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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!