Аннотация:Analysis of modern observations of the Earth's rotation velocity (www.iers.org) revealed that the spectrum of velocity variations (period of observations 1962 - 2014) contains the following characteristic periods: 1 year, six months, 28 and 14 days [Levin & Sasorova, 2015]. If we need to calculate the total angular momentum of the Earth, we consider a closed system which includes three rotational processes: rotation around the Sun in an elliptical orbit (1), rotation around its axis (2) and rotating with the Moon around the barycenter (3).
According to the law of conservation of angular momentum, change of velocity at movement of the Earth on the ecliptic (from Vq = 30.28 km/s at perihelion to VQ = 29.27 km/s at aphelion) should give rise to occurring of variations in the velocity of rotation around the axis.
In accordance with works on the theory of the Earth's figure (A. Clairaut, K. Maclaurin) for every oblate spheroid growth of the rotation angular velocity should lead to increasing the flatness of the meridian section of the planet [Pitjev et al., 2002]. The magnitude of the relative variation of the rotation angular velocity of the Earth is approximately equal to the relative change in the length of day (LOD) and is Δω/ω ≈ 10-8. [Sidorenkov, 2002]. From the theory of the Earth's figure shows that the relative change of the radius vector of the spheroid (dr/r) is a function of flatness (ε), latitude (φ) at the measuring point and relative variation of the rotation velocity dr/r ≈ 2ε (1/3 – sin2φ) dω/ω.
Then on the polar caps and in high latitudes growth of angular velocity should lead to an increase in flatness (a reduction of the radius vector), and in the equatorial zone and adjacent areas will be a simultaneous increase in the radius vector. Putting dr ≈ 1 - 10 mm, r ≈ 6 *109 mm, ε ≈ 1/300, φ = 900, dω/ω ≈ 10-8, we obtain (with an amplitude change of the radius vector of about 1 - 10 mm), a fairly good agreement between the calculated and observed data. Analysis of results of GPS observations over the last 10 years shows similar materials in the global network [http://sopac.ucsd.edu/].
It should also be noted that the kinetic energy of rotation of the spheroid, while rotating at a constant angular velocity (as defined by Newton), is estimated as E = ½ I ω2 ≈ 1029J. In the case of an unstable rotation of the Earth is dE = I ωdω, where easy to obtain dE/E = 2 dω/ω. Assessment of additional energy arising from the instability of the planet's rotation, we obtain from the relation dE = 2 E dω/ω ≈ 2 1029 10-8 ≈ 2 1021 J. The total energy released by all earthquakes of the world each year is approximately 1017 - 1018 J.
Thus, the cyclic variations of the Earth`s figure shape with a period of 1 year and an amplitude of about 10 mm, recorded by GPS-receivers, transmit substantial mechanical energy to solid Earth. The role of cyclic pulsations shape of the Earth should be the subject of further research in the geodynamics.
References:
1. International Earth Rotation and Reference System Service, http://www.iers.org
2. Levin B.W., Sasorova E.V. On relation between variations of the Earth`s rotation velocity and its seismic activity. Doklady Earth Sciences. 2015. V. 464. No. 3. P. 1-5.
3. Pityev N.P., Titov V.B., Kholshevnikov K.V. Figures of equilibrium for celestial bodies. Sankt-Retersburg State University. 2002. 108 pp. (Russian).
4. Sidorenkov N.S. Physics of the Earth`s rotation instabilities. M. Nauka. Publishing Company Fizmatlit. 2002. 384 pp. (Russian).
5. Scripps Orbit and Permanent Array Center, http://sopac.ucsd.edu/