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According to Xiaodong Song et al.’s study about difference rotation in the Earth’s inner core, a physical model of lunar motion changing the angular momentum of the Earth’s circles is presented in this work. The Lunar motion makes there be a huge gap existing in the core angular momentum between far lunar hemisphere and near lunar hemisphere. The gap results in the difference rota-tion in the Earth’s inner core, meanwhile, it increases the angular velocity of far lunar hemisphere and decreases the angular velocity of near lunar hemisphere. The Earth’s liquid outer core gene-rates an astro-geodynamical effect including the difference rotation among the Earth’s circles. It is found that when the moon moves into the apogee or the perigee of the lunar orbit, and the moon phase is the upper and lower chords (i.e. semi-diameter place), the true anomaly of the moon will change from 270-degree back (or forward) to 90-degree; this results in the mantle shell of the Earth westward, and forms lunisolar precession, the vernal equinox westward and Chandler polar motion.

Formation mechanism of lunisolar precession and lunar orbit nodes regression is still a scientific conundrum. According to difference rotation research achievements presented by Song Xiaodong et al. for the earth’s inner core, the author puts forward a physical model of “lunar orbit motion changing angular momentum of various circles of the earth”. Due to the mass of earth-moon system which is located inside the earth as well as liquid state characteristics of the earth’s outer core, it is deemed that angular momentum of all circles of the earth can be varied by lunar orbit motion so that a huge gap is generate between angular momentums of far and near lunar hemispheres of the core. In addition, difference rotation is also formed for the core (solid inner core and liquid outer core). Considering that conservation of angular momentum of the earth, mantle crust westward is caused together with lunisolar precession and spring equinox westward. It is found that inner core of the earth wavers inside the liquid core along with lunar orbit motion to change the location of the earth’s center of mass. When elliptical orbit motion of the moon enters a place near the sun or the earth (that is, semi-diameter place), true anomaly of the moon changes from 270˚ back (or forward) to 90˚. This results in lunar orbit nodes westward and Chandler polar motion. Such a finding has a significant meaning to explain the formation mechanism of lunisolar precession and spring equinox westward. Profound implications in the “Greatness in Simplicity; Rare Voice of Big Sound” said by Lao Tzu in Tao Teh King and the “Heaven and earth have made great beauty, four seasons have clear without proposed, does not talk contribution has everything” given by Zhuangzi can be experienced.

The case that the earth revolves around the sun for a round can be divided into a sidereal year and a tropical year. Similar to the earth, revolution of it around the earth forms a sidereal month or a synodic month. If the moon revolves for 360˚ around the earth, it is referred to as a sidereal month, which is the actual cycle of moon revolution equal to 27.3216 days. The sidereal month regards fixed stars in astrospace as its directional signs. In the case that it is calculated according to phase variation cycle of the moon, for example, a cycle from crescent to crescent or full moon to full moon, it is named as the synodic month with a length of 29.5306 days. “revolution orbit plane for the moon moving around the earth is also known as the plane of moon’s path which does not coincide with the ecliptic plane; otherwise, an inclination of 5˚9’ is formed by them and it is known as obliquity of the moon path. If these two planes intersect with each other to form a straight line, this line is named as nodal line. In addition two nodes exist between the nodal line and the celestial sphere. ... When it moves through a node from the south of ecliptic to its north, one is an ascending node while the other is descending node.” “One critical feature of nodes is that they keep moving (westward) with a cycle of 18.6 years; moreover, they move for 19˚21 each year. The time required by the moon to move through the node for the second time is 27.21222 days, known as a nodal month.” “The moon rotates around the earth in an elliptical orbit and the earth is situated at a focus. Time interval for the moon to pass perigee between two times is an anomalistic month which is equal to 27.55455 days. ... Perigee of the lunar orbit also keeps moving with a cycle of 8.85 years.” [

