Motion of the Earth's centre of mass. Physical principles
It has been found that the residual (Chandler) motion of the Earth’s rotation pole results from the forced translational motion of the Earth’s rotation axis relative to the geographic axis. The Earth’s rotation axis moves parallel to itself without changing the angle of inclination to the ecliptic p...
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Головна астрономічна обсерваторія НАН України
2005
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| Cite this: | Motion of the Earth's centre of mass. Physical principles / D.G. Kiryan, G.V. Kiryan // Кинематика и физика небесных тел. — 2005. — Т. 21, № 5-додаток. — С. 376-380. — Бібліогр.: 3 назв. — англ. |
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| author | Kiryan, D.G. Kiryan, G.V. |
| author_facet | Kiryan, D.G. Kiryan, G.V. |
| citation_txt | Motion of the Earth's centre of mass. Physical principles / D.G. Kiryan, G.V. Kiryan // Кинематика и физика небесных тел. — 2005. — Т. 21, № 5-додаток. — С. 376-380. — Бібліогр.: 3 назв. — англ. |
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| description | It has been found that the residual (Chandler) motion of the Earth’s rotation pole results from the forced translational motion of the Earth’s rotation axis relative to the geographic axis. The Earth’s rotation axis moves parallel to itself without changing the angle of inclination to the ecliptic plane. The translational motion of the Earth’s axis of rotation is caused by the motion of the Earth’s center of mass in the Earth’s body in the range from 1 to 30 meters relative to the Earth’s surface. The motion of the Earth’s center of mass in space is due to the motion of the consistent inner core of the Earth in the liquid outer core under the action of the total (internal and external) gravitational field. Formulae for calculation of the trajectory of the Earth’s centre of mass from astronomical observations are suggested. The comparison of our calculations and observational data on variations in the latitudes of places and acceleration of gravity has shown that they are in good agreement. Our model has been shown to adequately describe the physical process of motion of the Earth’s centre of mass inside the Earth’s body.
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MOTION OF THE EARTH’S CENTRE OF MASS. PHYSICAL PRINCIPLES
D. G. Kiryan, G. V. Kiryan
Laboratory of Dynamics of Mechanical Systems, Institute of Problems of Mechanical Engineering
V.O., 61 Bolshoy pr., 199178 St.-Petersburg, Russia
e-mail: diki@mail.wplus.net
It has been found that the residual (Chandler) motion of the Earth’s rotation pole results from
the forced translational motion of the Earth’s rotation axis relative to the geographic axis.
The Earth’s rotation axis moves parallel to itself without changing the angle of inclination to
the ecliptic plane. The translational motion of the Earth’s axis of rotation is caused by the motion
of the Earth’s center of mass in the Earth’s body in the range from 1 to 30 meters relative to
the Earth’s surface. The motion of the Earth’s center of mass in space is due to the motion of
the consistent inner core of the Earth in the liquid outer core under the action of the total (internal
and external) gravitational field. Formulae for calculation of the trajectory of the Earth’s centre
of mass from astronomical observations are suggested. The comparison of our calculations and
observational data on variations in the latitudes of places and acceleration of gravity has shown
that they are in good agreement. Our model has been shown to adequately describe the physical
process of motion of the Earth’s centre of mass inside the Earth’s body.
INTRODUCTION
In the middle of the 18th century the Russian scientist M. Lomonosov made an attempt to reveal experimentally
the motion of the Earth’s centre of mass. In 1883, G. Schiaparelli put forward the hypothesis that there is a re-
distribution of masses inside the Earth that leads to noticeable movements of the axis of inertia and the Earth’s
axis of rotation. However, this idea was neither supported nor developed. The goal of our investigations of
the motion of the Earth’s centre of mass and axes of rotation was to reveal the physical laws governing the mo-
tion of the Earth’s axes of rotation in space and to suggest the method for taking into account this motion in
astronomical observations and solution of problems of gravimetry, satellite navigation, metrology, etc.
