The following idea is also due to John Conway. You can determine the local
time at night by looking at the Big Dipper and Polaris, and doing a simple
calculation.
The first thing is to look at the line joining Polaris to the two pointer
stars of the Big Dipper. Here's a picture that shows what you might see:
Conway suggests looking at the line from the Big Dipper to Polaris as
if it were the hour hand of a clock centered on Polaris. You read off the
time in the sky from this hour hand. In the drawing, the time
in the sky is about 1:25 (you have to do the best you can). This can
be a little tricky, see below.
Write the time in the sky as hh:mm, in this case, 1:25.
Now write down what Conway calls the time in the year. This is gotten
from the date by writing it as if it were a time, as follows: Suppose the
date is the d'th day of month m. Then write the time in the year
as m:2d. For example, on January 20, the time in the year would be
1:40.
To get the local time (on a 24-hour clock), calculate
local time = 06:30 - 2 (sky-time + year-time).
In the above example, we would have
local time = 06:30 - 2 (1:25 + 1:40) = 06:30 - 2 (3:05) = 06:30 - 06:10 = 00:20,
which corresponds to 20 minutes after local midnight. If you get a negative
number, just add 24 hours.
The result is local time. It doesn't take into account Daylight Savings
Time (so you have to add an hour if you are on Daylight Savings Time), and
it doesn't take into account your longitude away from the center of your
time zone. The correction for longitude is 4 minutes for each degree you
are away from the center of the time zone. In Austin, TX, since we are 31
minutes west of the center of our time zone, you have to add 30 minutes
to the result to correct for this effect (because if you are west of center,
the sky will read earlier than a standard clock). In January we are on Standard
Time, so the only correction would be for the longitude effect, and our
final result in the example would be
Central Standard Time = 00:50 (approximately).
Conway points out one caution: Near 3:00 and 9:00 sky-time, it
is somewhat difficult to read the clock. The picture shows it correctly:
You should draw the line from Polaris to the pointers, and see what angle
that makes with the vertical. If it is a 90 degree angle, then it is 3:00
(or 9:00 on the other side). Because of the curvature of the sky, it can
appear that the sky-time is closer to 00:00 (12:00) than it actually
is, so be careful! One way to judge this is to compare the angle to the
corner of a small card, or to use your hands to mark off a 90 degree angle,
placing the corner on Polaris with one side of the card (or your hand) pointing
straight up.