 |
| Titel |
Plane Mercury librations |
| VerfasserIn |
Yu. V. Barkin, J. M. Ferrandiz |
| Konferenz |
EGU General Assembly 2009
|
| Medientyp |
Artikel
|
| Sprache |
Englisch
|
| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 11 (2009) |
| Datensatznummer |
250022249
|
|
|
|
|
|
| Zusammenfassung |
| Introduction. In 1988 I. Kholin [1] has developed a precision method of determination of
parameters of rotation of planets on complex radar-tracking observations on two radio
telescopes making base and definitely carried on surface of the Earth. His American
colleagues for the period approximately in 4 with small year have executed a series of
radar-tracking measurements on a method and I. Kholin’s program [2] and have obtained for
the specified period 21 values of angular velocity of rotation of this planet [3]. With the help
of numerical integration of the equations of rotary motion on the found values they managed
to determine with high accuracy the basic dynamic parameter in the theory of Mercury
librations (B - A)-Cm = (2.03± 0.12) -
10-4 and the corresponding to it the value of
amplitude of the basic librations35”8 ± 2”1. These results have served as convincing
arguments for the benefit of the Peale’s assumption, that a core of Mercury is liquid, or in
partially molten [4]. Authors also managed to obtain for the first time parameters of
resonant librations in a longitude which opening from radar observations was predicted
earlier [5]. Its amplitude makes about 300”, the period is equal approximately to 12
years.
In the paper [6] parameters of the perturbed rotational motion have been determined with
the help of the analytical theory and with formal using of results of mentioned work [3] on
determination of 21 values of angular velocity of Mercury. In result the estimations of
amplitudes of forced librations of first five harmonics with the periods: 87.97 d, 43.99 d,
29.33 d, 21.99 d and 17.59 d have been obtained. The appropriate amplitudes make
values:34”05 ± 1”27, 3”59 ± 0”13, 0”354 ± 0”013, 0”072 ± 0”003 and 0”016 ± 0”001.
The amplitude and the period of free librations of Mercury in a longitude are determined:
290”9 ± 67”0 and 12.37 ± 0.23 yr, consequently. The phase of this variation has
made28401 ± 1402.
In the paper we construct the similar theory of Mercury librations in longitude by using
three characteristics of Mercury rotation determined in the paper [3]. Two from these
parameters are values of angle of librations in longitude and angular velocity in moment of
passage of perihelion of Mercury orbit on 17 April 2002: (δg)0 = 0007 ± 0001,
(δÏ-Ï )0 = (2.10± 0.06)-Ï ars/d. Third parameter determined in [3] is a dynamical
coefficient: K = (B -A)-(4Cm ) = (5.08± 0.30) -
10-5. B > A are principal moment of
inertia, corresponding to equatorial axes of inertia; Cm is a polar moment of inertia of the
mantle of Mercury.
1 Analytical theory of plane Mercury librations. This theory describes forced and free
librations of Mercury in longitude in the frame of plane problem about resonant librations of
Mercury considered or as non-spherical rigid body, or as system of rigid non-spherical mantle
and liquid ellipsoidal core. Saving the main terms for the perturbations of angle of
librations δg and angular velocity Î´Ï in both mentioned cases we will have formulae
[6]:
δg = K(E sin M + E sin2M + E sin 3M + E sin4M + E sin5M )
1 2 3 4 5+K0 sin(E -KM- - φ)
(A) |
|
|
|
|
|
|