\setcounter{figure}{0}
\setcounter{table}{0}
\hspace*{3.0in}Name:{\hrulefill} \\
\hspace*{3.25in}Date:{\hrulefill}

\begin{Large}
\section{\bf Heating and Cooling of Planets (and Daytime Observations)}
\end{Large}

\subsection{Heating and Cooling Introduction}

With this lab exercise we will investigate the ability of the radiant
energy from the Sun to heat an object (planet, sidewalk, water-filled can).
How rapidly, or how much, an object warms is dependent upon several factors,
which are discussed below.   The knowledge you should gain from this lab
includes how the rate of warming depends upon the reflectivity of an object,
and how effectively an object (surface of a planet, for example) can cool
via emission of radiant energy.\\
\\
The local temperature at a given location on a planet, including the air temperature near the ground, is  dependent upon a number of important factors.  Global factors include the tilt of the planet's rotational axis relative to its path around the Sun and the eccentricity of the planet's orbit.  Naturally, local factors can also affect the local temperature.\\
\\
Several global and local factors that affect a planet's globally-averaged temperature and also the local temperature are as follows:

\begin{itemize}

\item The length of daylight hours, dependent upon the rotation rate of a planet, determines the ratio of solar heating during the day and infrared cooling (emitted to space) during both the day and night.

\item The slant angle of the incoming sunlight affects the local sunlight intensity and explains why sloped parts of your face such as your nose sunburn more easily than the more vertical regions. This effect is a function of latitude and season on those planets that have a non-zero axial tilt.

\item The degree of ellipticity of a planet's orbit can affect the seasonal 
changes or can induce sunlight intensity variations that are similar to axially-induced seasonal variations.  This has a major impact for Mercury and Pluto and somewhat less for Mars.  For the Earth it only causes about $\pm$3\% variations in incoming solar intensity throughout a year. 

\item The degree to which the atmosphere serves as an insulating blanket (including greenhouse effects) can affect the daily averaged temperature and the range of temperature between the coldest and warmest times of a day.

\item For the terrestrial planets, the albedo (percent reflectivity) of the local clouds and surface can also greatly affect short term temperature variations as well as the planet's globally averaged temperature.  See Figure~\ref{cans-fig}.
\begin{figure}[htb]
\centerline{{\includegraphics[width=10cm]{cans.pdf}}}
\caption{The white can has a high albedo and reflects most of the light (80\% in this case).  The black can has a low albedo and absorbs most of the light (only 20\% reflected here), and this can will be more likely to heat.}
\label{cans-fig}
\end{figure}

\end{itemize}

\subsection{Heating and Cooling Rates}

%In this lab you will consider the effect of albedo on heating and
%cooling rates. \\
%\\
Divide into groups of 3--4 people.  Each of these groups will be provided one soft drink can that has been painted white and two additional cans that have been painted black.  Each group will also be provided with three thermometers, one for each can. Additionally, each group will be provided with two pieces of `insulating' cardboard.  \\
\\
Working in the shade of the observatory domes, place your three cans on one of the pieces of cardboard provided (this will insulate the cans from the cold, or hot, ground).  Add 200 milliliters of cold water (colder than the local air temperature) to each of your 3 cans.  When the cans are filled, place a thermometer in each of the cans.  The thermometers will have been in the cold water prior to this, so they will already be at the approximate water temperature.  Allow the thermometers to equilibrate with the water in the cans for 3 minutes or so.\\
\\
Now take the cans and place them in the sunlight on the piece of insulating cardboard.   Record the temperatures of these three sunlit cans in Table~\ref{cans1-tab}.  (Be sure to keep track of which black can is which).  Also, record in Table~\ref{cans2-tab} the temperatures of the shaded white and black cans.  {\it These two cans, which all four groups will use, will be located on the north side of the open telescope dome.  Each group will record data for the two shaded cans, plus their three cans, for a total of five cans.}\\
\\
At five minute intervals (use a watch with a second hand or its equivalent), record in the tables the temperatures indicated on each of the five thermometers (again, taking care to not mix up the two black sunlit cans).   Continue this process through 25 minutes.  This will give you one temperature at time `zero' and 5 subsequent temperature readings.\\
\\
After 25 minutes have passed and you have tabulated the minute 25
temperature, place the `can-cozy' (insulator) on one of the black cans and move your three sunlit cans into the shade.  Continue to measure the temperatures of all five cans at 5-minute intervals through 45 minutes.
    
