63,000 MegaWatts of Power is Available for Modern Society The Sun and Moon transfer that much (average) power to the Earth in Gravitational Precession, all due to our Equatorial Belt! That’s nearly as much total production of electricity as by all operating nuclear plants in the U.S. There is a serious flaw that exists in the understanding of the Precession of the Earth. Every student in school is taught that the Earth “wobbles” or Precesses and they are told that this process is very slow where it takes nearly 26,000 years to complete a cycle. That IS technically true, but it is very misleading! Precession of the Earth is NOT a smooth process! It is amazingly herky-jerky! We will first discuss the Precession that exists due to the Sun, but then we will focus on the more interesting Precession due to the Moon. There are two important characteristics of the Earth that are important here. First, the Earth spins on an axis that is TILTED at a significant angle, around 23.5. Second, because of our rapid daily spinning, the shape of the Earth is distorted in having an “Equatorial Belt”. On, for example, the Summer Solstice, the Sun in the sky is about 23.5 north of the plane of the Equator and the Equatorial Belt. This results in a differential gravitational attraction of the Sun to the nearer edge of the Belt and the further edge of the Belt (due to the inverse square distance dependency of gravitation). The collective (Calculus) gravitational effect on the entire Belt then tends to try to stand the Earth more vertically upward, which causes the Precession effect per Eulers’ Differential Equations. So there IS significant Precession during the Summer Solstice. Simple Integral Calculus over the circumference of the Belt shows that with that geometry, the instantaneous force and power acting on the Earth is virtually double what might be expected of a “constant solar precession”. But at the moment of the Spring Equinox, the Sun is directly over the Equator in the sky and it no longer pulls the Belt upward or downward, and there is NO Solar Precessional action occurring at the Spring Equinox. Again, the Calculus is quite simple to mathematically confirm this. Instead of there always being a CONSTANT Precessional effect, the Solar Precession ABSOLUTELY STOPS twice every year, at the Spring Equinox and the Autumnal Equinox. The gravitational differential force of the Solar Precession therefore goes from zero at March 21, to a maximum force and effect three months later, then back down to zero three months later on Sept 21, and then again up to a maximum at the Winter Solstice. A second Calculus Integration over the year gives the math that shows the annual average Precession effect. In school, you were only told about the AVERAGE of that (annual) Solar Precession effect! We now calculate how much kinetic energy there is in our AVERAGE precession. It is 1/2 * I * ω2. We know that the rotational inertia (I) of the earth is 8.07 * 1037 kg-meters2. The angular rotation of the precession is ω or one precessional revolution in 25,800 years or one radian in 1.296 * 1011 seconds. Therefore, the AVERAGE kinetic energy the Earth has in Precessing is around 2.4 * 1015 joules. This energy is transferred to the Earth from the Sun and Moon. In planetary dynamics, that is not very much, but it still is Kinetic Energy that did not used to exist! As a CONSTANT force, that would have minimal importance. But the fact that it keeps wildly increasing and decreasing every few months, there is a considerable amount of gravitational effect that keeps going back and forth between the Sun and Earth as Precession. LaPlace, LaGrange, Leverrier and other brilliant early astronomers all made an ASSUMPTION that now appears to have been slightly wrong! They correctly recognized that Conservation of Energy must apply to planets orbiting the Sun. They also assumed that Angular Momentum is ALWAYS Conserved which turns out not to always be true! Given those two conditions, it is rather easy to mathematically show that two planets might perturb each other in a variety of ways, but NEVER by ever being able to change the radius of each others orbits. And so they all agreed on an absolute statement to that effect, that planets could never alter the semi-major radius of each others orbits. THAT statement is now seen to be clearly incorrect, but ONLY when gyroscopic-types of effects apply. Their reasoning and their resulting conclusions are generally true. However, this presentation shows that there are two processes that violate the Conservation of Angular Momentum, which then PERMITS planets to (very, very slowly) alter each others orbital radii. It is the gyroscopic precessional processes by which planets can affect each other. One is called Regression of the Nodes of the orbit. The other is called the Precession of the Equinoxes. Those brilliant scientists and mathematicians and others must certainly have seen toy gyroscopes that APPEAR to have very constant Precession, and made that incorrect assumption. They even developed the calculations to show that such a toy gyroscope gradually precesses FASTER as friction gradually slows the rotor spinning down, but that turns out to be a rather different effect. They had overlooked an obvious fact