Page 1 of 5
European Journal of Applied Sciences – Vol. 12, No. 2
Publication Date: April 25, 2024
DOI:10.14738/aivp.122.16660
Ciobanu, M. Z. (2024). The Eart’s Rotation Axis And The Moon‘S Orbit. European Journal of Applied Sciences, Vol - 12(2). 31-35.
Services for Science and Education – United Kingdom
The Eart’s Rotation Axis And The Moon‘S Orbit
Monica Zoe Ciobanu
Astronomical Institute of the Romanian Academy, Bucharest, Romania
ABSTRACT
In the XX century the diminution of the obliquity of the ecliptic came to be
recognised as a certitude. This paper presents only a possible supposition
regarding the connection of this astronomical phenomenon with the forces acting
on the Moon, and on the Earth’s rotation axis.
Keywords. The obliquity of the ecliptic, nutation, the Earth - Moon special relation.
INTRODUCTION
In the middle of XVIII century, Bradley detected a wobble of Earth’s rotation axis. To explain
this phenomenon Euler created the well- known formula of, moment of inertia, and the theory
of a solid body with a fixed point; further, our planet in cases regarding its rotating body, were
no more considered as a simple point having mass, but as a solid body with a fixed point
submitted to external forces and to their moment. Euler also succeed in explaining the Earth’s
rotation axis wobble as being caused by the orbital moment of that external forces which do
not pass through the fixed point. The main periodical component of the Earth’s rotation axis
wobble, is due to the retrogradation of Moon’s nodal points, with a period of 18,6 years, known
as the nutation period.
Naturally, during the XX century it became known that the Earth’s inner structure is more
complicated, not simply a rigid one; under Earth’s surface there is a complicated constitution,
with special forms of materials submitted to great gradients of temperature, pressure and
density.
Indeed, from the Earth’s surface to the centre, O, of its inner core the density rises to a
incomprehensibly great value (which may be more than 15 tonnes per cubic meter). This value
of density allows to be considered there, the gravity centre of the hole Earth, and to place there
also the centre of the celestial equatorial axis Oxyz and also the centre of the inertial system of
axis OXYZ in this same centre, O, (as Euler did). The Oz axis is the support of Earth’s rotation
axis and the OZ axis is normal to ecliptic plan. The angle between Oz and OZ reflects the angle
between the celestial equatorial plan and the ecliptic plan, known from the geocentric times as,
the obliquity of the ecliptic. Let it be supposed as a first approximation, that the inertial system
of axes represents the ecliptic system of coordinates and the Earth’s orbit supposed being an
invariable plane.
ABOUT THE OBLIQUITY OF THE ECLIPTIC
After lecturing the papers of R.R. Newton {1} and Liske {2} it was interesting to begin to
investigate, the values of the obliquity of the ecliptic more in past.
Page 2 of 5
Services for Science and Education – United Kingdom 32
European Journal of Applied Sciences (EJAS) Vol. 12, Issue 2, April-2024
(The value admitted now for the diminution of obliquity of the ecliptic is -46,”836 769 per Julian
century. {3})
It is well known that the most precise determination of obliquity of the ecliptic in past, is the
Newcomb’s value for 1900.O, {1} and for now the value for 2000,0{3}:
Obliquity of the ecliptic 1900.0:
23°,452294 – 0°,013 012 5 T – 0°,000 001 64T2 + 0°,000 000 503T3
(More simply 23° 27’ 8’’,2584)
Obliquity of the ecliptic 2000.0:
23 °,4392794444 – 0°,01301021361T -5°, 0861 x 10-8T2 + 5°,565 x 10-7T3-1,6x 10-10T4 -1°,2056
x10-11T-5 (More Simply 23 ° 26 ‘21”.406)
(In which T is the time in Julian centuries (36525 days) from the epoch 1900 January 0.5.
respectively from 2000 January 0.5)
From these two relations, naturally it results simply, a yearly mean diminution of obliquity of
ecliptic between 1900.0 and 2000.0 as being: - 0”,46.
