\documentclass[10pt]{article}% uses letterpaper by default %---------- Uncomment one of them ------------------------------ \usepackage[includeheadfoot, top=1in, bottom=1in, hmargin=1in]{geometry} % \usepackage[a5paper, landscape, twocolumn, twoside, % left=2cm, hmarginratio=2:1, includemp, marginparwidth=43pt, % bottom=1cm, foot=.7cm, includefoot, textheight=11cm, heightrounded, % columnsep=1cm, dvips, verbose]{geometry} %--------------------------------------------------------------- \usepackage{fancyhdr} \usepackage{verbatim} \usepackage{url} \pagestyle{fancy} \usepackage{graphicx} \usepackage{setspace} %\doublespacing \singlespacing %\onehalfspacing %\newcommand{\exercisename}{} \rhead{Earth, Moon, and Planets Lab (Tue 7-10pm)} \chead{} \lhead{Exercise set 8} \renewcommand{\rightmark}{} \lfoot{Roban Hultman Kramer} \cfoot{\thepage} \rfoot{Spring 2006} \newcommand{\degrees}{\ensuremath{^\circ}} \newcommand{\arcmin}{\ensuremath{'}} \newcommand{\arcsec}{\ensuremath{"}} \newcommand{\hours}{\ensuremath{^\mathrm{h}}} \newcommand{\minutes}{\ensuremath{^\mathrm{m}}} \newcommand{\seconds}{\ensuremath{^\mathrm{s}}} \begin{document} \begin{center} \huge Exercise set eight \end{center} \section{Outdoor: Observing Saturn} \subsection*{Materials} telescope \subsection*{Instructions} You will be observing Saturn and its rings and moons, tonight. \subsubsection*{Pre-Observation} \begin{enumerate} \item Can you think of any ways to tell moons from stars during your observations tonight? \item Imagine you are facing South and looking at the sky with your naked eye. North will be ``up'' (i.e. farther from the horizon in front of you) from this perspective. Draw two arrows at right angles to each other, one pointing North and one East as you would see it on the sky and label them. Label the set of arrows ``looking South''. Also make sets of arrows for ``Looking East'', and ``Looking North''. \item Some telescope setups will flip the image of the telescope either ``left-right'', or ``up-down'', or both. Draw the same sets of arrows as in the previous question, but this time as seen through a telescope that flips the image both ways. \item Think of a way to tell which way is North and which way is East in the telescope. Remember that the telescope may flip the image one or both ways. Hint: you can move the telescope and you can also watch how things move in the telescope due to the Earth's rotation. \item Saturn is currently $8.85$~au from the Earth ($1$~au~$=1.5\times10^8$~km). Saturn's diameter is $1.2 \times 10^5$~km. Calculate the Saturn's angular diameter. \item Show me your answers to these questions before you go out. \end{enumerate} \subsubsection*{Observation} Observe Saturn with the telescope. You may try out different eyepieces. \begin{enumerate} \item Is the image in the telescope flipped one or both ways? \item Draw a circle representing the field of view of the telescope. Label the North and East edges of the circle. \item Draw Saturn, its rings, and anything you think might be a moon of Saturn within the circle. \item Record approximately how far each moon is from Saturn on the sky (in Saturn diameters). \item Record the focal length and type of the eyepieces you use. \item Record the focal length and diameter of the telescope. %Newtonian: Diameter $305$mm, Focal length $1500$mm. \end{enumerate} \subsubsection*{Post-Observation} \begin{enumerate} \item The ``field of view'' of a particular telescope-eyepiece combination is the angular width of the region of the sky visible through the telescope. From your previous calculations and your observations, estimate the field of view of the setup you used. \item Calculate the projected distances between Saturn and each potential moon. \item Magnification measures how much larger, in angular extent, objects appear when viewed through a