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The planet, small, dark circle, crosses in front of the star as seen from Earth. In the process, it blocks out some light. The light curve, shown on the bottom, is a plot of brightness versus time, and shows that the star brightness is steady until the exoplanet starts to cover up some of the visible surface of the star. As it does so, the star dims. It eventually returns back to its normal brightness only to await the next transit.}}{142}} \newlabel{exotransit}{{11.9}{142}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {11.3.2}Direct Detection}{142}} \@writefile{lof}{\contentsline {figure}{\numberline {11.10}{\ignorespaces A coronagraphic image of an exoplanet orbiting the star Fomalhaut (inside the box, with the arrow labeled ``2012''). This image was obtained with the Hubble Space Telescope, and the star's light has been blocked-out using a small metal disk. Fomalhaut is also surrounded by a dusty disk of material---the broad band of light that makes a complete circle around the star. This band of dusty material is about the same size as the Kuiper belt in our solar system. The planet, ``Fomalhaut B'', is estimated to take 1,700 years to orbit once around the star. Thus, using Kepler's third law (P$^{\rm 2}$ $\propto $ a$^{\rm 3}$), it is roughly about 140 AU from Fomalhaut (remember that Pluto orbits at 39.5 AU from the Sun).}}{143}} \newlabel{fomalhaut}{{11.10}{143}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {11.3.3}Radial Velocity (Stellar Wobble)}{143}} \@writefile{toc}{\contentsline {subsection}{\numberline {11.4}Characterizing Exoplanets from Transit Light Curves}{144}} \@writefile{lof}{\contentsline {figure}{\numberline {11.11}{\ignorespaces An exoplanet transit light curve (bottom) can provide a useful amount of information. The most important attribute is the radius of the exoplanet. But if you know the mass and radius of the exoplanet host star, you can determine other details about the exoplanet's orbit. As the figure suggests, by observing multiple transits of an exoplanet, you can actually determine whether it has a moon! This is because the exoplanet and its moon orbit around the center of mass of the system (``barycenter''), and thus the planet appears to wobble back and forth relative to the host star.}}{144}} \newlabel{transit}{{11.11}{144}} \@writefile{toc}{\contentsline {subsection}{\numberline {11.5}Deriving Parameters from Transit Light Curves}{145}} \@writefile{lof}{\contentsline {figure}{\numberline {11.12}{\ignorespaces The light curve of Kepler 1b as measured by the {\it Kepler} satellite. The numbers on the y-axis are the total counts (how much light was measured), while the x-axis is ``modified Julian days''. This is a system that simply makes it easy to figure out periods of astronomical events since it is a number that increases by 1 every day (instead of figuring out how many days there were between June 6$^{\rm th}$ and November 3$^{\rm rd}$). Thus, to get an orbital period you just subtract the MJD of one event from the MJD of the next event.}}{146}} \newlabel{kepler}{{11.12}{146}} \@writefile{lof}{\contentsline {figure}{\numberline {11.13}{\ignorespaces Transiting exoplanet \#1. 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This faint band of light is composed of the light from thousands and thousands of very faint stars. The Milky Way spans a complete circle across the celestial sphere because our solar system is located within the ``disk'' of the galaxy. }}{161}} \newlabel{bandoflight}{{12.1}{161}} \@writefile{lof}{\contentsline {figure}{\numberline {12.2}{\ignorespaces A diagram of the size and scale of our ``Milky Way'' galaxy. The main regions of our galaxy, the ``bulge'', ``disk'', and ``halo'' are labeled. Our Milky Way is a spiral galaxy, with the Sun located in a spiral arm 28,000 ly from the nucleus. Note that the disk of the Milky Way galaxy spans 100,000 ly, but is only about 1,000 ly thick. While the disk and spiral arms of the Milky Way are filled with young stars, and star forming regions, the bulge of the Milky Way is composed of old, red stars. }}{162}} \newlabel{milkyway}{{12.2}{162}} \@writefile{toc}{\contentsline {subsection}{\numberline {12.3}Galaxy Types: Spirals Ellipticals, and