deletions | additions       diff --git a/subsectionAims__To_u.tex b/subsectionAims__To_u.tex  index d876f60..1507ed7 100644  --- a/subsectionAims__To_u.tex  +++ b/subsectionAims__To_u.tex 
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in clumps called groups or clusters.  Our own galaxy, the Milky Way, lives in  a rather insignificant cluster we call the Local Group. This cluster  has two big galaxies, our own and the Andromeda Galaxy (M 31), (M31),  in orbit around each other. Each of these two big galaxies is a spiral  galaxy, with a radius of about 10 kpc (kilo-parsecs, one parsec = 3.26  light years $= 3.1