Dr. Uwe Trittmann, Otterbein University
Fall 2015
INTRODUCTION
An incremental skylab or iSkylab is a term paper with an observational component. The paper will be developing over the course of the semester as you add a new section every three weeks or so. This allows for revisions, as the individual sections are graded and handed back. In the end you will have explored one aspect of observational astronomy in detail, and documented your results in a proper, scientific way.
STAGE 1 – Observation
As you saw or will see in the lecture, it is rather tricky to observe the universe, i.e. to construct a good description of the cosmos and its parts from a glance at the sky. Even if things seem obvious they may lead to wrong conclusions. For instance, the sun and the moon have the same angular size up in the sky. We may therefore conclude that they have the same physical size, but actually the sun is 400 times bigger, yet also 400 times farther out. The main problem is our vantage point on Earth, namely that the earth is moving in several different ways. Earth rotates around itself, it rotates around the sun, and with the sun it rotates around the center of the galaxy, etc. What is more, the associated rotation axes are not aligned, e.g. the earth axis is tilted 23.5 degrees with respect to the axis of earth’s orbit around the sun (which is the reason for the seasons). This makes observing the universe from earth as challenging as observing a fairground when riding on a spinning merry-go-round. Of course, this does not mean that we cannot say anything definitive about the universe. It just means that we have to use our intellect to translate from what we see to what we actually have observed.
First, let’s establish that the earth indeed rotates. How do we know that earth is moving in this complicated way? Our impression is that the sun, the moon and the stars are moving when we observe the sky for a length of time. But even here a subtlety lays hidden: the sun and the moon do not move in exactly the same way as the stars, only to a good approximation.
Given that one rotation is plainly obvious ( diurnal or day-and-night rotation), we start with the more delicate observation that the sun and the moon move with the stars from East to West, but they do so with a slightly different speed, so they are moving with respect to the stars. This drift

is slow (a month for the moon) or very slow (a year for the sun), so we have to pay close attention, i.e. keep good notes of our observation and repeat them over a longish period of time.
For the first stage of the iSkylab, choose one of the options below: observe the sun during daytime or the moon, typically, but not necessarily, at night, depending on your preference and schedule.
Sun Option
What: Determine how the height of the sun above the horizon at a specific time is changing as the days pass by measuring the length of the shadow it casts with a gnomon (essentially a stick in the ground).
Time: Once you know how to do it, this only takes a minute per observation.
Commitment: Do this over several, not necessarily consecutive days, at exactly the same time .
Weather: Need to see the shadow for a minute, so can do on partly cloudy, possibly hazy but not overcast days.
Moon Option 1
What: Determine the height of the moon above the horizon with the help of a quadrant
(essentially a bob dangling from a protractor), and see how it changes as the days go by.
Time: Once you know how to do it, this only takes a minute per observation.
Commitment: Do this over several, not necessarily consecutive days, at exactly the same time .
Weather: Need to see the moon for a minute, so can do on partly cloudy, possibly hazy but not overcast days.
Moon Option 2
What: Determine the position of the moon with respect to the stars by sketching the position and the shape of the moon and the bright stars in the sky. Document changes as the days go by.
Time: Once you know how to do it, this takes several minutes per observation.
Commitment: Do this over several, not necessarily consecutive days, exact time does not matter .
Weather: Need to see the moon and the stars for several minutes, so it needs to be a cloudless night with good seeing.

Detailed Instructions
Sun Option
There are two pieces of data you want to record over as many days as possible: the altitude
(angle above the horizon) of the sun and the direction (azimuth angle) of the sun with respect to a reference direction, usually North.
The latter is an easy measurement. Just observe the direction of the shadow, make a mark on the ground that is going to survive for several days, and record it in a notebook.
For the altitude of the sun, you’ll have to use a little trigonometry, because the sun is too bright to directly measure the angle with a quadrant. Use a stick called a gnomon and measure the length of the stick above ground, and the length of the shadow the sun casts. The ratio of the two is the tangent of the altitude angle. Drive your stick (gnomon) into a level, smooth (ideally no grass) piece of ground, making it as close to vertical as possible. If the ground is not level, use a board or piece of cardboard to cast the shadow on. Use the carpenter’s level to make sure the board is level and the gnomon vertical. Before you remove the stick from the ground, carefully measure the length of that part of the stick above ground. This procedure should be exactly repeated on the other days.
Convert your measurements of the shadow’s length and the gnomon’s height to an altitude of the sun as follows.
First, compute the ratio
length of stick length of shadow
A shadow length to Sun gnomon height
Next, use your calculator to compute the arc tangent
(arctan or tan -1 ) of the ratio. Your result is the altitude of the sun. Repeat the observation and data taking on other days, but the Sun exactly the same time (up to the minute is best).
How shadow length and gnomon height determine the altitude A of
Tasks: (Please type and repeat the question.)
1.
Compile a data table and describe how exactly you measured the position of the sun.
2.
Why do you need to measure two angles (directions)?
3.
Describe how the position of the sun changes as the days go by: how does the altitude change? How does the azimuth change?
4.
What can we conclude from this? (Is the sun moving? Is the earth moving? How? With respect to what?)
5.
Cross-checks: In light of what you know from other sources, is your observational data reasonable? What would change if you observed an hour later, what if an hour earlier?
6.
Estimate your uncertainties or errors (see appendix).
7.
Comments and advice for the next generation of observers.

