Возмущения первого порядка во вращении Земли…
17
First-order perturbation in the rotation
of the Earth caused by the gravitational moments
from the Moon when describing the precision
of its orbital motion
© Yu.V. Barkin
1
, M.Yu. Barkin
2,3
1
Sternberg SAI, Lomonosov Moscow State University, Moscow, 119991, Russia
2
Bauman Moscow State Technical University, Moscow, 105005, Russia
3
Moscow Aviation Institute, Moscow, 12599, Russia
The article presents the analytical theory of a rotary motion (the theory of a pre-
cession, nutation and the compelled fluctuations of poles) developed for non-
spherical Earth on the basis of the equations of a rotary motion in Anduaye's
variables. We constructed perturbation of the first order in rotation of the planet
under the influence of the gravitational moments from the Moon in the conditions
of its real orbit set by the high-precision theory of EL 421. All calculations are
executed in ecliptic system of coordinates of date and presented in the form con-
venient for the analysis. Tabulation of perturbations for all variables of Anduaye
is executed.
Keywords:
action-angle variable, Liouville problem, Fourier series, elliptic integral.
REFERENCES
[1] Barkin M.Yu.
Izuchenie vozmuschennykh vraschatelnykh dvizheniy nebesnogo
tela s prilozheniem k teorii vrascheniya Zemli
[Study of perturbed rotational
motions of the heavenly bodies with application to the theory of the Earth's rota-
tion]
.
Ph.D. Thesis (Phys.&Math.). Moscow, 2014, pp. 154.
[2] Barkin Yu.V. Perturbated rotational motion of weakly deformable celestial bod-
ies.
Astronomical and Astrophysical Transactions
, 2000, vol. 19, issue 1, pp.
19–65. DOI
:
10.1080/10556790008241350.
[3] Barkin Yu.V., Kudrjavtsev C.M., Barkin M.Yu. Perturbations of the first order
of the Moon rotation.
Proceedings of International Conference “Astronomy and
World Heritage: across Time and Continents”.
Kazan, 2000, 19–24 August.
KSU, pp. 161–164.
[4] Kinoshita H. Theory of Rotation of the Rigid Earth.
Celest. Mech
., 1977, vol. 15,
pp.277–326.
[5] Kudryavtsev S.M. Long-term harmonic development of lunar ephemeris.
As-
tronomy & Astrophysics
. A&A 471, 1069–1075. DOI: 10.1051/0004-
6361:20077568.
Barkin Yu.V.,
Dr. Sci. (Phys.&Math.), professor, leading researcher in Sternberg Astro-
nomical Institute at Lomonosov Moscow State University. Sphere of scientific interests
includes theoretical mechanics, celestial mechanics. е-mail:
Barkin M.Yu.
, assistant lecturer of the Theoretical Mechanics Department in Bauman
Moscow State Technical University, assistant lecturer of the Theoretical Mechanics De-
partment in the Moscow Aviation Institute (Technical University). Sphere of scientific
interests includes theoretical mechanics, celestial mechanics. е-mail:
