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
Dan Green BSc(Hons) Earth and Planetary Science
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.
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.
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
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 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 Newtons. This gravitational force holds the two bodies together like the bar between the two ends of a barbell. With a normal barbell there is a position along the bar that could be described as the point of balance. This would normally be the centre of the bar, i.e. equidistant from the extreme ends of the barbell because the bells of the barbell are of equal weight. This is not so with the Earth-Moon barbell.
The movements of the barycentre, why, how and the extent to which it moves, are explained in this illustrated, 1200 word article
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.
Formation of the Earth and the Moon, Tides and Gravity
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Page constructed: 16th January 2003 - modified 28th June 2011