Calculate the length of a parsec if you are on mars

[warfreak131]

Homework Statement

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

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?

 

[Spinnor]

Homework Statement

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

The Attempt at a Solution

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

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

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

Is this correct?

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?