EARTH’S CENTRE OF MASS AND CENTRE OF FIGURE
What does the trajectory of the intermediate pole mean? The coordinates of the intermediate Earth’s
rotation pole published by IERS are calculated from observations of coordinates of known stars with corrections
for nutation and precession. Therefore, primary observations of the motion of the instantaneous Earth’s rotation
axis (Fig. 1) in space are converted to numerical data on the motion of the Earth’s axis of rotation. O1 and �ω1
are the rotation axis and the proper Earth’s angular velocity; Oi and �ωi are the instantaneous rotation axis and
instantaneous angular velocity of the Earth’s rotation; Onut and �ωnut are the instantaneous position in space
of the nutational axis and the angular velocity of the nutational rotation, Opr and �ωpr are the instantaneous
position in space of the precessional axis and the angular velocity of the precessional rotation of the Earth’s
axis; O∗ is the Earth’s centre of mass; and O is the centre of the figure of the Earth. Figure 2 shows, on a virtual
plane parallel to the equator, the residual motion of the Earth’s rotation pole (axis) corrected for the secular
motion. Without introducing new notions, it can be concluded from the aforesaid that the residual motion of
the Earth’s rotation axis is translational, i.e., the Earth’s rotation axis moves in the space of objects parallel to
itself. However, the rotation axis is an imaginary line passing through the Earth’s centre of mass. Therefore,
it is the Earth’s centre of mass that moves in the space of objects.
Variations in latitude. Without discussing the essence of the physical processes responsible for appearance
and motion of the instantaneous Earth’s centre of mass, we consider the latitude variations taken from [1]
(Pulkovo, Johannesburg, Onkativo, Basewather). Schematically, the set of observed latitude variations is shown
in Fig. 3 and Fig. 4. In constructing the schemes, the property of the plumb-line to indicate direction toward
the Earth’s centre of mass was used. The points in the schemes correspond to those given in Table 1. It is
evident from Fig. 3 and Fig. 4 that the latitudes in the North and South change synchronously, and the nature
of latitude changes is the same (motion of the centre of mass). In the consideration of the nature of motion of
c© D. G. Kiryan, G. V. Kiryan, 2004
376
-0.3 -0.2 -0.1 0 0.1 0.2 0.3
x [arcsec]
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
y
[
ar
cs
ec
]
eopc04(var) interval: 2439048 - 2450737
dk
iry
an
.fi
g2
11690
1
Figure 1. Axes of the Earth’s rotation �ωi = �ω1+�ωnut+
�ωpr
Figure 2. Trajectory of the Earth’s pole of rotation
Figure 3. Scheme of variations in latitudes of the points
at the same meridian in the N and S hemispheres
Figure 4. Scheme of latitude variations of the points
with a difference in longitude of 180◦
Table 1.
ϕi λi
1. Pulkovo +59◦ 46′ 18′′ 30◦ 19′ 45′′
2. Johannesburg −26◦ 10′ 55′′ 28◦ 04′ 30′′
3. Onkativo −31◦ 55′ 10′′ 296◦ 18′ 00′′
4. Basewather −31◦ 55′ 13′′ 115◦ 55′ 00′′
the Earth’s pole of rotation (trajectory of the intermediate pole eopc04, given by IERS), angular movements of
the rotation axis relative to the Earth’s centre of mass are excluded. If we assume that the Earth’s centre of mass
moves along the axis of maximum moment of inertia (the z axis of the geocentric equatorial coordinate system),
the observed simultaneous changes in the latitudes of Pulkovo, Johannesburg, Onkativo, and Basewather cannot
occur. If the centre of mass moves in the equatorial plane (or close to it), and the Earth’s rotation axis
executes the translational movement, the whole set (without any exception) of the observed simultaneous
latitude variations receives a natural explanation. Taking into consideration the structure of variations in
the latitudes of the observation points, physical laws, and following the Newton’s rule
”We are to admit no more causes of natural things than such as are both true and
sufficient to explain their appearances”,
we can state that latitude variation results from spatial variation in the orientation of the plumb-line. Thus,
variations in the latitudes and longitudes of the points of the Earth’s surface observed by astronomers are
caused by the natural phenomenon, i.e., motion of the centre of mass. The astronomer determines the current
377
latitude of the place ϕ∗
i relative to the local normal in the astronomic (moving) coordinate system rather than
in the geocentric (fixed) system. Every measurement of the angle occurs under the conditions of constantly
changing spatial position of the reference system origin O∗ and position of the plane of the measured angle ϕ∗
i .