Moon Option 1:
This option closely resembles the Sun Option, so review the latter.
Use your home-made quadrant to measure the moon’s altitude above the horizon at a specific time. This may involve some planning, because to moon has to be visible at that time for several days!
For the azimuth angle (see Sun Option), record the position of your feet, as you place them parallel to the direction of the quadrant, and point the quadrant in the direction of the moon. to object being sighted to horizon
A homemade quadrant. The thread indicates the angle of the object from the horizon.
thread weight thumbtacks
Repeat the observation and data taking on other days, but exactly the same time (up to the minute is best). Note that the moon moves quite a bit with respect to the stars in one day. This means the moon might not yet have risen, the next time you want to observe it at the same time!
Tasks: (Please type and repeat the question.)
1.
Compile a data table and describe how exactly you measured the position of the moon.
2.
Why do you need to measure two angles (directions)?
3.
Describe how the position of the moon changes as the days go by: how does the altitude change? How does the azimuth change?
4.
What can we conclude from this? (Is the moon moving? Is the earth moving? How? With respect to what?)
5.
Cross-check: In light of what you know from other sources, is your observational data reasonable? What would change if you observed an hour later, what if an hour earlier?
6.
Estimate your uncertainties or errors (see appendix).
7.
Comments and advice for the next generation of observers.
Moon Option 2:
The procedure for this option should be pretty clear from the description above: sketch the moon phase and a good part of the sky. Make sure to include enough stars in your sketch, so you can positively identify where the moon is with respect to the stars. The whole point of this option is to realize how the moon moves with respect to the stars (not with respect to the ground, as in the other options). In

particular, be sure to sketch a good part of the sky to the East (“left”) of the moon, because this is where the moon will move in the next couple of days. Note that the moon moves quite a bit with respect to the stars in one day, and therefore rises later each day. Since the moon orbits the earth in a month (28 days), you can estimate the moon moving 360 degrees/28 days = 13 degrees per day. How much is that in the sky? Stretch out your arm and make a fist; it will cover about 10 degrees, see figure above. Do this exercise to figure out where the moon will be the next night before you begin to sketch, so you can plan the layout of your drawing. Repeat the observation and sketching on other days. Make sure you note the date and time on the sketches.
Tasks: (Please type and repeat the question.)
1.
Sort your dated and timed sketches in a folder.
2.
Describe how the position and the appearance of the moon changes as the days go by.
3.
What can we conclude from this? (Is the moon moving? Is the earth moving? How? With respect to what?)
4.
Why is the moon showing different phases? Why is the moon sometimes visible during day time, and sometimes during the night?
5.
Cross-check: In light of what you know from other sources, is your observational data reasonable?
6.
Estimate your uncertainties or errors (see appendix).
7.
Comments and advice for the next generation of observers.
Good practices for all options:

Start your observations early to avoid bad weather.

Plan your observation session and be prepared to realize that you forgot something important when you actually start observing. That’s okay and part of the learning process.

Ask for advice! Some of the instructions in the manual might not make sense to you or may seem ambiguous. Seeing what questions you have is a great way for me to improve the manual. By discussing the manual, you will have a better observing experience – and will help future students, too.

Scientific writing is specific and precise. Always qualify your statements: “The moon moved” is not sufficient; you need to specify with respect to what it moved (the ground? the stars?), and also how much, in which direction and during which time. Also, compare to relevant things when making a quantitative statement. “The error is small” is not sufficient: small compared to what? other errors? the value of the variable that you measured?. “The value is as close to the accepted value as possible” – sounds good, but doesn’t say anything: Why is it not possible to get closer? Is it really close? Close compared to what?

Thinking (and writing) like a scientist takes getting used to. Do not get frustrated if you don’t get it right the first time. Solicit, look over the comments of the graded report, resubmit an improved report – and receive credit for it.

