Hipparcos Data

Add hipparcos_color.dat to the plot using the Data $\rightarrow$ Import menu. This file has $B-V$ and the absolute $V$ magnitude based on the Hipparcos parallax.

1. Print the plot with the Hipparcos data.
2. About how large is the difference in $m-M$ for distances from Hipparcos parallax and from ZAMS fitting?
3. If this is due to a systematic measurement error in the Hipparcos data how large would the parallax error be in milli-arcseconds to account for this, and what fraction of the actual measured parallax would this error be?
4. In more general terms, if we can measure parallax to an accuracy of a milli-arcsecond, what is the most distant star for which we can measure its distance within 20%?
5. In main sequence fitting, what would you estimate the error in $m-M$ to be for data like those found by Johnson? What distance error does this imply? What is the most distant main sequence star for which we can measure its distance within 20% using a telescope of the size of HST?