The dependence of the latitude of a place on the position of the Earth’s centre of mass in the Earth’s body is
illustrated by comparison of the model and observed corrections to the latitude of Pulkovo (Fig. 5). The obser-
vational data and our calculations of latitude variations for other observatories in the Southern and Northern
hemispheres of the Earth also demonstrate a convincing agreement.
MOTION OF THE CENTRE OF MASS
Thus, the residual (Chandler) motion of the Earth’s rotation axis is governed by the motion of the Earth’s
centre of mass in the Earth’s body. The physical and mechanical characteristics of the inner and outer structural
shells of the Earth are such that the central Newton forces of interaction between the mass of the Earth’s inner
consistent core and gravitating masses in the surrounding space (mainly those of the Moon and the Sun) cause
movement of the inner core in the liquid, low-viscosity medium of the outer core relative to the Earth’s surface.
The direction and velocity of motion of the Earth’s centre of mass are determined by the continually changing
summary vector of the impulse of interaction between the inner consistent core mass and gravitating masses
in the Universe. The forced anharmonic motion of the centre of mass exhibits a regular pattern. The cyclicity
of motion relative to the centre of the figure of the Earth in the geocentric equatorial system is determined by
the half-difference between the frequency of variation in the distance from the ascending node to the perigee
point of the Moon’s orbit and the frequency of the Earth’s revolution around the Sun. As analysis has shown,
the duration of the cycle of the 2π-rotation of the centre of mass (the axis of the maximum moment of inertia,
rotation axis) with respect to the centre of the figure of the Earth ranges from 350 to 550 days (Fig. 6).
The distance between the Earth’s centre of mass and centre of the figure of the Earth continually changes from
1 to 20 meters. In more detail, the physical processes responsible for appearance of the moving Earth’s centre
of mass and kinematics and dynamics of its motion are described in [2].
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model
observation
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eopc04(var): rws-5/rws_cycle.dat, 27 points
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an
.fi
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Ca = 431.963
Figure 5. Variation in the latitude of Pulkovo Figure 6. Cycles of the Earth’s centre of mass
MONITORING OF THE CENTRE OF MASS
The residual motion of the Earth’s rotation axis O1 (axis of maximum moment of inertia) is the consequence of
motion of the Earth’s centre of mass O∗. To have a clear idea of the motion of the Earth’s centre of mass O∗
in the space of objects as a natural phenomenon, systematic observations of the motion of the Earth’s centre
of mass in the regime of monitoring and calculation of its current coordinates with a prescribed accuracy are
necessary. Monitoring of the Earth’s centre of mass will allow studies of the effect of external and internal
forces on the gravitating mass of the consistent inner core of the Earth, of the spatial and temporal structure of
the gravitational field on the Earth’s surface, and also of the geodynamic parameters of the Earth. Coordinates of
stars (with an accuracy to proper motion) and geocentric coordinates of the point of astronomical observations
on the Earth’s surface (with the accuracy to displacement of continental plates) do not vary in time, and
therefore the observed changes in the orientation of the local normal relative to stars characterize the motion of
the instantaneous Earth’s centre of mass O∗ in the Earth’s body. In observations of the changes in the orientation
of the local normal relative to known stars, the observers detect angular values ϕ∗
i and λ∗
i and variations in
these angular values Δϕi and Δλi, i.e., they determine the current orientation of the local normal in space.
