Background: Most things we know about stars are based on first knowing their distances. There are several ways of measuring distance, and here we will use 2 of them. One involves knowing both the apparent absolute magnitudes of stars - in other words, comparing how bright a star looks to how much light it's really putting out. The other involves parallax - looking at how much a star appears to wobble due to the motion of the Earth around the Sun. a. Predict and Explain: Use the parallax data to predict which star in Your Personal Constellation is closest. Explain your answer. (Note: You don't need to calculate at this point: just inspect the data to decide which star is closest). b. Calculate: Calculate the distances of at least 3 stars from Your Personal Constellation using absolute and apparent magnitudes. c. Calculate: Check your calculation in part b for the closest star by calculating the same distance using the parallax data. In this case, you should also estimate the maximum and minimum likely distances from the Sun by adding and subtracting the uncertainty to the parallax and recalculating the distance in each case. d. Compare: Describe whether or not your answer makes sense and if it agrees with your answer to part b with your answer to part a. If they don't agree, explain which one has a mistake, the calculation or the prediction, and how you can tell