Why is the time between moon phases irregular?

For example, between Full Moon on 2006 Jan 14 09:48 UTC and Last
Quarter on 2006 Jan 22 15:14 UTC there are 8 days, 5 hours and 26
minutes.

However, between Full Moon on 2006 June 11 18:03 UTC and Last quarter
on 2006 June 18 14:08 UTC there are only 6 days, 20 hours and 5
minutes.

That's over a day of difference! However, isn't the moon phase cycle
supposed to be 29.53 days?

I know what libration is - but wouldn't libration affect only the
angle at which we see the moon, not the light/shadow on the moon
itself (and hence its phase)?

Hi tombo06-ga,

Because of the eccentricity of the moon's orbit, its distance from the
surface of the earth varies throughout the cycle of its orbit. The
closest approach ("perigee") is 363,104 km and the furthest retreat
("apogee") is 405,696 km.

Around perigee (when the gravitational force between earth and moon is
strongest), the moon moves faster in its orbit, having a maximum
orbital speed of 1082 m/s. Around apogee (when the gravitational force
is weakest), the moon moves slower, having a minimum orbital speed of
968 m/s.

Therefore, at perigee the moon will move more rapidly from the angle
at which a given phase occurs to the angle at which the next phase
occurs (a sun-moon angle of 180 degrees for full moon, 90 degrees for
quarter moon and 0 degrees for new moon). At apogee the moon will move
more slowly from phase to phase.

You can view the dates of perigee and apogee for 2006 at the following page:

"The Sun, The Moon, Earth and Eclipses"
http://www.delscope.demon.co.uk/news/skywatch1SMEE.htm
(scroll to the section titled "APSIDES OF THE MOON")

There you will see that an apogee occurred on January 17 2006 (during
your "slow" phase change) and a perigee occurred on June 16 2006
(during your "fast" phase change).

The variation in the orbital motion also manifests itself as
longitudinal libration. Because the moon's rotation is constant but
its orbital motion is not, one of them can "get ahead of" the other or
behind it, enabling us to see a few degrees around the edges of the
closest lunar hemisphere.

Libration does affect the perceived phase, because although the
terminator (line between dark and light) is not changed by the angle
at which we view it, the terminator will occur in a different part of
the perceived disk if we are looking from a different angle. A great
animation of this can be found by clicking the "animation" link on the
following page:

"The Moon's Orbit"
http://home.insightbb.com/~lasweb/lessons/moonorbit.htm

I trust you find this answer satisfying, otherwise please request clarification.

Regards,
eiffel-ga


Additional links:

"Moon - Wikipedia"
http://en.wikipedia.org/wiki/Moon

"Libration of the Moon"
http://www-spof.gsfc.nasa.gov/stargaze/Smoon4.htm


Google Search Strategy:

"moon phases" "varies because"
://www.google.com/search?q=%22moon+phases%22+%22varies+because%22

"lunar orbit"
://www.google.com/search?hl=en&q=%22lunar+orbit%22

"lunar orbit" libration
://www.google.com/search?hl=en&q=%22lunar+orbit%22+libration

---

Request for Answer Clarification by tombo06-ga on 15 May 2006 10:06 PDT

You know that an answer is good when it seems obvious in retrospect. Great job!

I'd like one clarification though:

I asked "isn't the moon phase cycle supposed to be 29.53 days?"

Obviously, the differences due to speed at perigee/apogee would cancel
themselves out at the end of each full cycle, and it makes sense that
its duration would be a regular 29.53 days.

But, when calculating times from full to full moon during my "fast"
and "slow" phase changes, there is still a difference:

From and including: Saturday, January 14, 2006 at 9:48:00 AM
To, but not including : Monday, February 13, 2006 at 4:44:00 AM
The duration is 29 days, 18 hours, 56 minutes and 0 seconds

From and including: Sunday, June 11, 2006 at 6:03:00 PM
To, but not including : Tuesday, July 11, 2006 at 3:02:00 AM
The duration is 29 days, 8 hours, 59 minutes and 0 seconds

There's still a ~10 hour difference. Why?

And the strict answer to "is the moon phase cycle 29.53 days?" would be NO, right?

I'd like to know what's its variation, if that's still within the
scope of my question. (an answer like "from 29.49 to 29.54 days" would
be great)

I'm asking this because I'm working on a lunar calendar by the way.

Great answer otherwise, thanks!

---

Clarification of Answer by eiffel-ga on 15 May 2006 14:18 PDT

Hi tombo06-ga,

I agree with rracecarr-ga's comment that the variation in time from
one full moon to the next is primarily due to the variation in the
earth's orbital speed around the sun due to its non-circular orbit.

A standard figure for the mean lunar month is 29.5305888531 days, or
12.369 cycles per year. The time from one new moon to the next is
called a lunation, or synodic month. A web page at Eric Weisstein's
World of Astronomy states that "any particular phase cycle may vary
from the mean by up to seven hours":
http://scienceworld.wolfram.com/astronomy/SynodicMonth.html

On that same page is a formula for calculating the length of any
specific lunar month, given a Julian date. The following web page
explains how to find the Julian date corresponding to a specific
lunation:

Lunation
http://scienceworld.wolfram.com/astronomy/Lunation.html

That page also refers to a table by Meeus of every lunation from 1900
to 2100, during which time the shortest lunation is 29 days 06 hours
35 minutes and the longest is 29 days 19 hours 55 minutes.

I trust you find this additional information useful.

Regards,
eiffel-ga

Great answer, clarification, and comment. Thanks!

Full moon comes when the sun-earth-moon are lined up as close to a
straight line as they get during a partular lunar cycle.  The angular
speed of the earth around the sun is important, as well as the angular
speed of the moon around the earth.  Just like the moon around the
earth, the earth moves in an elliptical orbit around the sun,
sometimes closer and faster, and sometimes farther and slower.  In
January, the earth is closest to the sun, so moves the fastest, and so
the extra amount the mooon has to move in its orbit to regain a
straight line configuration is maximum.  So the time from one full
moon to the next is longest in January.