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

1. Feb 8, 2010

### warfreak131

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

$$\tan(1 sec) = \frac{2.3 \cdot 10^{13} cm}{d}$$

$$d=\frac{2.3{\cdot}10^{13} cm}{Tan(\frac{1}{3600})}$$

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

Is this correct?

Last edited by a moderator: Feb 8, 2010
2. Feb 8, 2010

### Spinnor

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?