**TIPS ON TAKING AND WRITING UP SKYWATCH DATA**

RECORDING

When you make an
observation or conduct an experiment, you must carefully record data. In astronomy, one must not only record the
values which are measured (the altitude of the sun above the horizon, the
position of a planet in relation to the stars, etc.) but also the date and time
of the observation (specifying also Pacific Daylight, Pacific Standard, or
maybe even Greenwich Mean Time) and the observing conditions at the time
(clear, hazy, broken clouds, glow from city lights, etc.).

OBSERVING IN GROUPS

Many students would like
to work in groups while carrying out their Skywatch observations. We have no objections to this __so long as
each person contributes to the observations in a significant fashion and each
person separately writes up his or her own report.__ In such a report, you should mention the
names of your collaborators and who did what.

DISPLAY OF RESULTS

When a scientist
communicates results to colleagues, he or she wants to display data in a manner
which makes it as easy as possible for the reader to understand. The data will usually be arranged in a table
or in a graph. It is important that in
your Skywatch write-ups you present your data in a clear manner. Besides a neat "final" display,
you must also submit your original notes, sketches, etc., as taken in the
field.

ERRORS

In every measurement we
make, there is an unavoidable error, regardless of the quality of equipment or
observing skill. It is important for a scientist to make a good estimate of
these errors.

There are two types of
errors: systematic and random. __Systematic
errors__ arise when we consistently perform our measurements in such a manner
that they are biased in a particular direction. Such errors can be very
difficult to recognize. The best way to
avoid systematic errors is to be very careful in the way the measurements are
made.

__Random errors__ are the errors that can
never be eliminated, only minimized.
The best way to estimate the size of the random errors is to repeat
measurements many times. In general, we get a slightly different value each
time the measurement is performed. The
differences between these values provide an estimate of the error. For instance, if most of a set of measurements
of the same quantity fall within a range of 8 units, we might reasonably guess
that the random error is about 4 on either side of the average. The average is
our best estimate of the measured quantity, but the true value could be as much
as 4 higher or lower.

The concept of averaging
many measurements of a quantity to obtain a more accurate determination of that
quantity is very important. If the
errors in the measurements are truly random, they should nearly cancel each
other out in the averaging process. The
more measurements we include in the average, the better the errors will cancel
each other. We should thus repeat
measurements as many times as is reasonable and then take the average of all
those measurements to arrive at a "best estimate" of the quantity
sought.

SIGNIFICANT FIGURES

The question of the
number of significant figures in one's measurements is closely related to that
of error. For example, consider a
simple homemade quadrant. With such a
device we may be able to measure a star's altitude above the horizon to the
nearest half degree. Thus we might
record a measurement of 35.5 degrees.
This measurement has three significant figures. To quote a measurement of 35.52 degrees made
with such a device is misleading because such an instrument simply cannot
measure angles to a precision of 0.01 degree.
However, if we were to use a navigator's sextant, we might indeed fairly
measure the altitude to be 35.52 degrees.
Because of this instrument's higher precision, we are justified in quoting
four significant figures.

When combining measured
quantities through arithmetic calculations, the final result should be
expressed with no more significant figures than the component with the *least*
number of significant figures. For example, suppose we have three quantities of
25.1, 37.22, and 44.33. If we multiply the first two and divide by the third,
our answer is 21.1, with three significant figures. We are only fooling
ourselves if we read off the calculator and then write down 21.07426122, or
even 21.07, since a chain of calculations, no differently than a chain pulling
an auto out of a snowbank, is only as good as its weakest link.

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**SAMPLE SKYWATCH WRITE-UP **(for Part A of "Celestial
Navigation")

** **

(to give you a general
idea)

OBJECTIVES: To determine the motion of the sun across
the sky near noon and thus measure my latitude and longitude.

DATE OF OBSERVATIONS: October 15, 2001.

LOCATION OF
OBSERVATIONS: Renton

WEATHER CONDITIONS: fair, with some clouds; little wind.

PROCEDURE: Outline exactly how you proceeded with your
observations, especially if different from the write-ups.

Shadow Shadow
Sun

Time (PDT) Azimuth Length Altitude (calculated) Comments

11:10 28
deg 29.8
cm 34
deg

11:40 21 25.3 38

11:50 19 24.9 39

12:00 17 24.5 41

12:10 p.m. --- ---- ---- Sun covered by clouds

12:20 12 23.8 42

12:30 10 23.3 43

12:40
9 22.8 43

12:50
7 22.3 44 Stick
knocked over by little brother;

set back as straight as possible

1:00
4 21.8 44

1:10
1 21.7 45

1:20 358 22.1 45

1:30 355 22.9 44

2:10 347 23.7 41

2:30 342 24.9 39 Retired
from observing

[Here you present the
requested plots of altitude angle versus time and the path of the tip of the
shadow. You also give your calculations for the longitude and latitude of your
observing site, based on your data.]

ERRORS IN MEASUREMENTS: A brief discussion telling the reader of the
estimated errors in your measurements, as well as probable causes. Then
estimate how uncertain are your derived values for latitude and longitude.

DISCUSSION OF
RESULTS: Here you tell the reader what
you have learned about both the heavens and about how to take observational
data, spotlighting any particularly interesting or unexpected results. You should also mention any new questions
your results raise and any suggestions you have for better ways that future
Astronomy students might carry out such a Skywatch.