ϕ∗
i (t) − ϕi = Δϕi(t) , λ∗
i (t) − λi = Δλi(t) . (1)
378
Then, by using the expression relating the coordinates of the moving astronomical system and the coordinates
of the fixed geocentric system, it is possible to calculate the geocentric coordinates of the Earth’s centre of
mass O∗. The expressions for transformation of coordinates for the general case when z(t) �= 0, i.e., the Earth’s
centre of mass goes out of the equatorial plane, were given in [2]. In this case z(t) = 0, the geocentric coordinates
of the centre of mass x(t) and y(t) are given by
x(t) = xi − zi
1
tan ϕ∗
i (t)
√
1 + tan2 λ∗
i (t)
, y(t) = yi − zi
tan λ∗
i (t)
tan ϕ∗
i (t)
√
1 + tan2 λ∗
i (t)
, (2)
where
xi = Ri cosϕi cosλi , yi = Ri cosϕi sin λi , zi = Ri sin ϕi . (3)
Current coordinates of the Earth’s centre of mass O∗ can be calculated from observations of known stars
performed from one or several points of the Earth’s surface. In the case observations are performed from
several points of the Earth’s surface with different latitudes and longitudes, it is possible to obtain data on
the component z(t) of the motion of the Earth’s centre of mass.
CENTRE OF MASS AND GRAVIMETRY
As the spatial position of the Earth’s centre of mass changes, the distance between the observation point and
instantaneous centre of mass varies. Acceleration of gravity g at the observation point for the current moment
of time is calculated from the difference between radii-vectors in terms of the hypothesis on the linear variation
in the acceleration of gravity in the direction of the Earth’s centre. It is generally believed that the motion of
the Earth’s centre of mass does not exceed several centimeters and does not exert a considerable influence on
variations in g on the Earth’s surface. In reality, the Earth’s centre of mass systematically moves from 1 to
30 meters relative to the points of the Earth’s surface. Fig. 7 shows calculated variations in the acceleration
of gravity at Potsdam. Our calculations were performed for a particular time interval, the actual trajectory
of motion of the Earth’s centre of mass was taken into account. For other points of the Earth’s surface,
the structure of variations in g is similar. The maximum amplitude of variation in g (here, g is a function of
motion of the Earth’s centre of mass) must be observed in the equatorial regions of the Earth’s surface, and
the minimum amplitude must be observed in polar regions. In 1981–1984, a Space Geodesy Research Group
(FGS, Germany) detected simultaneously temporal variations in acceleration of gravity g and variations in
the latitude by using a superconducting gravimeter and a zenith tube, respectively [3]. We calculated variations
in the acceleration of gravity g(t) from the observational data on coordinates of the instantaneous Earth’s
centre of mass during the period 1981–1984. For the same time interval, variations in the latitude ϕ(t) of
Bad Homburg were calculated (Fig. 8). Comparison of the observational data obtained by the FGS group
and our calculations leads to the conclusion that the suggested physical model of motion of the Earth’s centre
of mass and its mathematical description yield calculated Δϕ(t) and Δg(t) consistent with the observational
data on the motion of the instantaneous Earth’s centre of mass. Fig. 8 shows variations in g(t) and ϕ(t)
during the same time interval. It can be seen that the correlation is good. All the curves have common nodal
points with a periodicity of ≈ 1.2 years. A good agreement between experimental and calculated Δg(t) and
Δϕ(t) indicates that a superconducting gravimeter and zenith tube (tiltmeter) independently detect the same
geodynamic natural phenomenon, i.e., motion of the Earth’s centre of mass in its different manifestations.
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da
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in
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∆ ϕ , observation
∆g
Figure 7. Δg(t) at Potsdam Figure 8. Δg(t) and Δϕ(t) at Bad Homburg
379
CONCLUSIONS
Analysis of the IERS and observational data on variations in the latitudes of observatories has shown that
a) free nutation as an interpretation of the residual (Chandler) motion of the Earth’s rotation axis has no
physical sense and cause-effect relations with the surrounding material world;
b) calculations of variations in latitudes are performed without taking into account the principle of invariance
with respect to the latitudes of the Northern and Southern hemispheres of the Earth.
