deletions | additions       diff --git a/The_Virgo_cluster_is_so__.tex b/The_Virgo_cluster_is_so__.tex  index 5b8282b..649274b 100644  --- a/The_Virgo_cluster_is_so__.tex  +++ b/The_Virgo_cluster_is_so__.tex 
...
your results.  The method we will use in this exercise is galaxy diameters. If we  knew know  how big a galaxy really is, and could measure how big it appears, by simple trigonometry we could can  work out how far away it is. We can measure the apparent size of the galaxies in Hydra I using the  magnifying eyepiece with a measuring scale. Try measuring the size of  a few. The plate scale of all the plates is $1.12$ arcmin per mm. So  if you measure a galaxy as being 2mm long, its apparent size will be  the angle $2.24$ arcmin.  So we We  can measure the apparent size of galaxies in the cluster. But cluster, but  what is their real size? How big is a galaxy? We only really Well, one galaxy we  know the size of one galaxy at all well, quite well is  our own, the Milky Way. Here's where we make our first whopping great assumption. Why don't we assume that theone galaxy we know anything about, the  Milky Way, Way  is perfectly typical? So I.e.,  let us assume that all the galaxies in Hydra I are just like ours; ours:  they have radii of 10 kpc. So pick a bunch of galaxies in Hydra I. Measure I and measure  their diameters. Some of them will be nearly edge-on, but that shouldn't stop you measuring them. Multiply by the plate scale to get their angular size. Now size and  work out how far away they are! are.  You can get an answer for every galaxy you measure, and they won't all be the same. Throw out any ludicrously discrepant values, and average the rest to get your best guess of the distance to Hydra I.  One big problem is measuring the galaxy sizes. After all, galaxies don't have sharp edges, they just gradually  fade gently out. Where then out of visibilty  so where  do you measure define  the edge? There isn't really a good answer. The answer, the  most you can do is be self-consistent.  What distance do you get? Current best estimates lie in the range 35 --- 80 A good estimate is \~ 55  Mpc, but don't worry if your answer is outside far from  this, it is a very difficult measurement. Each student in the group should do their own measurements and you should compare the   results of each group member.  How might you go about improving   your estimate?  By far the worst feature of this calculation is the assumption that these  galaxies out in a distant cluster are just like our own galaxy. There are all sorts of reasons why this may not be true. For one, this cluster is a lot bigger than our local group. Thus just by chance, you   might expect group, so statistically speaking  it to include likely includes  a few rather large galaxies. Also,nobody understands  how and why galaxies form, and  it is quite possible likely  that they galaxies  form differently in big clusters. So these If  galaxies may be in Hydra are  nothing like our galaxy. How the Milky Way, how  can we get around this problem? One way is to be selective in our choice of galaxies to measure. We know that our galaxy, the Milky Way, is a spiral galaxy. So try measuring a distance using only spiral galaxies in Hydra I;  see the appendix for a description of different galaxy types.  Has your answer changed? We also know that the Milky Way is the largest spiral