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| Titel |
About the angles of inclination of the rotational axis and the angular momentum of Mercury |
| VerfasserIn |
Yury Barkin, Jose Ferrandiz |
| Konferenz |
EGU General Assembly 2011
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 13 (2011) |
| Datensatznummer |
250055822
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| Zusammenfassung |
| Abstract. The paper shows the ascending node of equator of Mercury (and the intermediate
plane orthogonal to the angular momentum) of epoch 2000.0 on the ecliptic does not coincide
with the ascending node of orbital plane of Mercury on the same plane, and ahead it at an
angle 23º4. Angular momentum vector of the rotational motion of Mercury form a constant
angle ÏG = 4′1 ± 1′1 with normal to the moving plane of the orbit. The observed inclination
of the angular velocityÏÏ = 2′1 ± 0′1, possible evidence of a significant amplitude free
movement of the poles of the rotation axis of Mercury (c amplitude of about 2 ’- 3’), as
predicted in [1].
Model. Resonant motion of Mercury on Cassini have been studied well-known authors:
Colombo, Beletskii, Peale, etc. Moreover, as a rule for the perturbed orbital motion was taken
on the motion of a uniformly precessing orbit (with a constant angular velocity nΩ < 0)
with constant angle of inclination of orbit plane i relatively the base plane (ecliptic
plane or Laplace plane). The orbit is elliptical and is characterized by constant
eccentricity e. In this study, the rotational motion of Mercury (as a celestial body with
nonspherical solid mantle and liquid core) on an evolving orbit, referred not to the Laplace
plane and the ecliptic of the given epoch. We take into account not only the uniform
precession of the orbit plane (the secular change in longitude of the ascending node
of the orbit Ω), but the slow change in orbital inclination (i) with small angular
velocityni.
The base model of Mercury’s orbit in the study of its rotational motion in this paper take
the mean orbit of this planet, whose parameters are given in the famous website
http://ssd.jpl.nasa.gov/?planets#elem: Planetary Mean Orbits (J2000) (epoch = J2000 = 2000
January 1.5):
i = 700028806, nΩ = dΩ-= - 446”30 (1/cy), ni = di= - 23”57 (1/cy).
dt dt
Period of orbital motion of Mercury is Tn = 2Ï-n = 87.969 days (n in the mean orbital
motion) and period of progressive precession of the line of node of the orbit plane on the
Laplacian plane is TΩ = 2Ï-|nΩ| =278898 years.
An estimation of the value of the angle of inclination of the angular momentum relative to
the normal to the mean orbital plane ÏG, is made on the basis of non-normalized values of the
coefficients of the second harmonic of the gravitational field of Mercury J2 andC22 (gravity
model HgM001 MESSENGER) [2]: J2 = (1.92 ± 0.65) -
10-5,C22 = (0.81 ± 0.08) -
10-5,
on parameters of physical librations and internal structure of this planet, derived from
satellite observations by apparatus Messenger, ground-based radar observations [3]:
(B - A)-Cm = (2.03 ± 0.12) -
10-4, ÏÏ = 2′1 ± 0′1 and based on theoretical
estimates [4]: C-(mR2) = 0.35,Cm-C = 0.5 ± 0.07. Here C and Cm are polar
moments of inertia of Mercury and its mantle. m and r are mass and mean radius of
Mercury.
Cassini’s motion of Mercury. Based on the method of investigation of resonant
rotational motion of Mercury, developed in [5], [1], for considered here the model of an
evolving orbit, we obtain the following analytical expressions and numerical values of the
generalized Cassini’s motion of Mercury (for the unperturbed values of the ascending node
h0 and inclination angle ÏG of the vector angular momentum of the planet relative to the
ecliptic of 2000.0):
h0 = arctan(- ni-nΩsini) = 2303677,
[ ( )]-1
ÏG = - nΩ-sini nΩ-cosi+ 1 J2C(-3.0)+ 2C22X (-3.2) = 4’2 ± 1′4.
n0 cosh0 n0 I 0 N
From these formulas it follows that due to influence of the angle h0 the value of
Cassini’s angle ÏG increases at 8.94%, compared with an earlier value for h0 = 0 [1],
[5].
Conclusion. If the secular change in inclination of the orbit of Mercury to exclude from
consideration, then these equations can be simplified and its solution will be h0 = 0 and
ÏG = 3’9 ± 1′3. That solution with h0 = 0 (for others values of Mercury parameters) before,
starting with the pioneering works of Colombo, Beletskii, Peale et al., have been studied
actively. We emphasize here that the rotational motion is not attributable to the Laplace plane
for the Mercury, and with respect to the mean ecliptic and equinox of epoch 2000.0. In [1] we
have suggested the existence of large amplitude free librations of Mercury in longitude with a
period of 12 years. As the main mechanism of excitation of free oscillations was
proposed mechanism of forced relative oscillations of the core and mantle of the
planet (which are non-spherical bodies and occupy the eccentric positions relative to
each other) under the gravitational attraction of the Sun and the planets and due to
perturbations in orbital motion. Naturally, this same mechanism is responsible for the
excitation of free motion of the pole and the free oscillations of angular momentum
vector in space. The results of this study can be regarded as a confirmation of the
existence of long-period (not Euler) oscillations of the rotation axis of Mercury with an
amplitude of about 2 ’- 3’. And if the prediction of the free librations in longitude
[1] has already received confirmation [3], to confirm the free oscillations of the
pole axis of rotation of Mercury in the body and the free oscillations of angular
momentum vector in space should be a new and more accurate data on the gravitational
field of Mercury and its librations. This issue should contribute to research on the
MESSENGER spacecraft on mercurial orbit in 2011. The action of the mechanism of
forced swing and wobble of the core and mantle of Mercury (and of others solar
system bodies) should lead to the formation of active geological structures with an
asymmetric distribution with respect to the northern and southern hemisphere and
especially pronounced in polar regions. The first position was clear evidence in the
asymmetric distribution of scarps and ridges of Mercury. We expect that the second
assumption will be confirmed in studies of the polar regions of the MESSENGER
spacecraft in March-April 2011. In conclusion the remark that the phenomenon is
revealed shift of the lines of nodes h0 = 2304 can make some adjustments in the
calculation according to radar observations of Mercury’s rotation carried out in
[3].
References
[1] Barkin Yu. V., Ferrandiz J. M. Mercury: libration, gravitational field and its
variations// Lunar and Planetary Science XXXVI. 2005. 075.pdf.
[2] Smith D.E. et al. The equatorial shape and gravity field of Mercury from
MESSENGER flybys 1 and 2// Icarus. 2010. V. 209. P. 88–100.
[3] Margot J.L., Peale S.J., Jurgens R.F., Slade M.A., Holin I.V. Large longitude libration
of Mercury reveals a molten core // Science. 2007. V. 316. P. 710.
Barkin Yu.V., Ferrandiz J.M. Dynamic role of the liquid core of Mercury in its rotation//
Lunar and Planetary Science XXXIX. 2008.1206.pdf.
[4] Peale S.J. The free precession and libration of Mercury//Icarus. 2005. V. 178, no.
1, P. 4-18.
[5] Barkin Yu.V., Ferrandiz J.M. Dynamical structure and rotation of Mercury//
Astronomical and Astrophysical Transactions. 2005. V. 24, No. 1, February 2005. P. 61-79. |
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