## Unit Conversion: Astronomical Units, Parsecs and Light Years...

Hi everyone,
It's been years since I solved a physics problem for school. Now that I'm back at it I could use some help on this problem:

Question

"The astonomical unit (AU) is defined as the mean centre to centre distance from Earth to the Sun, namely 1.496 x 10^11 m. The parsec is the radius of a circle for which a central angle of 1s intercepts an arc of length 1AU. The light year is the distance that light travels in 1 year. (a) How many parsecs are there in one AU?

The attempt at a solution

I can do simple conversions of units, but I'm having trouble figuring out the connection between AUs and parsecs. I know that Arc length = r * angle (in rad) which leaves me with 1 AU = 1 parsec * 1s. But then again s is seconds, not radians...
Another way I attempted the problem was to assume that the arc of a circle whose radian is 1 parsec is so large that I can assume that the arc is a straight line, is that a fair assumption?

I'd really appreciate any corrections or just a hint in the right direction, not the full answer, and then hopefully I can work out the other parts of the problem myself. Thank you in advance!
 PhysOrg.com science news on PhysOrg.com >> Leading 3-D printer firms to merge in $403M deal (Update)>> LA to give every student an iPad;$30M order>> CIA faulted for choosing Amazon over IBM on cloud contract

Recognitions:
Homework Help
 Quote by iwantpi Hi everyone, It's been years since I solved a physics problem for school. Now that I'm back at it I could use some help on this problem: Question "The astonomical unit (AU) is defined as the mean centre to centre distance from Earth to the Sun, namely 1.496 x 10^11 m. The parsec is the radius of a circle for which a central angle of 1s intercepts an arc of length 1AU. The light year is the distance that light travels in 1 year. (a) How many parsecs are there in one AU? The attempt at a solution I can do simple conversions of units, but I'm having trouble figuring out the connection between AUs and parsecs. I know that Arc length = r * angle (in rad) which leaves me with 1 AU = 1 parsec * 1s. But then again s is seconds, not radians... Another way I attempted the problem was to assume that the arc of a circle whose radian is 1 parsec is so large that I can assume that the arc is a straight line, is that a fair assumption? I'd really appreciate any corrections or just a hint in the right direction, not the full answer, and then hopefully I can work out the other parts of the problem myself. Thank you in advance!
Hi iwantpi, Welcome to Physics Forums.

The '1s' above is 1 arc second, an angle. Remember that degrees are divided up into 60 arcminutes, which are in turn divided into 60 arcseconds.
 1 parsec = 206264.984626 au I got it from aconverter.net, which I usually used. hope this help.

## Unit Conversion: Astronomical Units, Parsecs and Light Years...

Thanks for all the help you two and sorry bout the late reply. I figured it out. It wasn't so hard once you guys told me about the arc second thing. Thanks again.

 Tags astronomical units, conversion, parsecs, units

 Similar discussions for: Unit Conversion: Astronomical Units, Parsecs and Light Years... Thread Forum Replies Calculus & Beyond Homework 1 General Math 2 Astrophysics 0 General Astronomy 4 Astrophysics 1