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% TAguidePathoftheSun.tex
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% Peter Newbury
% Department of Physics and Astronomy, UBC 
% newbury@phas.ubc.ca
% Twitter @polarisdotca
% http://blogs.ubc.ca/polarisdotca
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% 7 Sept 2011
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% This work is supported by the Carl Wieman Science Education
% Initiative cwsei.ubc.ca.
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\lfoot{\small Instructor's Guide: Path of the Sun Tutorial}
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\begin{center}
  Instructor's Guide for\\[1ex]
  {\huge The Path of the Sun}
\end{center}

\titlebar{Description}{}

In this activity, student explore the pattern of the Sun's paths across the
sky throughout the year as seen by observers in Vancouver (latitude
49$^\circ$~N). To collect the observations needed to sketch the path,
students use the Nebraska Astronomy Applet Project (NAAP) ``Paths of the
Sun Simulator''.  The tutorial moves back and forth
between TA-lead explanations and demonstrations, student exploration and
data collection.  The TA has to keep track of the time and ``drive'' the
activities forward.


\titlebar{Learning Goals}{}

After this tutorial, together with lecture materials, students should be
able to

%\setlength{\itemsep}{0pt}
\vspace{-0.5\baselineskip}
\begin{itemize}
\item trace the motion of the Sun on the celestial sphere throughout the year 
\end{itemize}
\vspace{-0.5\baselineskip}


\titlebar{Set-up}{20 minutes}


The students will work together in groups of 2 or 3. We want them
to compare the path of the Sun on 4 different days throughout
the year: Vernal Equinox (Mar 20), Summer Solstice (Jun 20), Autumnal
Equinox (Sep 22) and Winter Solstice (Dec 22).  There is not
enough time for them to collect data on all 4 dates so half the class
will work on 2 dates (Mar, Jun) and we give them Sep, Dec, and the other
half of the class collects Sep, Dec and we give them Mar, Jun.

\medskip
Materials:
\begin{itemize}
\item Lab computer (or their own laptop) capable of running Flash
  through a web browser. The tutorial uses the NAAP simulator ``Motions of
  the Sun'' found at

  \url{http://astro.unl.edu/naap/motion3/animations/sunmotions.html}

\item The TA will demonstrate how to collect data from the simulator so
  a digital projector is needed. There are fewer technical problems if
  the TA can connect his/her own laptop to the projector.
\item (1 per group) diagram of the sky, photocopied onto 11$\times$17
  paper.  There are 2 versions of the diagram: one has Oct, Sep, Dec and
  the other has Oct, Mar, Jun.  
\item (1 or 2 per group) coloured markers
\item an overhead of the sky diagram with no paths drawn.  Please us a
  dry erase marker, not an overhead pen, to mark on the 
  overheads. You might want a narrow, black one for writing answers on
  the overhead and thick, coloured one for tracing the Sun's path
  ``today''
\end{itemize}


When we hand out all the pages for a tutorial at the beginning, students
often rush thru important steps because they think they have to get the
last page ASAP.  A better strategy for the students is to hand out pages
as needed:
  
\begin{itemize}
\item (1 per group) Intro and Part~1 (page 1)
\item (1 per group) Part 2 (pages 2,3 double-sided) There are 2 versions
  of Page~3: one asks students to find Sep, Dec and the other asks for
  Mar, Jun.  It works nicely to give one version to the West half of the
  room, one version to the East half. Be sure the students with
  worksheets asking for Sep and Dec have the sky diagrams with path for
  Mar and Jun, and vice versa. This way, when the activity is complete,
  all groups will have data for all four dates.
\item (1 per student) Part 3 (page 4)
\end{itemize}
\vspace{-0.5\baselineskip}

Before the tutorial, set out the coloured pens, 
Part~1 (Orientation) and sky graphic.  We'll distribute the two versions of Part 2
later.  Even though they don't need the sky graphic yet, the longer
they sit looking at it, the more familiar they'll be with what the
picture is showing and simpler it will be for them to imagine themselves
standing at the center of the diagram.

\medskip

As usual, invite the students to form groups of 2--3 as they arrive.
  
%\clearpage

\titlebar{Part 0: Introduction and Motivation}{5--10 minutes}

It's never a bad idea to let the students know why they are doing this,
or any other, tutorial.  Why should they care?  Why should they invest
the time and energy?  The answer should be more than the marks they'll
receive. 

