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% (C) 2010 by Eugeniy Mikhailov, <evgmik@gmail.com>
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\usepackage{listings}
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\begin{document}
\newcommand{\problem}[1]{%
	{\flushleft  \bf #1\\}
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\newcommand{\hw}[1]{%
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		\Large  \bf Homework #1%
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}
\newcommand{\mat}[1]{% matlab code
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\hw{01}

\problem{Problem 1 (5 points)}
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Suppose there were 2 naked eye observes as good as Tycho Brahe able to measure angles
with $4'$ accuracy. Would they be able to estimate the smallest distance to
the Mars? Suppose that observers are situated at the opposite point of the
Earth and do their measurement simultaneously.

\problem{Problem 2 (5 points)}
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Professor Mikhailov is extremely paranoid. Shall he worry that spy
satellite can see what chapter of our text book he is reading? Assume that
spy telescope is good as 2.5 billion dollars Hubble telescope with the
prime mirror diameter of 2.4 m. Disregard the atmospheric distortion, measure
the book font size yourself.

\problem{Problem 3 (5 points)}
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The parallax of Proxima Centauri is 0.772$''$. Let's hope that there is a
Jupiter sized planet. Would we be able to resolve the disk of the planet
with the Hubble telescope?

\problem{Problem 4 (5 points)}
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Do the same estimation as in the previous problem but for Betelgeuse star
which has a quite large diameter of around 1000 R$_\odot$, where the solar
radius (R$_\odot$) is $6.995\times 10^8$~m. The parallax of Betelgeuse is
0.00763$''$.

\problem{Problem 5 (5 points)}
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The maximum elongation of  Mercury from the Sun is $28^\circ$, estimate the
Sun to Mercury distance in astronomical units.

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\end{document}
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