Appendix: Writing a Scientific Report
I. Communicating your results
Communication is an important skill in science, as it is in all other fields of endeavor, for if scientists do not communicate their results to colleagues, the work is wasted. Scientific writing is generally simple and succinct. Data should be presented in a way that is clear and easy to understand, usually in the form of a table or in a graph. A sample of what a data table might look like is shown on the next page. If you consult any books or articles in the course of preparing your Skylab, you should cite your references using any format for the references you are comfortable with. You may 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
Skylab.
II. Recording data
When you make an observation or conduct an experiment, you must record all the relevant variables, or you risk your results being worthless. In astronomy, you must record not only the values you measure (the altitude of the Sun above the horizon, the position of a planet in relation to the stars, or whatever), but also the date and time of the observation (specifying Eastern
Daylight Time, Eastern Standard Time, or maybe even Greenwich Mean Time) and the observing conditions at the time (clear, hazy, broken clouds, glow from city lights, etc.).
Table 1. Measurement of azimuth angle and shadow length: example of a data table
Time (EDT) angle shadow length comments
8:05 AM
11:10
11:40

7:35
(degrees)
300
—
335

80
(cm)
55.6
—
25.3

67.7 sun covered by clouds sun’s first appearance since 10:30
[more data] sunset
III. Errors
Every measurement is unavoidably subject to error, due to factors beyond the experimenter’s control – vibrations from a truck outside might make an indicator needle jump while you’re reading it, for instance. It is important for a scientist to make a good estimate of the possible range of error (called uncertainty). The conclusions you reach in your experiment are only as good as your estimate of the uncertainty involved. Having very small uncertainties relative to your experimental values is not necessarily a measure of how well you did the lab (though you should try to minimize errors as much as possible).

Why should you have to worry about errors so much? What’s important is not your measurement per se, but the true value of what you’re trying to measure. Thus, your experiment is only useful insofar as it puts limits on the true value. Without error bars on your measurement, you aren’t saying anything about the true value. For instance, you might think you are being very precise if you say that your measurements indicate that a certain wavelength is 376.5 nm; but everyone knows that this isn’t the exact wavelength, because no measurement can be perfect.
How close is the real value to 376.5 nm? You haven’t said! If, on the other hand, you say that your measurements indicate that the wavelength lies between 376.4 nm and 376.6 nm, you’ve actually made a much stronger statement.
In the world of astronomy, people will be convinced by your work only if they respect your error analysis. If you do a poor analysis, no one will give your results much credence, and they will ignore the fact that you ever did the experiment. That is a terrible feeling for an experimenter, especially if you’ve spent thousands of dollars and months of your life working on it. The same thing goes in the “real” world, by the way. Say you are measuring the resonant frequency of the wings of a DC-10 aircraft. Suppose you measure 600 per second and don't bother to calculate the error bars. An engineer assumes you mean 600±1 per second and adds a system which runs at 630 cycles per second. Suppose your real error bars were ±200 per second. What happens?
Hundreds of people die when the wings break off. Clearly, people will be interested in how far they can trust your experiments.
Types of error . 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. For example, an observer may measure the magnitudes of some stars or galaxies and publish them, only later realizing that a new campground had opened upwind, sending smoke over the observatory every night, artificially dimming the objects. If you don’t take this possibility into account as part of your data reduction, you could be in for a nasty surprise. 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 (in the example, you would avoid this problem by observing “standard” stars every night to calibrate the brightness of other stars).
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 you measure the size of your room with a ruler, you may lay the ruler down differently, or you may read it differently. Suppose you measure 130.5", 132", and 131.5". You would take the average of these numbers, 131.3", as your answer. The range of values, 1.5" (the difference between the maximum and minimum values) provides you with some measure of the uncertainty of each measurement. (Scientists usually use a different measure called the standard deviation.) The more measurements you take, the more accurate your average will turn out to be, because if the errors in the measurements are truly random, they should just about cancel each other out in the averaging process.

Remember, error is not something magical which no scientific laws govern. True scientists recognize that error doesn’t come out of thin air, but always has a mechanism causing it, a source. If they see discrepancies with the values quoted in textbooks (“book values”) outside the limits of their errors, they look for a physical explanation. Maybe a new or overlooked effect is at work; maybe one is discovering new science! Paying careful attention to little discrepancies and reducing the error bars sufficiently to discern them are primary qualities of a Nobel prize winner.
Estimating your uncertainty.
Finding the sources of error is not always easy. However, if you list every possible variable that might affect your measurement, you have all the variables that can produce error. Then you need only go through the list, and for each variable that you don’t have control of, estimate how much error it introduces. If your error is random, you can repeat your measurement many times, and see how much your results vary. However, you may not have the time (or money) to repeat your experiment many times. In that case, you must use other methods to determine the uncertainty of your measurement. It is simple in the case that your measuring instrument has a known uncertainty. For instance, if you use a wrist watch to measure time, you most likely cannot read the time to better than one second (and perhaps it takes you another second to move your head to look at it). In more complicated measurements, you can deliberately change the variable causing the error and see how much your results change. For instance, if you think that changing your location will change the time a star passes behind a building, which is what you are trying to measure, you can deliberately move a step or two to the side and see how much your measurement changes.
IV. 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 you don’t really know what the last digit is. Such an instrument simply cannot measure angles to a precision of
0.01 degrees. 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 quantity with the least number of significant figures. For example, if we have three quantities of 25.1, 37.22, and 44.33 and 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 snow bank, is only as good as its weakest link.