\section{Extrasolar planet detection}

\subsection*{Materials} graph of velocity versus time for 51 Peg,
graph of relative flux versus time for HD209458b

\subsection*{Instructions}

51 Pegasi, in the constellation Pegasus, was the first star found to
have a planet orbiting it. The planet cannot be seen directly, even
with the worlds best telescopes. Instead is was detected indirectly
through its gravitational influence on the star around which it
orbits. The planet tugs on 51 Peg as it orbits, moving the star
slightly. Scientists can measure the motion of the star by looking for
a slight shift of the stellar spectrum, called the Doppler shift. 

For 51 Peg:
\begin{enumerate}
\item Find the period, $P$, and half amplitude, $v_\mathrm{max}$, of
  the star's motion.

\item How big is the shift in wavelength, $\Delta \lambda$ that
  corresponds to $v_\mathrm{max}$ (use $\lambda_0 = 6000$ Angstroms)?
  The typical width of a stellar spectral line at $6000$ Angstroms is
  about $0.1$ Angstroms. How does this shift compare to the width of
  the line? 

\item Find the radius of the planet's orbit and its mass (figure out
  which equation to use based on the information you have and the
  information you want to calculate). Assume the orbit is edge-on, and
  the stellar mass is $1 M_\mathrm{Sun}$.

\item How does the mass of the planet compare to the mass of Jupiter?
  Note: $M_\mathrm{J} = 0.001 M_\mathrm{Sun}$.

\item Where would this planet be in the Solar System if it were
  orbiting the Sun? In other words, how does the size of its orbit
  compare to orbits of planets in the Solar System?
\end{enumerate}


HD209458 was the first star found to have a transiting planet, meaning
that the planet passes in front of the star from the perspective of
the Earth during its orbit. Astronomers had already determined that
HD209458 had a companion by Doppler-shift studies, and careful
photometry revealed the slight decrease in the amount of starlight
reaching us as the planet obscured part of the star.

For HD209458b:
\begin{enumerate}
\item Show that the fraction of star light blocked by the planet when
  it is in front of the star is
  $(R_\mathrm{planet}/R_\mathrm{star})^2$. Hint: if we could image
  them, both the planet and the star would look like circular disks in
  the sky, like the Moon or the Sun.
\item Use the graph to determine what fraction of the star light from
  HD209458 is blocked by the planet HD209458b?
\item What is the radius of the planet compared to the star
  $R_\mathrm{planet}/R_\mathrm{star}$ in this case?
\item If you assume the star has the same radius as the Sun, how does
 the radius of HD209458b compare to Jupiter. Note: The Sun's radius is
 $10$ times larger than Jupiter's.
\end{enumerate}