Re: Lunar North Pole and Seasons

[Brian Whatcott <betwys@DIRECTVINTERNET.COM>]

At 04:18 PM 10/6/02, Zeke Kossover, you wrote:

...
> Does the moon have seasons?
>
> I teach that the earth has seasons because its axis of rotation is not
> perpendicular to its orbital plane. I think this is correct.
>
> Is the moon's axis of rotation perpendicular to the orbital plane of the
> combined earth-moon system? Perhaps not as the moon is tidally locked to the
> earth, and a rotation around the earth would then entail a constantly
> changing axis of rotation.
>
> Do any of the moons in the solar system have seasons?
>
> Marc "Zeke" Kossover

As a response that speaks to the lunar season issue, I copy
this contribution from Raoul Mårtens to the History of Astronomy
 list, this morning.

Brian W

From: Raoul Mårtens <raoul@MARTENS.PP.SE>
Subject: [HASTRO-L] Re. the term Inequality of the moon's motion
To: HASTRO-L@LISTSERV.WVU.EDU
Precedence: list
Status: U
X-UIDL: PcU50tHkIe0rpAE

However essential the history of the term 'inequality' may
be, the observations behind it seem to need more attention.
The following is an attempt to start a discussion regarding
the history of the observation of the lunar 'inequalities',
in particular the moon's 'wobble! or 'annual inequality'.
Please advise if any part of below account is incorrect.

Ptolemy mentions two perturbations of the moon's longitude:
1. an oscillation of the nodal line of c. 9' during the
fortnight from syzygy via quadrature on to syzygy;
2. an oscillation in longitude of 1.3 degree during 32 days
from syzygy via quadrature on to syzygy, called 'evectio'.
1. is called 'first inequality' and 2. 'second inequality'.
However, Ptolemy does not mention the 'annual inequality'.

1.& 2. result from from change in the moon's elongation from
the sun. Neugebauer says: (A History of Ancient Mathematical
Astronomy 1975, Book VI, B § 8, p. 1103 f) "The mathematical
theory of perturbation shows the accumulated effect of these
varying forces is a progressive displacement of the apsidal
line, wellknown since antiquity." However, it may be ancient.

The moon's wobble, an oscillation in latitude between the sun's
nodal passages in a cycle of 346.6 days (the eclipse year) is an-
aloguos to the 'evectio': both are due to the moon's changed el-
ongation from the sun when the moon alternates between syzygy and
quadrature. Because of its length of nearly a year this 'wobble'
of the moon has frequently been called its 'annual inequality'.

At a lunar eclipse in 1594 Tycho Brahe observed a perturbation,
called 'variatio', implying that the moon's speed increases at
syzygy and slows down at quadrature. 1598 Brahe observed the
'annual inequality' i.e. the moon's 'wobble' as mentioned by
Neugebauer (op. cit. Book 1 B 4.3-4 and Book VI B 8.3 D) and
by Thom in Megalithic Remains in Britain and Brittany, 1978.
p. 8: "This wobble has a period of 173.3 days or half the ec-
lipse year and, in fact, eclipses of the sun and moon occur
only when DELTA (Greek letter) is at or nearly at a maximum.
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
One of the objects of our previous book (Thom 1971)(Megalithic
Lunar Observatories, my comment) was to show that the wobble,
in spite of its small amplitude, was known to Megalithic man.
This perturbation would have been visible to these people only
at the standstills, when the variation in the declination pro-
duced by the main movement had approached zero. The small value
of DELTA made it necessary to use an observing method sensitive
enough to detect a change of declination of one or two arc min-
utes. A technique which made this possible is described fully
in Chapter 1 of Thom 1971." (too long to be reproduced here)
Regardless hereof it is beyond dispute that megalithic astro-
nomy was particularly preoccupied with the lunar standstills,
likely because eclipses and extreme tides occured near there.
At 'major standstill' the moon's ascending node is located at
or near the First Point of Aries. (Compare Fig 2.1 Thom 1971
and Fig. 2.1 in Thom 1978 (major standstill in March 1969).
The rapid and great change of the moon's declination near to
a 'major standstill' is dramatic and confirms its ocurrence.

Neugebauer points out that the phenomena in question resemble
"the tidal forces, which produce high tides always at two dia-
metrically opposite points of the earth." Though Thom doesn't
refer to tides in this argument, no doubt the tidal phenomena
were known to the prehistoric inhabitants of the coasts of the
British Isles and Brittany and they must have noted that both
eclipses and extreme tide occur near to the lunar standstills.

In Principia Newton stated that the greatest floods occur at the
syzygies and the smallest at the quadratures, at the time of both
equinoxes and that the largest difference between floods occur at
the solstices, particularly when the moon's ascending node is lo-
cated at the 'beginning of Aries' i.e. at its "major standstill".

Chaucer's 'The Franklin's Tale' shows that this was known in
England in the 14th century, see Donald W. Olson et a.: High
Tides and the Canterbury Tales, Sky & Telescope, April 2000.
The extreme tide referred to in Chaucer's tale is believed to
have occured Dec. 19, 1340, the year of Chaucer's birth, when
the earth was near perihelion and the moon in both perigee and
the ascending node i.e. at "major standstill", as Newton said.
Would the moon's wobble have been visible in this connection
and what did Newton say in Principia about this phenomenon?

Sincerely
Raoul Martens
Brian Whatcott
  Altus OK                      Eureka!

This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.