\begin{table}[htb]
\begin{center}
\caption{The effect of albedo on local heating and cooling rates.  Times 0-25 are during the
sunlit heating phase, and times 30-45 are during the shaded cooling phase.  ({\bf 10 points})}
\begin{tabular}{|c|c|c|c|}\hline
Time & Temp. of White Can & Temp. of Black Can 1 & Temp. of Black Can 2 \\ \hline
  0  &                   &                     &                     \\ \hline
  5  &                   &                     &                     \\ \hline
 10  &                   &                     &                     \\ \hline
 15  &                   &                     &                     \\ \hline
 20  &                   &                     &                     \\ \hline
 25  &                   &                     &                     \\ \hline
 \hline
 30  &                   &                     &                     \\ \hline
 35  &                   &                     &                     \\ \hline
 40  &                   &                     &                     \\ \hline
 45  &                   &                     &                     \\ \hline
\end{tabular}
\label{cans1-tab}
\end{center}
\end{table}

%\newpage

\begin{table}[htb]
\begin{center}
\caption{Heating and cooling rates in the shade.  These cans remain in the shade throughout the course of the entire experiment. ({\bf 10 points})}
\begin{tabular}{|c|c|c|c|}\hline
Time & Temp. of White Can & Temp. of Black Can    \\ \hline
  0  &                   &                      \\ \hline
  5  &                   &                      \\ \hline
 10  &                   &                      \\ \hline
 15  &                   &                      \\ \hline
 20  &                   &                      \\ \hline
 25  &                   &                      \\ \hline
 30  &                   &                      \\ \hline
 35  &                   &                      \\ \hline
 40  &                   &                      \\ \hline
 45  &                   &                      \\ \hline
\end{tabular}
\label{cans2-tab}
\end{center}
\end{table}

\newpage

\subsection{Heating and Cooling Questions}

\begin{enumerate}

\item  Plot the values of each of the five temperatures versus time {\it using five different line styles or symbols} on the graph paper provided.  Be sure to label each of the curves.  ({\bf 10 points})

\begin{figure}[htb]
\centerline{{\includegraphics[width=17cm]{graphpaper.pdf}}}
\caption{Plot of temperature ($^\circ$C) vs. time (minutes) for all five cans.}
\end{figure}

\item  For each can, calculate the average heating rate, using the equation given below, during the initial 25 minutes of the experiment (the time interval during which the three cans were in the sunlight).  The calculated values will be in units of degrees Centigrade per minute.  Insert your calculated heating rates into Table~\ref{canrates-tab}.  ({\bf 5 points})
\begin{eqnarray}
Heating~Rate = \frac{(Temperature~after~25~min.~-~Initial~Temperature)}{25~minutes}
\end{eqnarray}

\begin{table}[htbp]
\begin{center}
\caption{Heating rate values for different cans.}
\begin{tabular}{|c|c|}\hline
{\bf Can} & {\bf Heating Rate ($^\circ$C/min)}    \\ \hline
White can (in sunlight) &  \\ \hline
Black can 1 (in sunlight) & \\ \hline
Black can 2 (in sunlight) &  \\ \hline
White can (in shade) &  \\ \hline
Black can (in shade) &  \\ \hline
\end{tabular}
\label{canrates-tab}
\end{center}
\end{table}

\item  Which color can (black or white) has the largest heating rate when in the sunlight?   Did you expect this result? Why or why not?  Can you think of any other processes, in addition to radiative heating, that might have played a role in heating the water in these sunlit cans?  ({\bf 3 points})
\vspace{1.5in}

\item  What do you think was the process responsible for any warming or cooling experienced by the two shaded cans?  Is there a color dependence to
this temperature change in the shade?  Did you expect this?  Why or why not?
({\bf 5 points})
\vspace{1.5in}

\item  Subtract the heating rate you calculated for the shaded white can from the heating rate you calculated for the sunlit white can, and write this value below:\\

White can:  {\bf sunlit heating rate -- shaded heating rate} = \hrulefill \\

Subtract the heating rate you calculated for the shaded black can from the
heating rate you calculated for each of the two sunlit black cans:\\

        Black can Number 1: {\bf sunlit heating rate -- shaded heating rate} = \hrulefill \\

        Black can Number 2: {\bf sunlit heating rate -- shaded heating rate} = \hrulefill \\

