more on Interesting Problem? Crossing Several Time Zones on New Years

[David Farber <dave () farber net>]

------ Forwarded Message
From: Vaughan Pratt <pratt () cs stanford edu>
Organization: Stanford University
Reply-To: <pratt () cs stanford edu>
Date: Thu, 30 Dec 2004 12:03:11 -0800
To: <dave () farber net>
Subject: Re: [IP] Interesting Problem? Crossing Several Time Zones on New
Years

Dave,

Nice problem.  She's out of luck.  Assuming uniform velocity along a
great circle from NYC to Zurich, at around 9:42 pm EST she will be
crossing from the P (+3 hours) time zone, where it will be 11:42 pm, to
the O time zone (+2 hours), where it will be 12:42 am.  She'll have
missed midnight!

If the plane is delayed by more than 18 minutes, at 10 pm EST she will
most likely be in the P zone where it *will* be midnight then.  If the
plane is on time however, her best bet would be to split the difference
between the two time zones and celebrate it at 9:30 pm EST.  I suggest
settling on 9:30 PM before departure; this will simplify things by
removing the vagaries of the plane motion from the equation.

She could of course ask her airline when they think her flight will be
crossing from the P to the O time zone; if their answer is sufficiently
different from what the solid geometry of spheres predicts, go with that.

(The great circle calculations can be done either analoguely by
interpolating the hours along a thread stretched from NYC to Zurich on a
globe and looking to see which time zones the 9 pm EST and 10 pm EST
plane locations land in, or digitally with Microsoft Streets and Trips
measuring tool, which is smart enough to know that geodesics are
measured along great circles (as opposed say to rhumb lines on a
Mercator projection, which yield instead lines of constant bearing).
The benefit of the measuring tool is you can use it twice: once to mark
the great circle from JFK to Zurich---I got 3920 miles---and a second
time in conjunction with the location sensor to measure the distance
from JFK to where that great circle intersects meridian W 37.5 degrees,
the P-O boundary---I got 1870 miles, giving a flight time to the P-O
boundary of 7.75*1870/3920 hours or 3h 42m.)

Vaughan Pratt

> Briefly, a good friend is departing New York City at 6:00 PM local
> time on New Years Eve and crossing 6 time zones en route to Zurich on
> a flight lasting 7 hours and 45 minutes, thus arriving in Zurich at
> 7:45 AM local time on the morning of January 1st. She has asked me
> what time it will be *exactly* midnight on her flight so she can
> celebrate.

------ End of Forwarded Message


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