Analysis of the suggested corrections to latitudes and longitudes taking into account the principle of invariance
has shown that
1. The residual motion of the Earth’s rotation pole is the translational motion of the Earth’s rotation axis;
2. The translational motion of the Earth’s rotation axis (parallel to itself) is caused by the motion of
the Earth’s centre of mass in the Earth’s body;
3. The motion of the Earth’s centre of mass in the space (in the Earth’s body) results from the motion of
the consistent inner core of the Earth in the liquid outer core under the action of the total (internal and
external) gravitational field that varies in time;
4. The orientation of the plumb-line is determined by the motion of the Earth’s centre of mass relative to
the Earth’s surface;
5. There exists the spatial-temporal structure of the gravitational field on the Earth’s surface caused by
the moving Earth’s centre of mass;
[1] Kulikov K. A. Variability of Latitudes and Longitudes.–Moscow: Fizmatgiz, 1962.
[2] Kiryan D. G., Kiryan G. V. Motion of the Earth’s Center of Mass. Physical Principles.–St.-Petersburg:
St.-Petersburg State Polytechnical University, 2003. [http://www.wplus.net/pp/Diki/index.html]
[3] Earth rotation, Research group for space geodesy.–Frankfurt am Main: Druckerei Heinrich GmbH, 1998.
380
|
| id | nasplib_isofts_kiev_ua-123456789-79680 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0233-7665 |
| language | English |
| last_indexed | 2025-11-30T15:56:12Z |
| publishDate | 2005 |
| publisher | Головна астрономічна обсерваторія НАН України |
| record_format | dspace |
| spelling | Kiryan, D.G. Kiryan, G.V. 2015-04-03T18:41:32Z 2015-04-03T18:41:32Z 2005 Motion of the Earth's centre of mass. Physical principles / D.G. Kiryan, G.V. Kiryan // Кинематика и физика небесных тел. — 2005. — Т. 21, № 5-додаток. — С. 376-380. — Бібліогр.: 3 назв. — англ. 0233-7665 https://nasplib.isofts.kiev.ua/handle/123456789/79680 It has been found that the residual (Chandler) motion of the Earth’s rotation pole results from the forced translational motion of the Earth’s rotation axis relative to the geographic axis. The Earth’s rotation axis moves parallel to itself without changing the angle of inclination to the ecliptic plane. The translational motion of the Earth’s axis of rotation is caused by the motion of the Earth’s center of mass in the Earth’s body in the range from 1 to 30 meters relative to the Earth’s surface. The motion of the Earth’s center of mass in space is due to the motion of the consistent inner core of the Earth in the liquid outer core under the action of the total (internal and external) gravitational field. Formulae for calculation of the trajectory of the Earth’s centre of mass from astronomical observations are suggested. The comparison of our calculations and observational data on variations in the latitudes of places and acceleration of gravity has shown that they are in good agreement. Our model has been shown to adequately describe the physical process of motion of the Earth’s centre of mass inside the Earth’s body. en Головна астрономічна обсерваторія НАН України Кинематика и физика небесных тел MS4: Positional Astronomy and Global Geodynamics Motion of the Earth's centre of mass. Physical principles Article published earlier |
| spellingShingle | Motion of the Earth's centre of mass. Physical principles Kiryan, D.G. Kiryan, G.V. MS4: Positional Astronomy and Global Geodynamics |
| title | Motion of the Earth's centre of mass. Physical principles |
| title_full | Motion of the Earth's centre of mass. Physical principles |
| title_fullStr | Motion of the Earth's centre of mass. Physical principles |
| title_full_unstemmed | Motion of the Earth's centre of mass. Physical principles |
| title_short | Motion of the Earth's centre of mass. Physical principles |
| title_sort | motion of the earth's centre of mass. physical principles |
| topic | MS4: Positional Astronomy and Global Geodynamics |
| topic_facet | MS4: Positional Astronomy and Global Geodynamics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/79680 |
| work_keys_str_mv | AT kiryandg motionoftheearthscentreofmassphysicalprinciples AT kiryangv motionoftheearthscentreofmassphysicalprinciples |