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Homework Help: Calculate the length of a parsec if you are on mars

  1. Feb 8, 2010 #1
    1. The problem statement, all variables and given/known data

    In class, we use the CGS system, so I do all my work in cgs units and then convert at the end.

    The mean distance of Mars from the sun is 2.3 * 10^13cm

    1 arcsecond = (1/60) of (1/60) of 1 degree, = 1/3600th degree

    Let d = distance of 1 parsec

    3. The attempt at a solution

    [tex] \tan(1 sec) = \frac{2.3 \cdot 10^{13} cm}{d}[/tex]

    [tex]d=\frac{2.3{\cdot}10^{13} cm}{Tan(\frac{1}{3600})}[/tex]

    [tex]d=4.7{\cdot}10^{18} cm{\cdot}\frac{1 m}{100 cm}{\cdot}\frac{1 km}{1000 m}{\cdot}\frac{1 LY}{9.46{\cdot}10^{12} km}[/tex]
    [tex]d=4.7{\cdot}10^{18}{\cdot}\frac{1 LY}{9.46{\cdot}10^{12}}[/tex]
    [tex]d=4.97 LY[/tex]

    Is this correct?
    Last edited by a moderator: Feb 8, 2010
  2. jcsd
  3. Feb 8, 2010 #2
    Can you solve this by just taking the standard parsec and multiplying this by the appropriate ratio of the Earth's orbital radius to that of the orbital radius of Mars?
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