Irregulars}{162}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {12.3.1}Spiral Galaxies}{163}} \@writefile{lof}{\contentsline {figure}{\numberline {12.3}{\ignorespaces The Sb spiral galaxy M81. Notice the nice, uniform spiral arms that are wound tightly around the large, central bulge. Inside the spiral arms, there are large regions of glowing gas called HII regions--where stars are being born. These stand out as knots or clumps in the spiral arms. The dark spots, lanes, and arcs are due to dust clouds that are associated with these star forming regions. }}{163}} \newlabel{m81stretch}{{12.3}{163}} \@writefile{lof}{\contentsline {figure}{\numberline {12.4}{\ignorespaces The Sc spiral galaxy M51. Notice the large, clumpy spiral arms that are loosely wound around the small, central bulge. Inside the spiral arms of M51 there are very many large HII regions--M51 has many young star forming regions. Notice that there is also a lot more dust in M51 than in M81.}}{164}} \newlabel{m51stretch}{{12.4}{164}} \@writefile{lof}{\contentsline {figure}{\numberline {12.5}{\ignorespaces The Sab spiral galaxy M31. Notice the very large bulge, and very tightly wound spiral arms. Like the Milky Way, the Andromeda Galaxy has several small galaxies in orbit around it (just like planets orbit the Sun, some small galaxies can be found orbiting around large galaxies). Two of these galaxies can be seen as the round/elliptical blobs above and below the disk of the Andromeda galaxy shown here. Both are elliptical galaxies, discussed in the next subsection. }}{164}} \newlabel{m31big}{{12.5}{164}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {12.3.2}Elliptical Galaxies}{164}} \@writefile{lof}{\contentsline {figure}{\numberline {12.6}{\ignorespaces The classification sequence for spirals. S0 spirals are galaxies that show a small disk that is composed of only old, red stars, and have no gas, little dust and no star forming regions. They are mostly a large bulge with a weak disk, with difficult-to-detect spiral arms. They actually share many properties with elliptical galaxies. Sa galaxies have large bulges, and tightly wound spiral arms. Sb's have less tightly wound arms, while Sc's have very loosely wound arms, and have tiny bulges.}}{165}} \newlabel{spirals}{{12.6}{165}} \@writefile{lof}{\contentsline {figure}{\numberline {12.7}{\ignorespaces A typical elliptical galaxy, NGC205, one of the small elliptical galaxies in orbit around the Andromeda galaxy shown in Fig. \G@refundefinedtrue \text {\normalfont \bfseries ??}\GenericWarning { }{LaTeX Warning: Reference `fig:m31big' on page 165 undefined}. Most elliptical galaxies have a small, bright core, where millions of stars cluster around the nucleus. Just like the Milky Way, the density of stars increases dramatically as you get near the nucleus of an elliptical galaxy. Many elliptical galaxies have black holes at their centers. NGC205 is classified as an E5.}}{165}} \newlabel{elliptical}{{12.7}{165}} \@writefile{lof}{\contentsline {figure}{\numberline {12.8}{\ignorespaces The classification scheme for elliptical galaxies. Elliptical galaxies range from round (E0), to football shaped (E7). }}{166}} \newlabel{ellipticals}{{12.8}{166}} \@writefile{lof}{\contentsline {figure}{\numberline {12.9}{\ignorespaces The definition of the major (``a'') and minor (``b'') axes of an ellipse. }}{166}} \newlabel{ellipse}{{12.9}{166}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {12.3.3}Irregular Galaxies}{166}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {12.3.4}Galaxy Classification Issues}{166}} \@writefile{lof}{\contentsline {figure}{\numberline {12.10}{\ignorespaces The Large Magellanic Cloud (LMC). The LMC is a small, irregular galaxy that orbits around the Milky Way galaxy. The LMC (and its smaller cousin, the SMC) were discovered during Magellan's voyage, and appear as faint patches of light that look like detached pieces of the Milky Way to the naked eye. The LMC and SMC can only be clearly seen from the southern hemisphere. }}{167}} \newlabel{LMC}{{12.10}{167}} \@writefile{toc}{\contentsline {subsection}{\numberline {12.4}Lab Exercises}{167}} \@writefile{lof}{\contentsline {figure}{\numberline {12.11}{\ignorespaces An irregular galaxy that is the result of the collision between two galaxies. The larger galaxy appears