How do these `corrected' radiative heating rates, which account for other processes than radiative heating, compare between the one white and 
two black sunlit cans?  Is this in better or worse agreement with your
expectations?  ({\bf 3 points})
\vspace{1.0in}

\item  Let's examine the cooling rates, as indicated by the temperatures measured after minute 25 of the experiment.   Calculate the averaged cooling rates for {\bf each} of the five cans, using the minute 45 and 25 temperatures and the twenty minute interval:\\

\begin{eqnarray}
Averaged~Cooling~Rate = \frac{(Temp.~after~25~min.~-~Temp.~after~45~ min.)}{20~minutes}
\end{eqnarray}

White can (sunlit)   : averaged cooling rate = \hrulefill \\
  
Black can (insulated): averaged cooling rate = \hrulefill \\

Black can (bare)     : averaged cooling rate = \hrulefill \\

White can (shaded)   : averaged cooling rate = \hrulefill \\

Black can (shaded)   : averaged cooling rate = \hrulefill \\
\newpage

Of the three cans that originally spent 25 minutes in the sunlight, which
had the smallest cooling rate (cooled most slowly)?  Why do you think this is the situation?  Did you expect this?  Why or why not?  ({\bf 3 points})
\vspace{1.5in}


\item  Of the three sunlit cans, which had the {\bf greatest} cooling rate (cooled most rapidly)?  What processes do you believe are responsible for the cooling of this can?  Do these processes also play a role in the cooling of the other cans?  ({\bf 3 points})
\vspace{1.5in}

\end{enumerate}

\subsection{Daytime Observing Introduction}

Venus is the Earth's closest planetary neighbor.  It has been viewed by civilizations of people on Earth for centuries, for it shines brightly in the morning or evening sky, earning the name ``morning star'' or ``evening star.''  [At one time, it was thought to be two different objects, one that appeared in the evening sky and another that appeared in the morning sky.]  Venus shines so brightly in our sky in part because of its proximity to Earth, and in part due to its highly reflective cloud layers, which completely surround the planet and hide the surface from our view.\\
\\
Venus has also played a key role in our understanding of the universe around us.  For centuries, it was believed that the Sun, the Moon, all of the known planets, and the stars in the sky revolved around the Earth.  This belief was known as the {\it geocentric model} of the universe, which placed the Earth at the center of it all.  However, it was telescopic observations of Venus that changed our view of the universe.  Galileo Galilei (1564-1642) was the first person to use a telescope to observe Venus.  Over time, he noted that Venus, like the Moon, exhibited phases, changing from a small, disk-like object to a large crescent shaped object.\\
\\
Galileo was aware of a new model that described the universe, the Sun-centered, or {\it heliocentric model} developed by Nicolaus Copernicus (1473-1543).  This model was extremely controversial because it removed the Earth from its privileged position at the center of the universe.  Nevertheless, Galileo found that the heliocentric model could completely explain the observed phases of Venus.\\
\\
In this lab, you will observe Venus through a telescope, as Galileo did,
and deduce information about Venus' relative distance from Earth throughout
its orbit and its motion around the Sun.  You may also observe Mercury, 
weather permitting, since it can also be visible during the daytime.

\subsection{Telescopic Observations}

Observe Venus and/or Mercury through the telescope at the Tombaugh Campus 
Observatory and draw and label what you see on the observation log at the end 
of this lab. Comment in the space below on what you saw.  What shape were 
they?  Were they what you expected?  Were they disappointing?  Did they 
appear to be a certain color?  {\bf The more descriptive you can be, the 
better.  (3 points)}\\
\vspace{1.5in}

\subsection{Phases of Venus}

\begin{figure}[htb]
\centerline{{\includegraphics[width=16cm]{venusphases.pdf}}}
\caption{Phases of Venus as recorded through a 16'' telescope (slightly
larger than the ones at the Tombaugh Campus Observatory) at Calvin College.  
These images came from their web page: {\tt http://www.calvin.edu/academic/phys/observatory/venus.html}.}
\label{venphase-fig}
\end{figure}
\vspace{1in}
\noindent Figure~\ref{venphase-fig} shows five telescopic observations of Venus.  Using your knowledge of the phases of the Moon, fill in Table~\ref{venphase-tab} with the {\it name} of the phase shown in each panel of Fig.~\ref{venphase-fig}.  [More than one panel can show the same phase.]  ({\bf 5 points})
\begin{table}[htb]
\begin{center}
\caption{Phases of Venus corresponding to Figure~\ref{venphase-fig}.}
\begin{tabular}{|c|c|}
\hline
{\bf Panel} & {~~~~\bf Phase~~~~}\\ \hline
a & \\ \hline
b & \\ \hline
c & \\ \hline
d & \\ \hline
e & \\ \hline
\end{tabular}
\label{venphase-tab}
\end{center}
\end{table}

