Solar Time problem
You are a TV producer in Toledo OH and want to do a show on Groundhog Day. You team up with a colleague in Punxsutawney PA to do a simulcast when each of your groundhogs come out to see (or not see) their shadows. You carefully synchronize your watches to Eastern Standard Time, using the US Naval Observatory website, and set your cameras on your respective groundhog holes. At 11:00am EDT, the two crews start broadcasting their pre-shadow shows.
(a) How long must they wait for local solar noon to determine whether Punxsutawney Phil sees his shadow?
(b) How long must your crew wait?
Show all your work, assumptions, reasoning and sources of material. Your accuracy should be to the nearest minute of time. What does this mean in terms of positional accuracy on Earth's surface (in km)?