Some others value of yearly diminution values for obliquity of ecliptic, related to 2000,0 using
past astronomical determination:
➢ From Bradley- determination in 1759 result: ......-0’’,46
➢ From Ulugh Beg determination in 1437 result...... - 0”,47
➢ From Ptolemy ‘’ in 137 results.... - 0”,49
➢ From Hipparchus ‘’ in 128 BC result ...... -0”,64
➢ From Eratosthenes ‘’ in 250 BC result ...... -0”,66
➢ From Aristyllus and Timocharis in 290 BC result ....... -0”,51
It can be admitted that these values are of the same magnitude order.
Taking a look to the value for obliquity of ecliptic found by Millanowich in his remarkable work
regarding the climate; he found that the greatest value for obliquity was 24°,5 around 8700 BC
{4}, a simple calculus from that epoch until 2000.0 gives that a yearly diminishing for obliquity
of the ecliptic being the value of -0”36. Because this time interval of around eleven millennia is
very great and approximative, can be accepted that the value -0”,36 has also the same
magnitude order as 0”,46. Finally, from 8700 BC until now a yearly permanent diminution of
obliquity of ecliptic must be accepted, summing up to around one degree in eleven thousand
years until now.
THE MOON AND ITS ORBIT
Therefore, the Moon’s wobble phenomenon is composed of periodical components, its most
important periodical component being caused by the retrogradation of Moon’s nodal points.;
that means the greatest periodical changing in direction of Earth’s rotation axis is 9”,205 in 18,6
years.
Page 3 of 5
33
Ciobanu, M. Z. (2024). The Eart’s Rotation Axis And The Moon‘S Orbit. European Journal of Applied Sciences, Vol - 12(2). 31-35.
URL: http://dx.doi.org/10.14738/aivp.122.16660
A simple question arises: if the Moon having the great orbital moment which cause this
greatest periodical phenomenon of Earth’s rotation axis wobble, (the nutation), then the
Moon could not impose also a secular change in the Earth’s rotation axis position regarded
to the ecliptic plan?
A Simple Look at The Geological Past of Our Planet and His Satellite
Some interesting studies was made by G Kahn (Princeton University) and S. Pompeo (Colorado
state University) {5} on some mollusc fossil found in the geological past of our Earth when the
fauna was only marine. That fauna where related with the now well- known nautilus Pompilius,
whose life is impacted rigorously by the synodic period of the Moon. They found that in that
time, around 400 million years ago, the Moon was nearer the Earth, its orbit was smaller and
the duration of our terrestrial diurnal day was shorter; that means the rotational speed, of the
angular moment of Earth rotation axis was greater. In those times, the Moon’s synodic period
was about 9 days, but after a long time, step by step the synodic interval grew to 28,5 in present
days.
Deeper in time, from the middle of Archean eon the geological history of Earth noted the
appearance of solitary platforms (beginning with Wal bara -3,6 billion ago and ending with
Pangea -335 million ago) which grew and then broke; but after a long time, interval another
platform begins to form and grows until it also broke, and so on {6}. When a continental
platform grows becoming even a supercontinent and next breaks, or a great glaciation melt,
then the Earth’s gravitation centre could change its place inside Earth; in consequence the
angular momentum being greater at that time, a piece of that continent could be suddenly been
ejected in the celestial then equatorial plan of Earth. (In any case then in a short geological time,
dramatically geological events may occur as can be seen in Colorado canyon).
If the mass from ejected continental piece is great related to the Earh’s mass (as in Earth-Moon
case), the Earth’s moment of inertia diminishes and implies also a diminution of its angular
momentum and what is the most important consequence is that the Newtonian attraction
power of Earth on Moon diminish also.
In celestial mechanics it is known very well that the Earth-Moon dynamic has three distinct
particularity relations in contrast with the dynamic of all the others planets and their satellites
in our Solar system {7}.
Indeed
The ratio mass Moon/Earth is the greatest being 0,0123, In contrast with the ratio of mass for
all others satellite /planet parent; their ratio mass satellite/planet are under 1,7x10-8 for Mars,
under 4,7x10-5 for Jupiter, under 2,4x10-4 for Saturn, under 1.6x10-5 for Uranus, and under
2,1x10-4 for Neptune {3}.