\medskip

The two patterns explored in this activity are {\bf when} the Sun rises and
sets and {\bf where} the Sun rises and set. Ask them a few questions to
get them realizing such observations even exist, and perhaps why we care.

\begin{enumerate}
\item First do a quick orientation to the room, asking the students to
  imagine they're outside.  Trace out the horizon and directions North,
  East, South and West.  Ask them where the Sun rises (East) and sets
  (West) and trace the path of the Sun (with your arm or maybe with a
  laser pointer?)  across the Southern sky.
\item ``Does anyone know what time the Sun rose this morning''

  You're unlikely to get a correct answer. After all, what impact did it
  have on them? 

  ``If you don't know, that's alright. Does the time that the Sun rose
  really have any impact on you? Probably not.  What about this: What
  time will the Sun set on October 31?''

  This question (or make up your own question whose answer matters to
  you) matters because kids want to know when they can go out for
  Halloween and when you can expect people at the door. If nothing else,
  you can suggest

  ``...there are certain events, like some religious
  festivals that start at teh moment the Sun sets. There are people who
  care about that time so they can prepare. There has to be a way to
  {\bf predict} these times.''
\item ``Does anyone know {\bf where} the Sun set last night? No, no just
  'in the West' but exactly where? Was it North of West? South of West?
  How many degrees?''

  Again, we're not expecting students to have the ``right'' answer. We
  want them to realize that this question and observation exists. But
  why should anyone care?

  ``When does the Sun set {\bf exactly} in the West? Right, on the
  equinoxes. That's an important day for religious festivals and other
  events so this was a test for equinox: the day the Sun set exactly in
  the West.''
\end{enumerate}

\medskip

Emphasize the point for these questions
\begin{quotation}
  \noindent It's important to be able to predict {\bf when} and {\bf
    where} the Sun rises and sets.  By watching sunrises and sunsets and
  figuring out the pattern, {\bf we can predict the future}
\end{quotation}

Tell them about the ``computers'' they'll be using for the rest of the
tutorial:
\begin{quotation}
  The pattern is not simple because it depends on the daily rotation of
  the Earth on its tilted axis and the yearly revolution of the Earth
  around the Sun.  No one can do it in their heads.  We need a computer
  like Stonehenge or this ``armillary sphere (``ARM-i-larry'' or
  ``ar-MIL-ary'') (``armillary'' means ``rings'') or an actual computer
  for predicting the motion of the Sun, planets and stars across the
  sky.
\end{quotation}

\titlebar{Part 1: Orientation}{10 minutes}

Obviously, students need to learn how to use the NAAP
simulator. Education research demonstrates quite clearly that students
do not learn the scientific concepts behinds simulations if they are
simply given a recipe to follow. Likewise, saying, ``Here's a
sim. Explore it for 10 minutes...'' doesn't work very well, either. A
better approach is to challenge them with a couple of tasks. This
approach gets them exploring the features of the simulation while
constantly watching the outcome of each change they make, watching the
connections between the properties of the underlying concepts.

Invite the students to follow the web address on Page~1 to the NAAP
simulation and to answer the 2 questions we pose, the altitude of the
Sun on July 1 and the location of the most northerly sunrise.

While they're working on these tasks, wander around the room. Be
available to help but be careful not to give the answers (``64.0
degrees'') or how exactly how to find the answer (``Spin the clock hands
until 12 noon and read the altitude here.'') Instead, ask questions that
will guide them to the solution, for example, ``As you change the time,
what properties of the Sun are changing? Where is that recorded?''

In the past, most students have been able to figure out the answers to
the two questions (the Sun's altitude is $64^\circ$ at noon on July 1
and its most northerly rise is around azimuth $52.7^\circ$, or
$90-52.7=37.3^\circ$ North of West on June 20).


\titlebar{Part 2: The Path of the Sun}{20 min}

When it looks like everyone has finished the tasks, or are close, hand
out Page~2 \marginpar{hand out Page~2} and gather
their attention so you can demonstrate how to use the simulator to collect
data and sketch the Sun's path. You can reassure them that even if they
didn't figure out all the features of the simulation, they know enough
to proceed. 

