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\begin{Huge}
\begin{center}
ASTR 110 LAB MANUAL - INSTRUCTOR'S GUIDE
\end{center}
\begin{center}
\copyright NMSU Astronomy Department \\
{\bf Fall 1999}
\end{center}
\end{Huge}

This volume provides a guide for lab instructors to accompany the NMSU
ASTR 110 lab manual. It describes the overall philosophy of the labs
and provides some guidelines and hints for how to make the labs most
effective for the students. It also describes the necessary information
to make sure that the labs are set up and prepared for properly. 

The basic philosophy of these revised labs is to maximize the amount
that the students experiment during the labs, and to minimize the amount
the lab instructor lectures the students. Students get enough lectures
during classtime; the labs provide an ideal opportunity for the students
to play around with various equipment and concepts in an effort to
learn by expermentation. The instructor should make every effort to
keep the amount of introduction at the beginning of the lab session to
a minimum; it is important to make sure everyone understands what
the lab is about, but the goal is to have students figure out concepts
by experimenting with them, \textit{not by being told about them}.

There are sometimes techniques in the labs which some or all of the
students may not be familiar with, e.g., scientific notation, unit
conversion, etc. Rather than giving a lecture about these beforehand,
it is probably better to let things come up and discuss them as they
do; this avoids lecturing to students who already know certain things,
doesn't turn off the students who aren't familiar with these ideas or
find them boring to hear about, and makes it clear that we'll only 
discuss stuff which is relevant to what we are doing. The ASTR 110 labs
are not the appropriate place to give remedial math lectures; we want
students to explore astronomical concepts and realize for themselves
what is required to do this.

In general, all attempts should be made to make the labs relatively 
\textit{fun} for the students. The joy of scientific experimentation is
just playing around with equipment and ideas. There is no real need for
students to get the \textit{right} answer; overall, in science, we never
know what the right answer is in advance anyway. It does a disservice to
the students to have them try to perform the labs in order to get some
predetermined answer; this is not the way science works.

The inevitable problem with this sort of approach (i.e., don't worry about
the answer) is that students are preoccupied with their grades, and everyone
feels that the grade depends on getting the correct answer. For this
reason, I advocate adopting a relatively lenient approach towards grading,
and the instructor must award points for well thought-out explanations for
results, even if the results do not come out as the instructor would have
liked.

In fact, experience has shown that measurements by the students in the
lab are often made quite sloppily, so it is fairly common for results not to
come out very well. Instead of making students feel that have done
something wrong, the instructor might take advantage of this opportunity
to show that measurements are not always trivial and measurements with
their corresponding results and interpretations are not always correct. An
underlying theme through the labs is the concept of \textit{measurement
error and repeatability}, and at all stages, students should be encouraged
to estimate errors by repeating measurements, comparing with other
groups, etc.

\chapter{How Many Galaxies Are There in the Universe?}

This lab provides an introduction to measurement, measurement error,
error estimates, and extrapolation. 

The instructor might start by telling the students that the lab is about
estimating the number of galaxies in the Universe, but in the process to
explore how measurements are made and how they often have significant
uncertainties.

Start by having students work in groups to determine the number of chairs
in the classroom; however, they only have one minute to do this. After
the minute, have the groups present their number and how they determined
it. Note the variation in the derived number. Now give each group 3 minutes
to do an exact count. After completion, note how the variation is smaller
than using the estimation methods: but still, usually, there is some
variation. Make sure to mention how working together can help to 
minimize work, get more accurate results, and get error estimates.

Now move on to a count which requires estimation: the number of chairs
in the University. Give students 5-10 minutes, then again collect the
answers and descriptions of the techniques. Note whether people took
advantage of the more precise knowledge of the number of chairs in the
classroom or not, and discuss advantages/disadvantages of various results.

