2. To establish that the Sun is a star, we need to compare it to other stars, taking distances into account. Here, we'll compare V-band luminosities of the Sun and the star aCen A (Rigel Kentaurus), which is the brightest member of the aCen system. (a) aCen A has parallax " ~0.755". What is its distance in AU? In meters? (b) Assume, for a moment, that the Sun and the aCen A are identical in every respect. Using your result from part (a), how many times brighter than aCen A would you expect the Sun to appear? (c) At a distance of 1 AU, the Sun's V-band flux is F 180 W m, while a Cen A's V-band flux is Facen A ~ 3.6 10-9 W m2. What do these observations say about the hypothesis that the Sun and aCen A are similar objects? (d) Conceptual question: Did you actually need to know the value of the AU in meters to answer part (c)? Why or why not?