\subsection{Heliocentric Model}

Figure~\ref{venorbit-fig} shows a schematic of the orbits of the Earth and Venus in the heliocentric model.  Using Fig.~\ref{venorbit-fig}, label the various Venus circles, labeling each one with the letter corresponding to the phases seen in panels of Fig.~\ref{venphase-fig} ({\bf a}, {\bf b}, {\bf c}, {\bf d}, and {\bf e}).  In other words, match the pictures of Venus in Figure~\ref{venphase-fig} with the orbital locations in Figure~\ref{venorbit-fig}.  Shade in one half of Venus in each location to illustrate which side is receiving sunlight.  ({\bf 5 points})

\begin{figure}[htbp]
\centerline{{\includegraphics[width=10cm]{venusorbit.pdf}}}
\caption{Orbit of Venus around the Sun.}
\label{venorbit-fig}
\end{figure}
\clearpage
~ ~ ~\\
\newpage
\hspace*{3.0in}Name:{\hrulefill} \\
\hspace*{3.25in}Date:{\hrulefill}\\

\subsection{Take Home Exercise (35 points total)}

In the space provided, answer the following questions:
\subsubsection{Heating and Cooling}

\begin{enumerate}

\item  What relationship is there between the `can cozy' and some planetary
characteristic of Venus, or Earth, or Mars?  ({\bf 10 points})
\vspace{2.0in}

\item  If you had conducted this experiment in July, how might your results differ from those we have obtained during this time of year?  What if you had conducted this experiment in mid-December?  ({\bf 5 points})
\vspace{1.0in}

\subsubsection{Daytime Observations}

\item  It takes Venus approximately 7 months to complete one orbit around the Sun.  However, we observe Venus through a full set of phases in slightly less than that time.  What other motion needs to be accounted for when predicting when we will see a particular phase of Venus from Earth?  ({\bf 5 points})
\vspace{1.5in}

\item  Comment on the role that the telescope played in changing our view of the universe in the 1600's.  Do you think this role still continues today?  Please give an example to support your viewpoint.  ({\bf 10 points})
\vspace{2in}

\item  Summarize the difference between the geocentric and heliocentric models of the universe and discuss how Galileo's observations of Venus influenced this debate.  ({\bf 5 points})
\vspace{2in}
\end{enumerate}
\subsection{Possible Quiz Questions}
\begin{enumerate}

\item Name one factor that could change a planet's globally averaged
temperature.

\item How does an atmosphere change a planet's temperature?

\item What is meant by the term ``albedo''?

\item How does a hot object cool?

\item What does the term ``inferior planet'' mean?
\end{enumerate}

\subsection{Extra Credit (ask your TA for permission before attempting, 5 points)}

Consider the image of a crescent Saturn below, taken by the Voyager 1 spacecraft on November 16, 1980.
\begin{figure}[htb]
\centerline{{\includegraphics[width=9cm]{sat_vgr1.jpg}}}
\end{figure}

\noindent Remember that Saturn is about 9.5 AU from the Sun.  With a good enough telescope, would you ever be able to see a similar view of Saturn (that is, in the crescent phase) from Earth?  ({\bf 1 points})\\
\vspace{0.75in}\\
If so, sketch a diagram similar to Figure~\ref{venorbit-fig} in the lab, showing a possible arrangement of the Sun, Earth, and Saturn that would allow you to see a crescent Saturn.  ({\bf 2 points})\\
\vspace{1.5in}\\
If not, explain why we are sometimes able to see a crescent Venus but never a crescent Saturn.  Drawing a diagram may help.  ({\bf 2 points})

\newpage

\begin{figure}[htbp]
\centerline{{\includegraphics[width=13cm]{observation.pdf}}}
\end{figure}

%\newpage

%\begin{figure}[htbp]
%\centerline{{\includegraphics[width=13cm]{observation.pdf}}}
%\end{figure}