\medskip

Using the computer hooked up to the projector, demonstrate how to
collect the observations needed to trace the path of the Sun
``today''. That is, do it for whatever date you're running the
activity. Ask them to follow along at their own computers.

\begin{description}
\item[location and date] Check that the location is set to Vancouver (latitude
  $49^\circ$~North) either by dragging the latitude bar on the map or
  typing 49 into the latitude text box. Set the day to today's date, by
  draggin the bar or entering the date into date text box.
\item[time of sunrise] There are a couple of ways to simulate
  sunrise. You can drag the Sun in the ``animation'' window over to the
  Eastern horizon (you can click-and-drag the celestial sphere
  to change the point-of-view.) You're watching for the moment when the
  Sun's altitude is $0.0$. Notice the clock hands spin. You can also
  grab those clock hands and spin them around until the Sun rises. When
  you've got the time for sunrise, write it on your copy of Page~2, ask
  them to write it on theirs.
\item[location of sunrise] With the Sun on the Eastern horizon, read off
  the azimuth, also given in the window below the animation. Convert
  that to degrees North or South of (due) East at azimuth $90^\circ$. We
  do this conversion because azimuth is not very intuitive. It is much
  easier to visualize angles North or South of East.
\item[highest altitude] The time used in the simulation is local time,
  not standard or daylight saving time. So, the Sun reaches it's maximum
  altitude close to 12 noon. Students might not know that fact (yet) so
  it might be better to drag the Sun up from the horizon, watching for
  the location when the azimuth is exactly $180.0^\circ$ and then
  ``noticing'' that it occurs at about 12 noon. Record the maximum altitude and have
  them record it, too.

  Notice this is the moment when the Sun crosses the gray circle, the
  meridian, in the animation window. In the morning, the Sun is ``before
  the meridian'' or in Latin, ``ante meridiem'' ``a.m.'' while in the
  afternoon and evening, the Sun is past the meridian, ``post
  meridiem'', ``p.m.''
\item[time of sunset] Drag the Sun down to the Western horizon or spin
  the clock hands. Watch for the time when the Sun's altitude drops to
  0. Record the time...
\item[location of sunset] ...and location, again converting from
  azimuth to degrees North or South of due West at azimuth $270^\circ$.
\item[Sun's path] Switch to the overhead of the celestial sphere. Ask
  the students to follow along with you: Mark
  the location of sunrise, the maximum altitude and the location of
  sunset, and connect the dots with a nice curve. Label the sunrise and
  sunset times and put the date on the curve.

  (It might be possible to project an image of the celestial sphere and
  then draw the curve on the projection. Be sure, of course, that you're
  projecting onto the whiteboard, not the projector screen.)
\end{description}

With this demonstration complete, ask the students to do the same thing
for the 2 dates on their worksheets.


\titlebar{Part 3: Questions}{Remainder of tutorial}

As groups finish Part~2 and draw their 2 paths on the sky diagram, hand
out \marginpar{hand out Part~3 as needed} the Question sheet.  

\medskip

\begin{enumerate}
\item This question asks for the length of the day, which means the
number of hours of sunlight during the day, not 24~hours. They'll use
their own data for 2 dates and read the data off their diagrams for the
other 2 dates. 

\item The days are longer in the summer and shorter in the
  winter but they are ``balanced'' or ``symmetric''.  They should shade
  in 1/2 of the graph: over the course of a year, half the time is day
  and half the time is night.

\item In the short, 50-minute tutorials, we don't have time to
  fully-explore the role that latitude plays in the path of the
  Sun. However, students have likely heard, in class and elsewhere,
  about the strange pattern at the North Pole, the ``Land of the
  Midnight Sun.'' This question asks them to simulate the Sun's motion
  there. Depending on exactly when this activity runs, the Sun may or
  may not rise (or set). It certainly doesn't set on June 20 (``midnight
  Sun''). The Sun does rise, in a way, on the Vernal equinox around
  March 20.

\item This question explores a ``break'' in the pattern. They're likely
  to learn that on the equinoxes, the Sun rises at 6:00~a.m. and sets at
  6:00~p.m. That's a good approximation but it's not correct. The
  students observe slight variations from this ideal pattern that are
  due to the Earth's variable speed around the Sun and the Sun's
  analemma. Though this lab doesn't discuss the analemma, it could
  prime the students to watch for it in an upcoming class or reinforce
  it if the analemma has already been discussed in class.
\end{enumerate}


\titlebar{Clean-up}{5 minutes}

After the tutorial, be sure to return the projector to the Main Office.




\end{document}

