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% (C) 2010 by Eugeniy Mikhailov, <evgmik@gmail.com>
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\newcommand{\hw}[1]{%
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		\Large  \bf Homework #1%
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\hw{04}

\problem{Problem 1 (5 points)}
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Find the required precision of speed measurement to detect Mars like
planet around Sun like star at the distance of 1.4 AU.


\problem{Problem 2 (5 points)}
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Solve problem 7.6 from the textbook (Binary star parameters).


\problem{Problem 3 (5 points)}
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Observation of a binary system yields that one of the star is moving along an ellipse
like orbit in $xy$ plane. The observed ellipse is stretched along x axis with apparent
values of the semimajor axis $a'=1.9803$~AU and the semiminor axis $b' =
0.3473$~AU. A
careful observation of both stars yields the location of the center of mass at
position $x_{c.m.} = 0$~AU and $y_{c.m.}=0.04862$~AU with respect to the
center of the observed ellipse.

Find the real eccentricity, semimajor axis $a$, and the inclination angle.
Assume that the real semiminor axis direction is orthogonal to the line of
sight. Note: the observed data has uncertainty.


\problem{Problem 4 (5 points)}
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Solve problem 3.12 from the textbook (derivation of Wein's displacement
law).


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