Now move on to the main exercise of the lab: estimating the number of
galaxies in the sky based on the Hubble Deep Field. Introducing this
picture and the techniques provides a good opportunity to present the
concept of angular measurements on the sky to describe the size of the
field. At this point, let small groups take over and proceed at their
own pace.  When they start to figure out the number of pictures needed
to cover the whole sky, or the amount of time needed to take this number
of pictures, they will run into large numbers on their calculators. By
walking around and talking with each group, the instructor can determine
whether students are familiar with the concept of scientific notation
and can help them understand it and learn how to work with it on their
calculators.  As students proceed through the lab, you can see whether
there is confusion about unit conversion, and address it accordingly. 

This labs leads to a very nice homework exercise which is included in
the lab summary: an estimation of the number of stars visible to the
naked eye in the sky. This gets students to go out and look at the sky
and also to use some of the ideas about estimation. Make sure to emphasize
that we are interested in \textit{naked-eye} stars, so the Hubble
Deep Field image is not relevant to this. Also make sure to note that there
is no correct answer; many students won't believe their numbers because
they don't think they are big enough.

\chapter{Mapping the Local Universe}

This lab presents basic concepts of making figures/maps and demonstrates
how these can be used to look at the distribution of galaxies in the local
universe. It also provides a good opportunity to emphasize the problem that
distances are difficult to determine in astronomy, so for many objects,
we only know about their \textit{direction}, but not their distance. 
Understanding the difference between 2D projections of object positions and 
full 3D positions is useful and will be important when doing the next
lab (Mapping the Galaxy), for which only 2D projection information is
used.

Students start by being given angular positions of an artificial
constellation. They are asked to describe the shape of the constellation
by looking at the table; this is essentially impossible. The idea is
to show that graphing the positions reveals additional patterns. Start
them off on the idea of graphing the positions by having them determine
the minimum and maximum values of right ascension and declination so
they can get appropriate limits for their plots. As they start to
lay out their plots, you can explore the idea of whether the two
different axes should have common scales (e.g., arcmin per inch). 

As they start to make the plots, they realize that it will take forever
to put all the points on the plot. This is where you can introduce the
advantage of computers for this sort of work. You can show them how the
computer plotting program works and the resulting graph. Probably it's
better to just demo this in front of the class than bother to haul out
all of the computers for students to do this themselves.

To use the plotting program, follow the link in the lab. You will first
need to select the data set: choices are Constellation Home (which is what you
want here), and several options from the Nearby Galaxies Catalog, which
you'll use later. After selecting the data set, you will get another page
where you have to select what to plot, and choose the limits. Some reasonable
defaults are given to plot RA vs. DEC for the constellation, with reasonable
limits. You can then hit the PLOT button to create the plot.

Next you move on to the difference between 2D and 3D positions. To
show examples of 3D distributions, the students will turn themselves
into a model of the Local Group in an effort to see directly how
nearby galaxies are distributed. This is a good time to let the students
just go at it by themselves. Make sure that they choose appropriate
limits (classroom must be no larger than 2.5 Mpc across, or Local Group
galaxies will all just be too close to each other to see accurately).
This exercise provides insights into group dynamics; again, try to
avoid getting too involved yourself, just enough to keep the students
on track. Make sure everyone gets assigned to a galaxy relatively quickly
and each person should try to locate themself in the classroom after
the limits have been determined by consensus; don't let one or two people
just go around telling everyone else where to stand. Of course, if several
students have problems figuring out where they should go, they can get
help from other students (or you).

After doing this, students start looking at the distribution of larger
numbers of galaxies.  At this point you discuss the idea of various
projections of 3D distributions onto 2D planes, then have the students
look at these projections for all nearby galaxies.  Show them plots of
the 50 nearest and the 50 brightest galaxies using the computer and
discuss what the projections mean.  The students then get to come up
with ideas about the distribution of galaxies in the Local Universe,
based on the projections in the Nearby Galaxies Catalog which are given
in the lab. It is important at this point to emphasize that there is not
a ``correct'' answer; we just want students to look at the plots and try
to describe what they see. In fact, the Supergalactic plane is definitely
discernable, but it does not jump out at you so strongly that someone is
``wrong'' if they don't see it. Note that the units on the plots of
the Nearby Galaxies Catalog are in Mpc; a distance of 1 Mpc is a bit over
3 million light years.