particular optical setup. The magnification of a telescope-eyepiece combination is just the focal length of the telescope divided by the focal length of the eyepiece $m = f_\mathrm{tele}/f_\mathrm{eyep}$. Calculate the magnification of the setup you used. \end{enumerate} \section{Outdoor: Measuring the Field of View} \subsection*{Materials} telescope, watch which indicates seconds \subsection*{Instructions} \subsubsection*{Pre-Observation} The ``field of view'' of a particular telescope-eyepiece combination is the angular width of the region of the sky visible through the telescope. \begin{enumerate} \item How could you measure the field of view of a telescope using the rotation of the Earth (you will need a watch)? \item Where would you need to point in the sky (it \textit{does} matter)? \item Show me your observing plan before you go out. \end{enumerate} \subsubsection*{Observation} Use the same telescope setup you used for the Saturn observations, if you've done them. Take the necessary observations to measure the field of view. Make sure to repeat your measurements at least 3 times. Record what eyepiece you are using (focal length and type), and the focal length and diameter of the telescope. \subsubsection*{Post-Observation} Calculate the field of view of your telescope setup. \section{On paper: The Mass of Saturn} \begin{enumerate} \item If you had more time to observe (i.e. many nights), how would you determine what was one of Saturn's moons and what was a star? \item Using the same observations you would use for the previous question, how could you determine the mass of Saturn (assuming you know the distance to it)? Hint: from your observations you could measure the apparent angular separation between Saturn and each moon as a function of time. \item Use the information below to find the orbital period for each moon listed (in days). It may help to count the number of periods that occur over a certain span of days. \item Find the orbital radius for each of the moons listed (in km). \item Use this information (and Kepler's 3rd law) to estimate the mass of Saturn (in solar masses). It may help to convert your periods to years. \end{enumerate} The projected displacement, in Saturn radii, East and South of Saturn every $24$ hours for two of Saturn's moons. Saturn's diameter is $1.2 \times 10^5$~km. \begin{tabular}{lrrrr} Date & Titan & Titan & Enceladus& Enceladus \\ & South & East & South & East \\ 2006/04/12& -15.104& 6.246& 3.950 & -0.352 \\ 2006/04/13& -8.957& 7.280& -0.638 & 1.432 \\ 2006/04/14& -1.514& 7.250& -3.753 & 0.001 \\ 2006/04/15& 6.150& 6.176& 1.659 & -1.425 \\ 2006/04/16& 12.942& 4.234& 3.364 & 0.371 \\ 2006/04/17& 17.915& 1.698& -2.449 & 1.339 \\ 2006/04/18& 20.344& -1.076& -2.704 & -0.705 \\ 2006/04/19& 19.821& -3.690& 3.201 & -1.147 \\ 2006/04/20& 16.337& -5.747& 1.932 & 1.000 \\ 2006/04/21& 10.334& -6.912& -3.637 & 0.906 \\ 2006/04/22& 2.693& -6.973& -0.952 & -1.227 \\ 2006/04/23& -5.379& -5.896& 3.928 & -0.578 \\ 2006/04/24& -12.558& -3.845& 0.011 & 1.375 \\ 2006/04/25& -17.661& -1.157& -3.889 & 0.241 \\ 2006/04/26& -19.872& 1.722& 1.049 & -1.432 \\ 2006/04/27& -18.893& 4.327& 3.659 & 0.135 \\ 2006/04/28& -14.967& 6.259& -1.913 & 1.401 \\ 2006/04/29& -8.781& 7.245& -3.133 & -0.484 \\ 2006/04/30& -1.314& 7.170& 2.783 & -1.268 \\ 2006/05/01& 6.333& 6.073& 2.464 & 0.811 \\ 2006/05/02& 13.086& 4.125& -3.348 & 1.070 \\ 2006/05/03& 18.002& 1.600& -1.559 & -1.080 \\ 2006/05/04& 20.364& -1.147& 3.804 & -0.781 \\ 2006/05/05& 19.771& -3.724& 0.645 & 1.278 \\ 2006/05/06& 16.223& -5.737& -3.920 & 0.466 \\ 2006/05/07& 10.173& -6.857& 0.426 & -1.394 \\ 2006/05/08& 2.511& -6.881& 3.855 & -0.098 \\ 2006/05/09& -5.551& -5.782& -1.340 & 1.420 \\ 2006/05/10& -12.694& -3.730& -3.471 & -0.255 \\ 2006/05/11& -17.740& -1.063& 2.304 & -1.347 \\ \end{tabular} \end{document}