(In consequence, beside Moon, all others satellites of great planets in our Solar system, even if
they could be ejected, the Newtonian attraction did not have a great decrease and their orbit
remains around the parent planet
because their //// mass related to planet parent mass are smaller ///)
Page 4 of 5
Services for Science and Education – United Kingdom 34
European Journal of Applied Sciences (EJAS) Vol. 12, Issue 2, April-2024
Between all 29 satellites with synchronous orbit, the eccentricity of Moon’s orbit is by far the
greatest, being 0,057{3}.
(Excepting the orbits of Titan and Iapetus, with 0.028 eccentricity, the most of the others
satellite with synchronous orbit, have the eccentricity under 0,010. In consequence their orbit
is more approximate to a circular one).
The diminution of Earth’s mass (after the Moon was ejected) obliged Moon’s orbit to become
more dependent of Sun’s attraction and in consequence step by step its synchronous orbit
becomes more elongated, turning towards ecliptic plane under Sun’s attraction.
(The Moon’s orbit is the only one laying near ecliptic plan -having five-degree inclination- in
contrast with all other’s synchronous satellites in our Solar system whose orbits lay near the
celestial equatorial plane of their planet parent.}
A Simple Supposition
Regarding the Moon mass and also the eccentricity and the inclination of its synchronous orbit
in comparison with the others’s satellites in our Solar system, all its peculiarity can be explained
supposing that the Moon could be an ejected body from our planet Earth.
In consequence at its same beginning the Moon’s orbit being a circular one, naturally the Moon
could be situated in the that time in the celestial equatorial plane, and its synodic period could
be even only around a day; but after, when the Moon’s orbit under Sun’s attraction became an
elliptical orbit the synodic period of Moon grew to nine days and after a long geological time,
now, to 28 days.
Briefly, if supposing that the Moon where ejected, can be admitted that its orbit inclination
related to the ecliptically plan, changed step by step supposing from about 24° -25° when it was
ejected in Precambrian, to five degrees now, during the great past geological time interval until
our days. In consequence the tangential forces on Moon orbit could impose not only a periodical
variation in Earth’s rotation axis direction but also an infinitesimal secular one.
Remembering Euler’s formula, it can be supposed that the mechanical momentum of tangential
forces of Moon’s orbit acting on Earth’s rotation axis, may cause the secular diminution of
obliquity of ecliptic; but the size of the secular variation in obliquity of ecliptic being of an
infinitesimal order, can be detected only after a very great interval of time.
For instance, from Timocharis and Eratosthenes, around three century BC (the obliquity of the
ecliptic was +23°46’) until now, the obliquity of ecliptic diminution was only around 20
arcminutes.
CONCLUTION
Because, in present, the secular diminution of obliquity can be recognised as a certainty, this
paper attempts only to present a simple supposition, trying to explain this astronomical
phenomenon.
Page 5 of 5
35
Ciobanu, M. Z. (2024). The Eart’s Rotation Axis And The Moon‘S Orbit. European Journal of Applied Sciences, Vol - 12(2). 31-35.
URL: http://dx.doi.org/10.14738/aivp.122.16660
For this purpose, it was used the well- known particularities of Earth- Moon dynamics
regarding some particularity of Moon’s mass, orbit’s eccentricity and orbit’s inclination (unique
in our Solar system). Supposing that the Moon could be ejected, then the mentioned
particularities could justify a secular variation of Earth’s rotation axis in direction, which may
contribute to the diminution of the obliquity of ecliptic.
References
{1} Newton, R.R., Mon. Not. R. Astro. Soc. (1974) 169, 331- 342
{2} J. H. Lieske, T. Lederle...1977 Astron. Astrophys. 58, 1-16 (1977)
{3} ASTRONOMICAL ALMANAC
{4} Wikipedia, the free encyclopaedia: Milankovitch cycles
{5} Barrere M, LA RECHERCHE Nr 95 janvier 1979
{6} Encyclopaedia of Geology; vol 3, second edition.
{7} Wikipedia, the free encyclopaedia: The Moon.