Finally, students are reminded (or introduced) to the idea of basic
morphological types of galaxies. All that needs to be introduced is
ellipticals vs. spirals vs. irregulars; no need to go into any finer
detail (E0-E7, Sa-Sc, tuning fork, etc.). Students in their groups can
do the exercise of determining the relative frequency of different
morphological types among the nearest galaxies.

Finally, students can be introduced to the morphology-density relation
by showing them some 2D projections of the Nearby Galaxy atlas with
points color-coded by morphological type. Use the computer plotting
program to do this; again, it's probably best to just demo this in
front of the class and discuss it rather than have all the students
try to do it themselves with the computers. To color code different
morphological types, use the "subsets" section of the plotting screen;
to get subsets of the data plotted with a particular color, check the
box, fill in an expression for the subset, and select the desired color.
For example, by selecting Set 1, filling in ITYPE<0 (it's important
that there are no spaces in your expression), and selecting Red, you
will get all elliptical galaxies plotted in Red. You can then select
Set 2 as well, with ITYPE>0\&ITYPE<10, Green, to get spirals plotted in green,
etc. etc. Absolute magnitude can also be used, maybe with different sizes
of points to show the difference between brighter and fainter galaxies...

\chapter{Mapping the Galaxy}

The lab attempts to show how we can infer something about the 3-dimensional
distribution of objects in space even if we cannot estimate distances,
just based on the relative number of objects seen in different directions.
It is important to emphasize this concept at the beginning of the lab,
namely that we are trying to learn about the distribution of objects in
space \textit{for objects to which we do not know the distance}. 

We start with the example of students in the classroom. Students are
asked to make maps of the \textit{directions} in which they see their
fellow students. Again, you must emphasize that distances are 
irrelevant to the type of map we want to make here, only directions. 

This initial exercise provides an opportunity to discuss how we can
construct a map of objects in different directions, namely by using
a ``globe'' or celestial sphere. You can discuss how we can represent
such a sphere on a piece of paper by slicing it up and pasting the
slices down. Show the ``sliced sphere'' and have everyone use the
same convention for which slice represents the front of the classroom,
the ``poles'' are up in the sky and down in the ground, etc.

Allow the students to start to make their maps. You will probably need to
help various groups understand and visualize what is going on. Once
the groups have completed their maps, have each group describe their
map, and draw attention to similarities and differences between the
maps for different groups (e.g., all groups should have objects only
in the ``equatorial plane'' since students are all located in a plane,
but groups in the middle of the classroom will have students at all
``longitudes'', whereas students at the edge of the classroom will have
blank ``longitudes''.

Once this is done, students try to generalize their results to several
ideal distributions: center of homogeneous distribution, edge of
homogeneous distribution, center of planar distribution, edge of
planar distribution.

At this point, you can try to discuss the choice of coordinate system,
i.e. what would the maps look like if the ``poles'' were off to the side
instead of up and down. This is probably a bit hard for students to
grasp, so you might just wish to help them a bit, then show them what
the map would look like. This is relevant for them to understand the
distribution of Milky Way stars. Actually, a good way to demonstrate this
would be to have some spheres already made up with planar distributions
but at different orientations to the equator; then these spheres could
be ``sliced'' showing the apparent location of the planar distribution on
our style of maps. This would also provide an excellent opportunity to
demonstrate to the students the sort of globes they will next be making.

After this, you move on to the distribution of astronomical objects on
the celestial sphere. This provides an opportunity to discuss constellations
(stars with similar directions, but not necessarily similar distances).
Students plot on their celestial spheres locations of open and globular
clusters, gaseous nebulae, and galaxies. The location of stars in the
Milky Way is already done for the students.