to have once been a normal spiral galaxy. But another galaxy (visible in the bottom right corner) ran into the bigger galaxy, and destroyed the symmetry typically found in a spiral galaxy. Galaxy collisions are quite frequent, and can generate a large amount of star formation as the gas and dust clouds are compressed as they run into each other. Some day, the Milky Way and Andromeda galaxies are going to collide---it will be a major disruption to our galaxy, but the star density is so low, that very few stars will actually run into each other! }}{168}} \newlabel{irregular}{{12.11}{168}} \@writefile{toc}{\contentsline {subsection}{\numberline {12.5}Summary (35 points)}{179}} \@writefile{toc}{\contentsline {subsection}{\numberline {12.6}Possible Quiz Questions}{179}} \@writefile{toc}{\contentsline {subsection}{\numberline {12.7}Extra Credit (ask your TA for permission before attempting, 5 points)}{179}} \@writefile{toc}{\contentsline {section}{\numberline {13}Hubble's Law: Finding the Age of the Universe}{180}} \@writefile{toc}{\contentsline {subsection}{\numberline {13.1}Introduction}{180}} \@writefile{toc}{\contentsline {subsection}{\numberline {13.2}Doppler Shift}{180}} \@writefile{lof}{\contentsline {figure}{\numberline {13.1}{\ignorespaces A waterbug, treading water.}}{180}} \newlabel{bug}{{13.1}{180}} \@writefile{toc}{\contentsline {subsection}{\numberline {13.3}Hubble's Law}{182}} \@writefile{toc}{\contentsline {subsection}{\numberline {13.4}The Age of the Universe}{185}} \@writefile{toc}{\contentsline {subsection}{\numberline {13.5}How Do we Measure Distances to Galaxies and Galaxy Clusters?}{186}} \@writefile{lof}{\contentsline {figure}{\numberline {13.2}{\ignorespaces If you draw concentric spheres around a light source (we have cut the spheres in half for clarity), you can see how light spreads out as it travels. The light passing through one square on the inner sphere passes through four squares for a sphere that has twice the radius, and nine squares for a sphere that has three times the radius of the innermost sphere. This is because the area of a sphere is 4$\pi $R$^{\rm 2}$.}}{187}} \newlabel{inverse}{{13.2}{187}} \@writefile{toc}{\contentsline {subsection}{\numberline {13.6}Questions}{188}} \@writefile{toc}{\contentsline {subsection}{\numberline {13.7}Summary (35 points)}{189}} \@writefile{toc}{\contentsline {subsection}{\numberline {13.8}Extra Credit (ask your TA for permission before attempting, 5 points)}{189}} \@writefile{toc}{\contentsline {section}{\numberline {14}How Many Galaxies are there in the Universe?}{190}} \@writefile{toc}{\contentsline {subsection}{\numberline {14.1}Introduction}{190}} \@writefile{toc}{\contentsline {subsection}{\numberline {14.2}Exercise Section}{190}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {14.2.1}Direct Measurement, Measurement Error}{190}} \@writefile{lof}{\contentsline {figure}{\numberline {14.1}{\ignorespaces A map of the NMSU campus from the NMSU WWW site}}{191}} \newlabel{campusmap}{{14.1}{191}} \@writefile{toc}{\contentsline {subsubsection}{\numberline {14.2.2}Estimation}{191}} \@writefile{toc}{\contentsline {subsection}{\numberline {14.3}How many galaxies are there in the Universe?}{191}} \@writefile{lof}{\contentsline {figure}{\numberline {14.2}{\ignorespaces A reproduction of the Hubble Deep Field image.}}{193}} \newlabel{hdf}{{14.2}{193}} \@writefile{toc}{\contentsline {subsection}{\numberline {14.4}The Mass and Density of the Universe (Contained in Galaxies)}{195}} \@writefile{toc}{\contentsline {subsection}{\numberline {14.5}Summary (35 points)}{199}} \@writefile{toc}{\contentsline {subsection}{\numberline {14.6}Possible Quiz Questions}{199}} \@writefile{toc}{\contentsline {subsection}{\numberline {14.7}Extra Credit (ask your TA for permission before attempting, 5 points)}{199}} \@writefile{toc}{\contentsline {section}{\numberline {15}APPENDIX A: Fundamental Quantities}{201}} \@writefile{toc}{\contentsline {section}{\numberline {16}APPENDIX B: Accuracy and Significant Digits}{202}} \@writefile{toc}{\contentsline {section}{\numberline {17}APPENDIX C: Unit Conversions}{203}} \@writefile{toc}{\contentsline {section}{\numberline {18}APPENDIX D: Uncertainties and Errors}{204}} \@writefile{toc}{\contentsline {section}{\numberline {19}Observatory Worksheets}{205}}