved from day to day.

The **transit time** is defined as the period from when the Sun or star
is first perfectly aligned in the sighting device until it returns to
exactly the same position in its east-to-west daily motion. Note that
the star will be at the same position in the alignment device each
night, but the Sun will change its position up or down slightly every
day. The change will hardly be detectable at the solstices, in June and
December; it will be greatest around the equinoxes, in March and
September.

**DISCUSSION**: Why is the star day about 4 minutes shorter than the
solar day? The Earth moves around the Sun in the same direction as it
rotates on its axis. So one sidereal rotation after sunrise, for
example, the Earth has also moved part way around the Sun, and must
rotate a little farther to reach dawn on the next day.

As viewed from Earth, the Sun appears to move toward the east, relative
to distant stars, about 1 degree, the equivalent of about 4 minutes of
time, each day. In a year, the Sun appears to move full circle (360
degrees) \-- on Earth we view the Sun from all angles as we complete an
annual orbit. You can demonstrate this by having one student play the
\"Sun;\" other students can walk around the Sun, and report on what
pattern of \"background stars\" (the classroom walls) they see during
\"noon\" (facing the Sun) and \"midnight\" (facing away from the Sun).
Our clocks are based on the solar day.

Why does the Sun\'s crossing point on the mark appear to gradually move
up, then down with the changing seasons? Earth acts like a gyroscope;
its rotation axis points in the same direction relative to distant stars
all year. (This is why you can always use Polaris to find North.) But
the rotation axis is tilted relative to the plane of Earth\'s orbit
around the Sun (called the \"ecliptic\"). If you mark the location of
the tip of a stick fixed in the ground at the same clock time every day
for a year, the marks will trace out a figure \"8.\" This shape is
sometimes called an \"analemma.\" They are often drawn on globes.

Do the day lengths vary with season? Measurements made in January and
July (June is almost as good) will show differences due to the Earth\'s
orbital speed. It is fastest during January, when Earth\'s elliptical
orbit brings it closer to the Sun. In July, Earth is at its farthest,
and moving slowest. Note that the apparent size of the Sun will vary
with season, and this can be demonstrated by timing the duration of its
transit across the mark

**FOR MORE INFORMATION:** Earth\'s motions relative to the Sun are
discussed and illustrated in most encyclopedias under \"Earth,\"
\"Earth\'s Orbit,\" \"Day\", or \"Seasons.\"