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| Titel |
Computer simulating observations of the Lunar physical libration for the Japanese Lunar project ILOM |
| VerfasserIn |
Natalia Petrova, Hideo Hanada |
| Konferenz |
EGU General Assembly 2010
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 12 (2010) |
| Datensatznummer |
250037769
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| Zusammenfassung |
| In the frame of the second stage of the Japanese space mission SELENE-2 (Hanada
et al. 2009) the project ILOM (In-situ Lunar Orientation Measurement) planned
after 2017years is a kind of instrument for positioning on the Moon. It will be set
near the lunar pole and will determine parameters of lunar physical libration by
positioning of several tens of stars in the field of view regularly for longer than one
year.
Presented work is dedicated to analyses of computer simulating future observations. It’s
proposed that for every star crossing lunar prime meridian its polar distance will be to
measure. The methods of optimal star observation are being developed for the future
experiment. The equations are constructed to determine libration angles Ï (t),Ï(t),Ï(t)- on the
basis of observed polar distances pobs:
(| f1(Ï,Ï,IÏ,pobs) = 0
|{ f2(Ï,Ï,IÏ,pobs) = 0
| f3(Ï,Ï,IÏ,pobs) = 0
|( or f(X) = 0, where ; f = - f1 -
| f2 |
|- f3 |- X = - Ï -
| Ï |
|- IÏ |-
(1)
At the present stage we have developed the software for selection of stars for these future
polar observations. Stars were taken from various stellar catalogues, such as the
UCAC2-BSS, Hipparcos, Tycho and FK6. The software reduces ICRS coordinates of star to
selenographical system at the epoch of observation (Petrova et al., 2009). For example, to the
epochs 2017 - 2018 more than 50 stars brighter than m = 12 were selected for the northern
pole. In total, these stars give about 600 crossings of the prime meridian during one
year. Nevertheless, only a few stars (2-5) may be observed in a vicinity of the one
moment. This is not enough to have sufficient sample to exclude various kind of
errors.
The software includes programmes which can determine the moment of transition of star
across the meridian and theoretical values of libration angles at this moments.
A serious problem arises when we try to solve equations (1) with the purpose
to determine libration angles on the basis of simulated pobs.. Polar distances are
calculated using the analytical theory of physical libration Petrova et al. (2008;
2009).
We cannot use Newton’s method for solution of the equation, because the Jacobian
| |
|| --fx11 --fx12 --f1x3-||
|| --fx2 --fx2 --f2x-||
J(X ) = || -f13 -f23 -3f3-|| = 0.
|| -x1 -x2 -x3 ||
We transformed equations to the iteration form xi = φi(X). Used iteration methods have
unsatisfactory convergence: inaccuracy in polar distance of 1 milliseconds of arc causes
inaccuracy of 0.01arcsec in Ï and in IÏ, and 0.1 arcsec in Ï.
Results of our computer simulating showed
It’s necessary to carry out measuring of polar distances of stars in several meridians
simultaneously to increase sample of stars.
It’s necessary to find additional links (relations) between observed parameters and
libration angles to have stable mathematical methods to receive solutions for lunar rotation
with high accuracy.
The research was supported by the Russian-Japanese grant RFFI-JSPS 09-02-92113,
(2009-2010)
References:
Hanada H., Noda H., Kikuchi F. et al., 2009. Different kind of observations of lunar
rotation and gravity for SELENE-2. Proc of conf. Astrokazan-2009, August 19 – 26, Kazan,
Russia. p. 172-175
Petrova N., Gusev A., Kawano N., Hanada H., 2008. Free librations of the two-layer
Moon and the possibilities of their detection. Advances in Space Res., v 42, p.
1398-1404
Petrova N., Gusev A., Hanada H., Ivanova T., Akutina V., 2009. Application of the
analytical theory of Lunar physical libration for simulating observations of stars for the future
Japanese project ILOM. Proc of conf. Astrokazan-2009, August 19 – 26, Kazan, Russia.
p.197 – 201. |
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