Converting parsecs to light years in the dumbest way possible I have to convert 132 parsecs to light years and I'm struggling to get the expected result. Here is my method:
$132 \text{ pc} = 132'' = 2,2' = 0,03(6)°$
I have an equation for stellar parallax which looks like this: $d = \Big( \dfrac{1 \text{ AU}}{\tan(0,03(6)°)}\Big)$
This should give me the distance to the object in Astronomical Units right? Well It doesn't and I have absolutely no idea why, I'd be very glad if someone could help me out
You asked for a dumb, tedious way of doing it. So here it is, in all its glory
One parsec is defined as $$\dfrac{1}{\tan(1'')} \text{ AU}=\dfrac{648000}{\pi} \text{ AU}$$
As $1 \text{ AU} = 149597870700 \text{ m}$, one parsec is equal to $$\dfrac{648000}{\pi} \cdot 149\,597\,870\,700 = \dfrac{96\,939\,420\,213\,600\,000}{\pi} \text{ m}$$
One light year can be calculated by multiplying $c$ by the number of seconds in a year: $$299792458 \cdot 86400 \cdot 365.25 = 9\,460\,730\,472\,580\,800 \text{ m}$$
Dividing the former by the latter, we get $\dfrac{1 \text{ pc}}{1 \text{ ly}} = 3.261564$