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\begin{document}

{\center {\bf Astronomy 103\\ Final Exam\\  May 12, 2014\\}}

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%{\bf Solutions: correct answers are marked in bold, red type.}

\bigskip
{\bf Instructions:  } 

{\bf No books, notes or calculator are allowed.} You have 2 hours to complete the exam, and please do not turn to the next page until instructed to do so.

\bigskip
{\bf You may find the following information helpful:}

\begin{itemize}
\item{1 AU $=3\times10^8$ km}
\item{speed of light $=3\times10^8$ m/s}
\item{Kepler's 3rd law: 
\[
a^3 = P^2 
\]
with the period $P$ in years and semi-major axis $a$ in AU.}
\item{Newton's law of gravity:
\[
F = \frac{GMm}{r^2}
\]}
\item{Peak wavelength and temperature of blackbody radiation:
\[
\lambda = \frac{3\times10^6}{T} \mbox{ nm}
\]
with wavelength $\lambda$ in nm (1 nm = $10^{-9}$ m) and temperature $T$ in Kelvin.}

\item{Conversion of mass into energy:  $E=mc^2$}

\item{Relationship between brightness $B$ and distance $d$:

\[
B_2 = B_1 \times \frac{d_1^2}{d_2^2}
\]}

\item{Relationship between luminosity $L$, temperature $T$ and radius $R$ of stars: 
\[
L=4\pi\sigma T^4 R^2
\]
where $4\pi \sigma$ are constants.}

\item{Hubble's law:
\[
v = H \times d
\]
where $v$ is velocity in km/s, $d$ is distance in Mpc, and $H$ is the Hubble constant, $H=70$ km/s/Mpc.}

\end{itemize}

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