\section{Indoor: Plan an observation}

\subsection*{Materials} star chart

\subsection*{Instructions}

In this exercise you will plan a series of observations that will
allow you to measure the rotation rate of the Earth by observing the
apparent movement of the sky.

Outline of the observations: you will find a bright star near the
horizon to the East or West and measure it's altitude several times
over the course of a few hours. From this you will calculate the rate
of change of the altitude in degrees per hour. \textbf{Explain why
this is approximately the rotation rate of the Earth. Why is it
important the the star be to the East or West? Why might this number
(even if you measured it perfectly) differ slightly from the true
rotation rate?} Hint: think of the path of a star through the sky, and
its relation to the stars altitude. 

Of course, we already know what the rotation rate should be, which
will help us plan the observation. Calculate the rotation rate of the
Earth using the fact that it rotates roughly $360^\circ$ in $24$
hours. 

If you pick a star to the West, you will have to worry about it
setting in between your observations. \textbf{If your observations
span three hours, how high does your star have to start out for it to
still be up at the end? How precise would your measurements have to be
in order to detect the change in altitude between observations taken
20 minutes apart?}

Read through the procedure for the next exercise and make sure you
understand it. If you have any questions, make sure to ask them before
you leave. If it is clear, you can go outside and pick a vantage point
and a star. If it is not clear, you can still pick a likely vantage
point, but you may have to adjust later. 

\clearpage
\section{Outdoor: Measure the rotation rate of the Earth}

\subsection*{Materials} you, star chart, angles
subtended by your thumb and fist from previous exercises

\subsection*{Instructions}

Pick a clear night when you can go out at least three times over the
course of at least three hours. Your observations must be at least 20
minutes apart, and the first and last must be at least three hours
apart.

\begin{enumerate}
\item Pick a spot to which you can return \textit{exactly} with a
  relatively clear view of the Eastern or Western horizon. Since we're
  in New York, your ``horizon'' might very well be the roof of a
  building. This is fine as long as the building is fairly far away
  and it forms a relatively horizontal line that you can use as a
  stable horizon.
\item Find a bright star that you can identify reliably near the
  Eastern or Western horizon, but make sure it will still be up for
  your subsequent observations.
\item \textbf{Record the exact time and measure the altitude of your
  star using your thumb and/or fist.} Repeat your measurement a few
  times so you can take the average later. \textbf{Record the
  precision of your measurement.}
\item Return to make at least two more observations over a period of
  at least three hours.
\end{enumerate}

Now you have a list of times and altitudes. \textbf{Calculate the
rotation rate of the Earth using each pair of observations.} (If you
have three observations you can pair them up three
ways). \textbf{Decide on a final value and estimate your
precision. Explain how you did so.} 

Now calculate the rotation rate of the Earth using the fact that it
rotates roughly $360^\circ$ in $24$ hours. \textbf{Does your
measurement agree to within your precision? If not, how do you explain
the difference?}