Chen Guoxian from Natural Disaster Prediction Committee of the Chinese Geophysical Society thoroughly studies lunar orbital motions with an aim to predict geo-hazards. In his opinion, “the length of lunar orbit (motion) cycle is decided by the location of the earth’s orbit corresponding to perigee of the moon; from the perspective of mathematical meaning, such a length is defined by elliptical eccentricity; that is, it is formed by elliptical focus changes specific to the center of the circle (Earth)”. The range of movement lies between O and O’ or Q and Q′, which are all focuses of the elliptical, in a bilateral symmetry manner, as shown in

(the date when winter begins is November 7 or 8) to February 15 of the next year (the spring-beginning-day is February 4 or 5); other time (season) is the forward movement period (from west to east) of the rotational pole” [

Findings of Chen & Song are very significant without any doubt, because a research orientation is provided for researches on lunisolar precession, lunar orbit node westward and Chandler polar motion mechanism.

“According to research accomplishments of inner core difference rotation published in 1996 by Song Xiaodong et al., it is estimated that the inner core of the earth rotates 1.1 more degrees from west to east than the outer core each year. From 1990 to 1996, it rotates 1/4 more circle accumulatively, which attracted attentions from international academia and is evaluated as one of the global top ten scientific news of 1996.” “People are aware that as no prominent changes occur to fast axis of centrosphere within a short term if compared with the inner core, ... causes for such variations are obvious differences that exist in rotation speed between centrosphere and the whole earth. Therefore, as long as variation rules with time of the fast axis of inner core can be mastered, the different rotation rate between inner core and other solid circles such as the crust mantle is determined” [

Why the rotation speed of the earth’s inner core exceeds other regions of it? In conformity with research findings of predecessors, a physical model of lunar motion changing the angular momentum of the Earth’s circles is presented.

Moment inertia of the whole earth and the centrosphere (including inner core and liquid core) are shown below.

Then, angular momentum of the mantle crust is I_{mq} = I_{d} − I_{dh} = 8.79 × 10^{37} kg∙m^{2};

The average distance from earth-moon system to the earth’s core can be expressed as

of mass is:

mass of both far and near lunar hemispheres to the center of mass of the earth. Then, the linear velocity for center of mass of the far lunar hemisphere rotating around O, the common center of mass for the earth-moon system from west to east can be expressed as

Kinetic equation for earth rotation is presented below.

Where,

Then, in the case of the moon being located at perigee or apogee, distances from the center of mass of the earth-moon system to the geocenter are respectively worked out below.

On this basis, when centrosphere is at the perigee of the moon, linear velocity for the center of mass of the near lunar hemisphere rotating around the center of mass of the earth-moon system can be written into the following formula.

By contrast, when centrosphere is at the apogee, such a linear velocity can be expressed as follows.

The velocity direction of far lunar hemisphere from west to east is identical to that of earth rotation, while it is against the direction of earth rotation as far as the near lunar hemisphere is concerned. Linear velocity caused by earth rotation at

Consequently, the difference of angular momentum between far and near lunar hemispheres of the centrosphere can be calculated in line with the below formula.

With regard to the comparison between

It indicates that during orbital motions from perigee to apogee, angular momentum of the earth’s centrosphere circle is increased thanks to the orbital motion of the moon. Such a momentum makes the rotation of centrosphere (both the inner core and the liquid core) accelerated, giving rise to shaking of the earth’s axis so as to form polar motion and nutation. The increase in rotation of the centrosphere (both the inner core and the liquid core) is

As the angular momentum of the earth’s circles changes during the orbital motion of the moon, it is dynamic, transient and accumulative. For example, on January 1 of 2013, through astronomical year book consulting and computing, the earth-moon distance of the day is

espectively. As a result, on January 1 of 2013, the difference of angular momentum between far and near lunar hemispheres of centrosphere is also the angular momentum increment of the centrosphere on this day, which is expressed below.

