Physics Challenge Award Show II

Not a DeLorean.  You're doing it wrong.

[Update:  Prize Update / Added link to full solutions]

Welcome to the second Physics Challenge Award show!

[APPLAUSE]

Our judges have deliberated for several units of time and I now have in my hands the envelope holding our list of winners.  I could easily just tell you who won right now and save everyone some time, but award shows need some suspense to work effectively, so let's first give some tedious background information!

[APPLAUSE]

Betelgeuse, Betelgeuse, Betelgeuse!

A very cold person points out Betelgeuse

Betelgeuse is a massive star at the very end of its life and could explode any second now!  Every time I hear that I get really really excited.  Like a kid in a candy store that's about to see a star blow up like nobody's business.  This giddiness will last for a solid minute before I realize that "any second now" is taken on astronomical timescales and roughly translates to "sometime in the next million years maybe possibly."  Then I feel sad.

But you know what always cheers me up?  Calculating things!  Hooray!  So let's take a look at the ways Betelgeuse could end its life (even if it's not going to happen tomorrow) and how these would affect Earth.