How do I convert kilometers per second into parsec per year?

Question

I've worked out that a given galaxy is traveling at an apparent speed of 1.47x10^(4) km s^(-1) and I know that 1.0 parsec is roughly equal to 3.1x10^(13) but I'm completely blank as to how I now convert the speed from km s^(-1) to pc y^(-1).

any help would be hugely appreciated!

Answer 1

1 kilometer / second = 1.02268944 × 10-6 Parsecs / yr

http://www.google.com/intl/en/help/featu...

scroll down to calculator

Answer 2

1 Parsec = 3.1 × 10^16 meters  (not 10^13)  That would put you off by a factor of 1000 ;)      To make life easier, please write it as km /s   not km s^(-1)  

I typed "1 km/s = ? pc / yr" into google and got:

1 (km / s) = 1.02268944 × 10-6 pc / yr

so just multiply that by 1.47x10^4 :)  

Let's see if that makes sense using the numbers you provided (with the correction)

Standard conversions (always multiply by 1 while units cancel out, just like chem class)    For clarity I have annotated the "current" units off to the right, since the more conventional "across the board or paper" method doesn't work here in a text area

1.47x10^(4) km / s      (km / s)

* 1000 m / 1 km            ( m / s)

* 31556926 s / 1 yr     (m / y)

* 1 pc / 3.1x10^16 m      (pc / yr)

= 0.015 pc / yr (approx)

or using the google calculator directly  

14700 (km / s) = 0.0150335347 pc / yr

Use the automated tool to double check your work (you would have noticed the off by factor of 1000)   But not exclusively until you understand basic conversions.