According to the law of conservation of angular momentum, it is assumed that friction coefficient between liquid core of the earth and mantle crust is zero, centrosphere angular momentum of the earth system rises, so that angular momentum of both mantle and crust of the earth is negative. In other words, mantle crust moves westward which is against the direction of earth rotation. Hence, an equation of

Considering that the angular momentum of centrosphere is both dynamic and accumulative, angular momentum increment of it at the beginning of a year is set to be the initial value (on January 1

Matlab is adopted to establish a program to simulate orbital motions of the sun, the earth and the moon; in addition, accumulations of mantle crust’s dynamic angular moment during their orbiting within a year are computed (please see

Then, angular displacement within one year of the mantle crust westward is also figured out as follows.

“Equinox westward has an average velocity of 50.24’’/year and such a velocity is referred to be the precession of equinox” [

where the earth is located during its revolution at all seasons, reverse motion for pole of rotation (the north pole) occurs from November 1 of the year to February 15 of the next year”. Then, combining calculation chart for the annual accumulative intersection angle (second of arc) of the earth’s mantle crust given in

According to findings of Chen, “the (motion) length of the orbit of the moon is determined by the location for earth’s orbit specific to the perigee of the moon”; “projection curves of the moon on the beginning and the end of the year on ecliptic does not coincide with each other, as presented in

Song Guanyi finds that, “among positions where the earth is located during its revolution at all seasons, reverse motion for pole of rotation (the north pole) occurs from November 1 of the year to February 15 of the next year; other time (season) is the forward movement period (from west to east) of the rotational pole.” On this basis, it is found that, when inner core moves along with orbit motions of the earth and the moon, under the joint actions of solar wind and the moon orbit motion which change the angular momentum of centrosphere, it also wavers in the liquid core so as to alter the position of the earth’s center of mass. (Please refer to ^{th} round (upper/lower chord), because this phase is the radius vector in the case of true anomaly f = 90˚ or 270˚ and the radius vector of P = a⋅(1−e^{2}) [

Synergic orbit motions of the sun, the earth and the moon within one year can be described as follows. Under the joint action of solar wind and the moon orbit motion changing the angular momentum of centrosphere, solid inner core wavers in the liquid core so that the location of the center of mass is altered. At the same time, the orbit motion of the moon makes angular momentum of centrosphere go up continuously so as to accelrate the rotation of liquid core. As angular speeds of revolution formed between the liquid core and the moon, and the center of mass of the earth-moon sytem, are equal, a phenomenon of “projection curves of the moon on the ecliptic with 90˚ forward each year” appears in terms of the moon orbit motion. When the earth-moon system approaches the winter solstice location near the perihelion or the perigee, true anomaly for orbit motion of the moon revolution changes from f = 270˚ back (or forward) to f = 90˚. As a result, the phenomenon discovered by Song Guanyi occurs (Please refer to

(1) When the earth takes the moon rotating around the sun, orbit motion of the moon changes angular momentum of the earth’s circles so that a giant gap exists between angular momentum of far and near lunar hemispheres. As a result, not only is difference rotation formed, but give rise to shaking of the earth’s axis as well as polar motion.

(2) Orbit motion of the moon causes angular momentum difference for far/near lunar hemisphere and increases the angular momentum of centrosphere. Due to angular momentum conservation of the earth, mantle crust westward takes place to form lunisolar regression and equinox westward.

(3) It is found that when elliptical motion of the moon approaches perihelion or perigee (that is the semi-latus rectum phase), true anomaly for elliptical orbit varies (moves forward) to f = 90˚ from f = 270˚ back and automatic zero resetting adjustment takes place once for the angular momentum of the earth in perihelion. As it moves forward 90˚ each year and that is 180˚ for two years, “bi-aanual quasi-periodic variation” occurs to the earth rotation rate. Power producer for the earth’s 1.2 years of Chandler polar motion is deemed to come from the moon, while from the sun as far as its annual polar motion is concerned.

Yueming Wu,Mingfu Cao, (2016) Quantitative Study of Lunisolar Precession Mechanism. Journal of Geoscience and Environment Protection,04,185-193. doi: 10.4236/gep.2016.47021