that when a toy gyroscope is FIRST released on its pedestal, its Precessional motion MUST ACCELERATE from the initial non-precessing situation. Angular Momentum, a Vector quantity, around the z- precession axis simply BEGINS out of nothing! ZERO Angular Momentum around the z- precession axis rather quickly becomes some non-zero number, which then remains essentially constant thereafter. The so-called Law of Conservation of Angular Momentum says that cannot happen! This is the simplest and most obvious example of a clear Violation of that Law of Conservation of Angular Momentum. Around 250 years ago, a mathematician named Euler expanded Newton’s Laws of Motion to three dimensions, and his set of Differential Calculus equations provided new insights about things like pendulums and gyroscopes. Euler’s equations show that the net effect is NOT to “tilt the Earth upward” but instead to “rotate the position of the Earth’s spin axis slightly forward”, a process called Precession. My web page at mb-soft/public/precess.html includes the precise calculation of this effect. Consider the situation on about March 21 of each year, at the instant of the Spring Equinox. At that moment, the Earth is at a location in its orbit where the Sun appears to us to be exactly over our Equator. If you think about this for a moment, you should realize that there can be NO (solar) Precessional effect at that instant. Since the Sun is exactly OVER the equatorial belt, the Sun’s gravitational effect on the belt exactly cancels out, north and south. The correct calculation of the ANNUAL (solar) Precession of the Earth necessarily needs for the Euler Differential equations to be Integrated for the entire calendar year (as shown in that web page linked above). There are two enormous effects of this corrected insight. One is that the Precession of the Earth is NOT a smooth, constant process over 26,000 years! (Solar) Precession actually totally STOPS twice every year, at the Spring Equinox and the Autumnal Equinox, and it rapidly SPEEDS UP to about DOUBLE the normally assumed rate at every Solstice. It is an amazingly hectic process! The other is that starting and stopping of our Precessional motion transfers force and power and resulting Kinetic Energy of Precession that is being transferred back and forth between the Sun and the Earth. Due to Euler’s equations, we now see that Kinetic Energy of Precession can get TRANSFERRED from the Sun to and from the Earth, entirely due to that gyroscopic precession effect that Euler discovered long ago. The long-term effect of the Earth’s precession IS a transfer of (Precessional)Kinetic Energy TO the Earth, in our slow precessional movement. But more interesting is the fact that huge amounts of Kinetic Energy and Angular Momentum is given TO the Earth and taken BACK every few months! This is NOT an irrelevant amount of energy! Between March 21 and June 21, the Earth receives about 10,000 trillion joules of Precessional Kinetic Energy from the Sun! Then it gives back most of that during the following three months! The average rate at which this energy transfer is occurring is about 1,250 MegaWatts, which is about comparable to the electric power generated by a major nuclear power plant! There is also a similar Precessional effect on the Earth due to the Moon, based on what is called the Nodical Month (about 27.2 days). A long-term effect of the Earth’s precession IS a transfer of Kinetic Energy TO the Earth, in our slow precessional movement. But more interesting is the fact that huge amounts of Kinetic Energy and Angular Momentum is give TO the Earth and taken BACK every few days! Between the moment the Moon passes over our Equator in its orbit and about a week later when it passes a Latitude, the Earth receives about 40,000 trillion joules of Precessional Kinetic Energy! Then it gives back most of that during the following week! The average rate of power at which this energy transfer to and from the Moon to the Earth is occurring is about 63,000 MegaWatts, which is about comparable to the electric power generated by all of the nuclear power plants in the U.S.! There is a related effect regarding the Moon. The Moon’s orbit is Inclined at about 5 from the Ecliptic. Depending on just where the Nodes are at any time as compared to the Obliquity of the Ecliptic of the Earth, the net effect of this Lunar Precession can be greater or less. Lunar Precession is often considered as one of several forms of Nutation, slight wiggling of the Earth’s spin axis by a few feet. However, we do not yet know how to CAPTURE any of this spectacular amount of free power! The two possible methods that seem possible to me are the two methods described in a separate article regarding trying to capture some of the even more enormous kinetic energy bound in the daily spinning of the Earth. I personally have doubts regarding the method that the Soviets spent several decades studying, but maybe that method might have potential regarding trying to capture precessional power supplied by the Moon and Sun. The other method, of trying to find some way of using gyroscopic precession to capture some of the available power, might also have some potential. mb-soft/public9/earthro4.doc
Posted on: Wed, 31 Dec 2014 14:12:51 +0000