Concerning your explanation of the parsec. I thought that the distance from earth to sun was an arc between the legs of the angle of 1 s of a cicrle of radius of 1 parsec. You showed this as a straight line. Isn't the Trig identity ARC=R * angle??
You are exactly correct. However, due to the very small angle involved, you may substitute a straight line for the arc with little error. This problem can be solved with either the method you describe above (using the definition of radian measure of angles), or by the trigonometric set-up that I've suggested by using a striaght line instead of an arc.