Determination of the Geodetic Rotation of the Solar System Bodies by means of Spectral Analysis Method

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Determination of the Geodetic Rotation of the
Solar System Bodies by means of Spectral Analysis
Method

• G.I. Eroshkin and V.V. Pashkevich

Central (Pulkovo) Astronomical Observatory of
Russian Academy of Science St.Petersburg Space
Research Centre of Polish Academy of Sciences
Warszawa 2006
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The angular velocity vector of the geodetic
rotation for any point of Solar system

• Here the index A means any point of Solar
  system or any Major body of Solar system j
  index for the summing all Major bodies of Solar
  system of the mathematical model of DE404/LE404
  ephemeris gravitational constant
• mass of the j -th body c
  velocity of light in vacuum
• distance between points A and j
  , , and barycentric
  vectors of the coordinate and velocity of these
  points sign is a vector product . If the point
  A is not a centre of the mass of the Sun the
  vector is practically orthogonal to the
  plane of the heliocentric orbit, so the mass of
  the Sun is the dominant mass of Solar system.

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The problem of the geodetic (relativistic)
rotation of the Sun, major planets, and the Moon
is studied by using DE404/LE404 ephemeris and by
means of Spectral Analysis Method . For every of
these bodies the files of the ecliptic components
of the vector of the geodetic rotation were
formed over time span from AD1000 to AD3000 at
intervals of one day. Using the least-squares
method and spectral analysis methods the secular
and periodic components of the geodetic rotation
vector were determined. The mean longitudes of
the planets and the Moon adjusted to DE404/LE404
ephemeris were taken from Brumberg and Bretagnon
(2000).
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The Earth
For the Earth the component, orthogonal to the
plane of the fixed ecliptic J2000.0 was
determined
This result is a very good agreement with that
found analytically (Brumberg and Bretagnon,
2000). The method was applied to the other
bodies of the solar system.
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The Earth
For the Earth the component, orthogonal to the
plane of the fixed ecliptic J2000.0 was
determined
This result is a very good agreement with that
found analytically (Brumberg and Bretagnon,
2000). The method was applied to the other
bodies of the solar system.
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The Earth (in detail)
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The Moon
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The Moon
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The Moon (in detail)
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Mercury
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Mercury
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Mercury (in detail)
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Venus
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Venus
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Venus (in detail)
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Mars
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Mars
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Mars (in detail)
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Jupiter
Saturn
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Jupiter
Saturn
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Jupiter (in detail)
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Jupiter
Saturn
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Saturn (in detail)
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Uranus
Neptune
Pluto
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Mercury (in detail)
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• DISCUSSION
• DE404/LE404 ephemeris is used for the
  definition of the geodetic rotation of the
  reference frame of DE404/LE404 ephemeris

the angular velocity vector of the
reference frame of DE404/LE404 ephemeris.
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The angular velocity vector of the geodetic
rotation for any point of Solar system

• Here the index A means any point of Solar
  system or any Major body of Solar system j
  index for the summing all Major bodies of Solar
  system of the mathematical model of DE404/LE404
  ephemeris gravitational constant
• mass of the j -th body c
  velocity of light in vacuum
• distance between points A and j
  , , and barycentric
  vectors of the coordinate and velocity of these
  points sign is a vector product . If the point
  A is not a centre of the mass of the Sun the
  vector is practically orthogonal to the
  plane of the heliocentric orbit, so the mass of
  the Sun is the dominant mass of Solar system.

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Ecliptic components of the angular velocity
vector of the Barycentre of Solar system
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Ecliptic components of the angular velocity
vector of the Barycentre of Solar system (in
detail)
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• R E F E R E N C E S
• V.A..Brumberg, P.Bretagnon Kinematical
  Relativistic Corrections for Earths Rotation
  Parameters // in Proc. of IAU Colloquium 180,
  eds. K.Johnston, D. McCarthy, B. Luzum and G.
  Kaplan, U.S. Naval Observatory, 2000, pp.
  293302.
• Landau L.D. and Lifshitz E.M., The Classical
  Theory of Fields 1967, Moscow "Nauka" , pp.
  426-429. (in Russian)

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A C K N O W L E D G M E N T S
The investigation was carried out at the Central
(Pulkovo) Astronomical Observatory of Russian
Academy of Science and the Space Research
Centre of Polish Academy of Science, under a
financial support of the Cooperation between
Polish and Russian Academies of Sciences, Theme
No 31.