After plotting is done, the students draw inferences about the distribution
of each type of object in space. They should start with the Milky Way,
then move on to other objects. They can both infer the spatial distributions,
and then also compare these to the distribution of the Milky Way.

This can be a difficult lab. For some people, it is very difficult
to visualize the maps, although for others it is easy.  People are
confused about the idea of positions on a globe; when they look around,
they see people at different distances which they don't know how to
accomodate. Also, it's hard to grasp why they aren't located on the map
at all. A different approach might be good, perhaps with a large globe
which we could cut up.

\chapter{Measuring Distances Using Parallax}

The idea of this lab is to demonstrate to the students the basic idea of
measuring distances using parallax, and then to demonstrate that even though
the principle is straightforward, to get good distances in practice requires
accurate measurements. This lab also helps to show the concept of how
measurement errors limit our ability to determine distances accurately.

You can start the lab with a brief review of what parallax is. Then tell
them they are going to try to use the concept of parallax to measure distances
to objects in the classroom. First they need to figure out how they will
make the measurement. Install the ``ruler'' against one side wall. Have
students work in groups of 3-4; in each group, have them take turns standing
against the opposite wall, with a partner holding up a pencil while standing
anywhere from 3 to 20 feet from the observer (i.e., less than half the
classroom away). Have the observers blink eyes and notice motions against
the background ruler. Have each observer look at objects at three different
distances, and make sure that everyone confirms that the object appears
to move less as it is placed further away. Make sure everyone has a chance
to observe, then have them choose a ``qualified'' observer to make the real
measurements of how many tick marks the object appears to move at each
distance. Emphasize to them the need to try to make accurate measurements,
and, most importantly, make sure they estimate the uncertainty in their
measurement. You will probably find that students do not use fractional
numbers in their motion measurements, and you can discuss with them what
limitations that puts on their accuracies. Make sure the students leave 
their pencils at the distances they used so they can come back later and
measure the actual distances.

They next experiment with the affect of a wider baseline. Now instead of
looking with each eye in turn, have them look with one eye, then move
a few feet to the side and look again. They can compare the apparent 
motion with that of the same object using the shorter baseline.

Finally, we move to trying to quantitatively measure the distance to their
objects. To do so you need to discuss what we are actually measuring. 
In particular, you need to discuss how the observation of a changing 
\textit{direction} to an object is really an angular measurement. Once
they get this concept, you convert the measurement of tick marks to
an angular measurement. Do this by ``calibrating'' the ruler; have
students put a protractor to their eye, and extend lines (works well to
use pencils) out toward the directions of the two ends of the rulers.
They can then look up the angle, count the total number of tick marks,
and divide these to get the angle per tick mark. Using this conversion,
they can then convert their measurements of motion in tick marks above
to angular measurements.

Students then need to determine the baseline of their observations.

Then you show them the parallax diagram and equation. I don't think you
need to explain trigonometry, just say that you can quantitatively figure
out distances using trigonometry and give them the equation. They can
then figure out the distances to their objects.

They should then use their error estimates of motions to try to determine
the possible errors in their distance measurements. Probably the best way
to do this is to have them redo the calculation using their measurement with
their error estimate added.

Then they get to compare the parallax distance with the true distance. Here
the idea of errors will really be emphasized, as you will probably find that
their parallax distances are not very good!

Finally, conclude the lab by showing how parallaxes are used in astronomy,
i.e. how the baseline is the Earth's orbit, etc.

\chapter{Optics}

HINT: with lights on, draw dark lines using the protractor on the worksheet
so when you turn the lights off (necessary to see the light rays), they
will be able to see the angle measurements!

\chapter{Telescopes and Detectors}

\chapter{Kepler's Laws and Gravity}

\chapter{Blackbody Radiation}

\chapter{Spectral Lines}

\chapter{The Surface of the Moon}

\chapter{Comet lab}

\chapter{Our Sun}

\chapter{Hubble's Law: Finding the Age of the Universe}

\end{document}
