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Vanessa McBride
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Fixed latex backslash brackets again
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Teaching Materials/Data Wrangling/Examples/Exoplanets_sort_and_plot/Exoplanets_sort_and_plot.ipynb

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"\n",
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"The High Accuracy Radial Velocity Planet Searcher (<a href=\"http://www.eso.org/sci/facilities/lasilla/instruments/harps.html\">HARPS</a>) has found over one thousand exoplanets using the radial velocity search method. It has an accuracy of 1 m/s in radial velocity. \n",
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"\n",
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"How does this translate into limits on the masses and orbits of planets you can detect with HARPS orbiting a \\(1 M_\\odot\\) star?\n",
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"How does this translate into limits on the masses and orbits of planets you can detect with HARPS orbiting a $1 M_\\odot$ star?\n",
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"\n",
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"---\n",
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"From our lecture notes, we express Kepler's equation for the star-planet system as follows:\n",
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"$$\n",
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"v_* \\sin i = 28.4\\left(\\frac{P}{1\\mathrm{yr}}\\right)^{-1/3}\\left(\\frac{M_p\\sin i}{M_J}\\right)\\left(\\frac{M_*}{M_\\odot}\\right)^{-2/3}\\mathrm{ms}^{-1}\n",
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"$$\n",
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"where \\(v_*\\) is the velocity of the star, $P$ is the orbital period of the planet around the star (in years), $M_J$ is the mass of Jupiter, $M_*$ is the mass of the parent star in $M_\\odot$. \n",
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"where $v_*$ is the velocity of the star, $P$ is the orbital period of the planet around the star (in years), $M_J$ is the mass of Jupiter, $M_*$ is the mass of the parent star in $M_\\odot$. \n",
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"\n",
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"Using $M_* = 1 M_\\odot$, and Kepler's harmonic law $P^2 = a^3$ (remember, this works in this specific choice of units), we can rewrite the equation above as:\n",
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"\n",

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