Using Time Zones and Celestial Navigation
to Teach the Phases of the Moon
Aileen O’Donoghue, Priest Associate Professor of Physics
ABSTRACT
The phases of the moon are typically presented to introductory astronomy classes in a diagram showing the position of the moon, its appearance and
elongation at each phase, and the time of each phase's transit. Though wonderfully compact and efficient at conveying information, I have found it to be
overwhelming to non-science major students. Much of their difficulty arises from their vague definition of time which must be broadened for them to
understand the different rising, transit and setting times for the phases of the moon. Working with time zones helps them recognize that the time on their
watch is relative to a particular longitude and the transit of the sun at that longitude. Celestial Navigation extends this to the transit of all celestial objects and
helps them re-define "time of day" to a position on Earth relative to the Earth-Sun line in a practical way. Once they understand why a given object transits at
the same time for all time zones, extending this to the moon is much simpler. My students are quickly able to identify the transit times of the various phases of
the moon, and with some additional instruction, quickly learn how to figure out their rising and setting times as well.
9 pm
3 pm
2 pm
1 pm
12 am
12 pm
9 am
3 am
Time Zone’s Solar Noon
TIME ZONES
6 pm 5 pm
4 pm
6 am
Figure 1. Observers at different clock
times. In class, this diagram is animated
so that the Earth and various observers
rotate while the times hover in the sky
above each position
Clock Noon FOR ALL
Teaching about time zones has two primary benefits:
1) Working with the distribution of time zones, students begin to
grasp the idea that the time of day on their clock is determined by
their position on Earth relative to the Earth-Sun line. The ~15° width
of time zones cements the fact that Earth turns 15° per hour.
2) the various clock times of solar noon within a time zone gives the
students initial exposure to the association of the observer’s longitude
and the clock time of a celestial event.
CELESTIAL NAVIGATION
Solar noon is
(Degrees)(4 minutes/degree)
earlier than clock noon
1st
quarter
waxing
crescent
waxing
gibbous
waxing
gibbous
6pm
9pm
90
full
180 mdnt
Earth
Setting
Moon to
West
eastern
elongations
6pm
noon
6am
new
0
western
elongations
90
waning
gibbous
waning
crescent
full
waxing
crescent
Earth
rotation
noon
Rising
Moon to
East
Transiting
Moon Above
3rd
quarter
3am
Observer’s
Time Above
Time
Zone
East
side
Western
Observer’s
Solar Noon
West
side
Setting
Transit time gives position of star with respect to the sun
The transit time of Aldebaran
on December 15 is 11 pm.
6 pm 5 pm
4 pm
3 pm
9 pm
Standard
Time
2 pm
Aldebaran’s
Position on
December 15
nearly
opposite Sol!
Figure 3. Now that students understand the time of day as the
position on Earth relative to the Earth-Sun line, they can easily grasp
why a given star transits at the same clock time for all observers.
1 pm
11 pm
12 am
12 pm
3 am
9 am
6 am
3pm
mdnt
waning
gibbous
Degrees
West of TZ
center
Figure 2. Clicker questions in class have students practice
finding the times of solar noon from the observers’
longitudes (with respect to the time zone center) and
positions from observed times of solar noon.
Calculations of observer’s longitudes from celestial observations, the time
and an ephemeris (of transit times) promote student understanding of
1) the altitude of the celestial pole as a direct measure of the observer’s latitude.
2) the fact that the time on a clock is always relative to a particular longitude (reinforcing the idea
from the time zone exercises)
3) the ephemeris of transit times gives the positions of objects relative to the Earth-Sun line where
they “hover” as Earth turns underneath
1st
quarter
Degrees
East of TZ
center
Eastern
Observer’s
Solar Noon
Rising
Solar noon is
(Degrees)(4 minutes/degree)
Later than clock noon
new
9am
6am
waning
crescent
3rd
quarter
Figure 4. The standard moon phase diagram and an example of finding the
rising, transit and setting times of the waning gibbous moon using the
little observer.
FINDING RISING, TRANSIT, AND SETTING TIMES
Having worked through time zones and celestial navigation problems ,
the standard phases diagram can be introduced with elongations in addition to the times.
The last hurdle to overcome is to help the students realize that the times shown are the
transit times of the moon phase at that position. To facilitate their ability to figure out
the rising and setting times, we use a “little observer” printed on transparent film with
eastern and western horizons indicated (for looking south). They then use this with the
diagram to work out the rising, transit and setting times of the various phases..
CONCLUSION
Before I started including
time zones and celestial navigation in my
course, students truly struggled to understand
the different rising, transit, and setting times
associated with different phases of the moon.
Since I have included these additional topics,
they seem to understand it more completely
and with much less struggle. The evidence for
this is limited to my experience of their having
less trouble with the lab exercises and exam
questions where they find the rising, transit
and setting times of the different phases.
With only 24 students per year, statistics are
impossible. I am happy to collaborate and
supply materials to anyone who wants to do a
statistical study of the effectiveness.
Figure 5. Solutions to student exercises on Time Zones, Celestial Navigation, and Phase of the moon (answers in green).
Time
E
W
Little Observers …
take one!