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\rhead{Earth, Moon, and Planets Lab (Tue 7-10pm)}
\chead{}
\lhead{Exercise set two}
\renewcommand{\rightmark}{}
\lfoot{Roban Hultman Kramer} \cfoot{\thepage} \rfoot{Spring 2006}

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\begin{document}

\section{Indoor: Learn to use a sextant}

% Notes from 2006-02-07: need to more carefully specify where to stand
% and what to measure. Also, mirror adjustment was beyond most groups.
% Almost everyone needed individual tutoring on adjustment and vernier
% scale reading.

\subsection*{Materials} sextant, sextant manual

\subsection*{Instructions}

A sextant is a device for accurately measuring the angle between the
horizon and a celestial object (and other angles, too). This angle is
called the ``altitude'' of an object. This is the fundamental
measurement of celestial navigation, as you will learn in later
exercises.

Each person in group should follow the directions in the sextant
manual to learn to read the vernier and adjust the mirror, then
practice looking through it and taking an altitude.

You should set up controlled conditions so you can compare with
measurements made by others. Stand at one end of the hallway and
measure the angular height of the door at the other end. Make sure you
are all standing the same distance from the door and measuring the
height the same way. \textbf{Repeat your observations several times
  and record all of your measurements.} Compare with other students
and keep practicing to see how precise you can make your measurements.
This is a good time to make sure you understand how to rock the
sextant to get the best measurement.  

\textbf{Come up with a final value for the angular height and estimate
  your precision. Remember: precision is a number!} A good procedure
might be to discard any ``outliers'', take the average for your value,
and the standard deviation for your precision.

\section{Computer: Latitude, longitude, and time}

\subsection*{Materials}

computer with planetarium software

\subsection*{Instructions}

Your latitude, longitude and the current time determine what you will
see in the sky. In the exercise you will explore their effects on what
you see.

\subsubsection*{Exploring time}

First, some definitions.
\begin{description}

\item[``The zenith''] refers to the point directly overhead in the sky.

\item[``The meridian''] is the line running north-south through the zenith.

\item[``To transit''] is for a celestial object to cross the meridian.
  An object is at its highest point in the sky when it transits. (Note
  that a transit can also mean when one body passes in front of
  another.)

\item[``The altitude''] of an object is the angle between it and the
  horizon. The zenith has an altitude of $90\degrees$.

\item[``A sextant''] is a device for measuring angles precisely,
  particularly altitudes.

\item[``The azimuth''] of an object is the angle between its direction
  and due North, increasing to the East. Something above the Eastern
  horizon has an azimuth of $90\degrees$.

\end{description}

View the sky as it would appear right now from the roof.
\textbf{Record your latitude, longitude, and the time.} Always specify
what kind of time you are using, i.e. EST, EDT, UT.

First just watch the motion of objects in the sky over the course of
the whole night. \textbf{Which stars move the greatest angular
  distance across the sky?  Which stars move the least? Are there
  stars which never set? Where are they?} I'm looking for regions of
the sky, not the names of particular stars. 

\textbf{In light of what you've just found, which star(s) would you
  use as a ``compass'' to orient yourself?}

\textbf{Describe a procedure for using a sextant to determine when a
  star or planet transits. For which stars would this be easiest? For
  which would it be hardest?}

Now pick a bright star in the south-eastern sky to keep track of.
Watch its motion. \textbf{Record the azimuth, altitude, and time when
  it transits.}

\subsubsection*{Exploring longitude}

Set your time to when your star transits. Change your longitude by 30
degrees to the West in the planetarium software. \textbf{What time
  does the star transit now?} Explain your result.

\subsubsection*{Exploring latitude}

Set your location back to where you started.

This time I'm leaving things up to you a little more. Explore how the
sky changes as you change your latitude, and answer the following
question: \textbf{If you wanted to be able to go outside at any time
  of night and determine your latitude using only a sextant, how would
  you do it?}

\textbf{How could you determine your latitude using the Sun?} Hint:
you will need to make multiple observations. \textbf{If you also have
  a watch telling you the time at a known location (like the Greenwich
  Meridian at $0\degrees 0\arcmin 0\arcsec$) then you can also
  determine your longitude from the same observations. How?}

\section{On paper: Finding longitude from transit times}

\subsection*{Materials}

globe (optional)

\subsection*{Instructions}

\textbf{Draw a (large) circle to represent a view of the Earth looking
straight down on the North pole. Indicate which direction the Earth is
rotating in this diagram.} It may help to refer to a globe first and
think about where things rise and set.

\textbf{Draw a single line of longitude.} Let's say that line is going
through New York (longitude 73d 59m 39s) and the time is midnight
Eastern Daylight Time.

Now consider the star Scheat (pronounced ``SHEE-at'') in Pegasus that
transits the New York meridian at midnight on this particular day.
\textbf{Draw an arrow representing the direction to that star on your
  paper.}

\textbf{Now draw a second line of longitude $45\degrees$ to the west
  ($118\degrees 59\arcmin 29\arcsec$, which goes near Los Angeles).
  What time (EDT) will it be when Scheat transits in LA?  What will
  the local time be when Scheat transits in LA? What will the local
  time be, approximately, anywhere in the world when Scheat transits
  there?}

Now lets switch the problem around. It's September 22nd and you're on
an island somewhere in the pacific. You have a watch still set to
Eastern Daylight Time, a sextant, and a list of New York meridian
transit times for various stars. Your list tells you that on the night
of September 22nd, Scheat transits at 23:52 EDT (11:52pm EDT) in New
York. You start taking observations when Scheat starts to get high in
the northern sky. You determine that Scheat has reached its maximum
altitude when your watch says 5:17am EDT (though you know the sun only
set about 5 hours ago).
    
\textbf{Are you West or East of New York? How many degrees of longitude are
you from New York? What is your longitude?}

% Answers:
% Things rise later than in NY, so we are west of NY.

% 5:17 = 5.28 hours
% + 8/60 = 5.42 hours
% * 15 degrees per hours = 81.25 degrees

% 81.25 degrees + 73.99 degrees = 155.24 degrees longitude.

% If we use the sidereal rotation rate of 15.04 degrees per hour:
% 5.42 * 15.04 = 81.52 degrees 
% + 73.99 degrees = 155.51 degrees longitude
    
% Canada-France-Hawaii telescope is at 19:49:36 = 19.83 N, 155:28:18
% = 155.48 W, Mauna Kea, Hawaii.


\section{Outdoor: A first look at the sky}

\subsection*{Materials}

\textit{Turn Left at Orion} pages, sky charts, list of planets that
are up, lab notebooks

\subsection*{Instructions}

Find as many of the summer ``guideposts'' from \textit{Turn Left at
  Orion} as you can. Find any planets that are up. Find Polaris. Find
at least three constellations.

\section{Outdoor: A second look at the sky}

\subsection*{Materials}

\textit{Turn Left at Orion} pages, sky charts, list of planets that
are up, lab notebooks

\subsection*{Instructions}

Find as many constellations as you can. If it is very clear:
\textbf{figure out what constellation the Moon, Mars, and Saturn are
  in, and draw their positions with respect to the bright stars in the
  constellation.}

\end{document}