EARTH-MOON DYNAMICS PAGE
Earth-Moon dynamics has long
been a neglected subject. At a time when
the subject could have been scientifically examined in depth, science began to
focus on outer space. As a result, the study
of the Moon and its importance to the Earth in so many ways has been badly
neglected. The Moon has forged the
Earth’s surface and, as a result, helped to create its atmosphere. It has twinned with the Earth to form a
dual-planet system which revolves around the barycentre and, as a result we
have a tidal sea, without which evolution might not have taken place. This lack of serious study has led to most
of our ideas about the Moon and its relevance to the Earth relying on folklore
and ancient observations. On the
following pages are the synopses, with extracts of five articles which put the subject into modern perspective. All are written by
The articles have been
written to put the subject of Earth-Moon dynamics into the public domain. It is hoped that students will become
interested. For this reason, copies of
the features are available at nominal costs.
To request the full article, for personal use only, contact the author
at the e-mail address given at the end of the site.
Feature 1
Would we have had evolution without the Moon?
The Moon is currently moving
away from the Earth at the very slow rate of 3.8 cm per year. It has been moving away from the Earth ever
since its formation more than 4 billion years ago. During the first billion years of its
existence its contribution to the evolution of the Earth was immeasurable due
to the enormous mutual gravitational effect.
Excerpt from feature: The recessional rate must have
been higher the further back in time we go because to extrapolate back the
current 3.8 cm yr-1 recessional rate, the existing mean distance of
the Moon of 384,400 km would need more than the 4.6 billion years for which the
Earth is accepted to have been in existence. In fact, if the rate of 3.8 cm yr-1
had been constant over the Earth’s lifetime, the mean distance of the Moon from
Earth currently would be 174,800 km. If
we extrapolate the recessional rate back in time on an exponential basis, using
N = No.e-λt (exponential decay) we obtain a
recessional speed of some 10 km yr-1.
That is to say the Moon’s orbit, initially, recessed at this 10 km yr-1
rate and gradually slowed down. On this
basis it appears that the Moon has been closer to the Earth throughout most of
its lifetime and the further back in time we go, the closer it was. Importantly, however, since the
gravitational effect of a body is inversely proportional to (the square of) its
distance, the much closer Moon had a greater gravitational pull on the Earth.
As the Moon receded, the
gravitational pull, relax, pull effect declined but it still contributed to
evolution by being part of the dual-planet Earth-Moon system. This dual-planet system revolves around a
pivotal point known as the barycentre and it is this pivotal action which
causes the tides on Earth – another massive contributing factor to
evolution. This is discussed in this
3200 word article which also explains why it is that the Moon alone cannot
possibly be the cause of the tides. The
full article costs £2.50
Feature 2
Lecture 1: The
Moon’s contribution to evolution – without going around the Earth or spinning
on its axis
One of the illustrations
accompanying this feature. It graphically analogises the Earth and Moon
orbiting around a common pivotal point and indicates why the Moon appears to
orbit the Earth yet does not turn on its own axis.
Excerpt
for feature:
If we take the most rational explanation of the movement of the Moon away from
the Earth, i.e. ever since their original formation, then it follows that when
it was formed the Earth and Moon were in close proximity, even in
contact. This means that as the Moon began to orbit the Earth, it orbited
extremely rapidly, since its speed equates with its orbital speed today.
Let me mention at this stage that neither the sizes nor the densities of the
Earth and the Moon are known for the time in question. Various values of
the orbital parameters, speed, etc., can be calculated but the calculations
have to make too many assumptions to be considered as absolute.
However, it is safe to assume that when the proto-Earth/Moon became a dual
planetary system the early Moon rapidly orbited the Earth at about the time of
their formation. It continued to do so as it gradually moved away from
the Earth as its orbit expanded.
It is a misconception that
the Moon spins on its axis and this article, in the form of a lecture, explains,
with illustrations, how it does not.
Also explained is the barycentre, around which the dual-planet
Earth-Moon system rotates, the possible formation of the Moon itself and why it
is that the Moon’s gravity could not possibly cause the tides. This illustrated article is 2800 words long
and costs £2.50
Feature 3
Lecture 2: The
eccentricity of the Moon’s orbit
The moon orbits the Earth in
an elliptical orbit but, how elliptical?
There is a simple formula for calculating the ellipticity. However, if you use some of the ‘official’
figures you get the wrong answer.
Why? Because one of the foci of
the elliptical orbit of the Moon is assumed to be the centre of the Earth which
is wrong. The focus for calculation
should be the barycentre, deep within the Earth. This 750 word short essay, in lecture form,
explains how the error occurs and what the true ellipticity is. The full article costs £1.50
Feature 4
The Wobble of the World
Within the Earth, the location
of the barycentre moves correspondingly from P1 to A1 and P2 to A2 as the Moon
moves from perigee to apogee.
The world wobbles because
there is a pivotal point within the Earth around which the dual-planetary
system of the Earth and the Moon rotates.
This pivotal point is known as the barycentre. However, the barycentre is constantly moving
backwards and forwards in one direction on a daily basis and another on a nine
year basis. The result is that the world
wobbles.
Excerpt from feature: Both the Earth and the Moon have mass, the Earth having a mass some 80
times greater than the Moon. Since both have mass, they both have gravitational attraction and the total
gravitational attraction between the two bodies is 3.9 x 1020
The movements of the
barycentre, why, how and the extent to which it moves, are explained in this
illustrated, 1200 word article which costs £2.
Feature 5
Spiral Gravity - it makes
the world go around
Gravity spirals out from a
rotating mass and lags with increasing distance.
Any body with mass has
gravitational attraction. This gravitational attraction, or gravity,
diminishes in strength the further away one is from the body
mass. Gravity is usually graphically depicted as a straight
line either from a single body mass or between any two body masses.
With a rotating body, however, the gravitational attraction not only diminishes
with distance, but also lags as the distance from the body increases, giving
rise to spiralling gravity.
Excerpt from feature: Yet, as can be ascertained from
our own orbiting Moon, some of the orbiting bodies are speeding up. How do we
know this? Well, we fall back on Kepler’s Third Law which he postulated after
carrying out his work as mentioned above.
It has been confirmed by NASA that the Moon’s orbital distance is
increasing at a rate of 3.8 cm per year.
Not a lot, but, according to Kepler’s work, this means that the speed of
its orbit is increasing also and, if the speed of the orbit is increasing, it
beggars the question where does the additional momentum come from? That is not a difficult one to speculate on,
it has to be the Earth. In the future,
we will be able to see if other orbiting bodies are speeding up but, for the
time being, our technology does not enable that to take place today.
The effect of the spiralling
gravity is to maintain natural satellites in their orbits as is evidenced by
the prograde satellites throughout the outer reaches of the solar system.
This 1500 word illustrated essay explains how and costs £2.00.
For a translation of this page in Belorussian (by Bohdan Zograf) click here.
ADDITIONAL ARTICLE!
Formation of the Earth and the
Moon, Tides and Gravity
For a translation of this article in Ukrainian (by Mark Pozner) click here.
NEW ARTICLE!
Also, feel free to read some thrillers
Beware Spanish
developers!
E-mail: moontheory@hotmail.com
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