Y.B Kolesnik

Institute of Astronomy of the Russian Academy of Sciences, Piatnitskaya str. 48, 109017 Moscow, Russia

Comparisons of optical observations reduced to the FK5 system with DE200 show significant
linear trends of residuals, see Yao & Smith (1988, 1993), Standish & Williams
(1990), Seidelman et al. (1985, 1986), Kolesnik (1995, 1996). The present study
was primarily motivated by a desire to interpret the large discrepancy between numerical
ephemerides and the 20^{th} century optical observations. Other objectives
were: a) to check the level of consistency between early observations of the 18th
and 19th centuries and numerical ephemerides; b) to assess of the actual scientific
content of the early observations in view of the recent accuracy achieved by astrometry;
c) to revise of the value of the tidal acceleration of the Moon; d) to estimate
the ICRS offset with respect to dynamical equinox and its possible residual rotation.

A mass of 244,960 observations of the Sun, Mercury and Venus accumulated during
the historical period of astronomy were incorporated. All the observed material
can naturally be divided into three periods: 1750-1830, 1830-1900 and 1900-2000.
The first one can be characterized as a period of formation of classical astrometry.
Observations in this period were re-reduced later by Bessel, Airy, Le Verrier, Auwers
and Knox-Show. In the second period the quality of instruments and methods of investigation
progressively improved and observations of the daytime objects reached nearly 1
arcs econd ( arcs ) accuracy. At the beginning of the 20^{th} century the
moving-wire micrometer was introduced into common practice significantly reducing
personal errors. Typical internal errors of instrumental series in the 18^{th}
century observations of the daytime objects is 2 arcs in right ascension and 1.5
arcs in declination. The best instruments of the second half of the century reached
some 0.5 arcs -0.8 arcs . The level of 0.5 arcs has remained typical for the 20^{th}
century observations.

In the transformation procedure a set of corrections were formed by direct comparison of a standard star catalogue with the ICRS-based catalogue rotated from J2000 to the respective epoch by use of modern precession constant and Hipparcos based proper motions. The systematic differences are interpolated onto the observed positions of planets. Other corrections account for differences in modern and historical astronomical constants. The N70E catalogue (Kolesnik 1997) rigidly rotated onto Hipparcos frame was used as a reference catalogue. Observations were compared with DE405 ephemeris. The series (ET-UT) by Stephenson & Morrison (1984) were applied before 1955. After 1955 ET is equal to TDT or TT and directly related to atomic time TAI.

Conditional equations for the Sun are the same as applied by Newcomb. For Mercury
and Venus these are the same as given in Kolesnik (1995). The secular variation
of the corrections to the longitudes was determined separately from right ascension
and declination residuals. In the conditional equations for right ascensions the
equinox correction is omitted assuming that it will be absorbed in the solution
by corrections to the longitude of the Earth. Corrections to the longitudes were
derived in relatively short time span bins, and evaluation of secular variations
of longitudes was based on a set of stepwise individual solutions in bins. Corrections
to the mean longitude of the Earth ΔL_{0} were determined from the
right ascension and declination residuals of all objects. Corrections to the mean
longitudes of Mercury and Venus ΔL resulted from residuals in right ascension
only.

Figure 1a

Figure 1b

The individual solutions tracing the secular variations of the longitudes of the
Earth *ΔL _{0}* resulting from right ascensions and declinations
of the Sun, Mercury and Venus during the 20

**Table 1.** Second order approximations of the trends in secular variations
of the longitudes of the Earth ΔL_{0 }and Mercury and Venus ΔL
in the 20^{th} century. Index indicates from which kind of observations
(right ascensions or declinations) longitude corrections are derived. T = (t-1960)/100
with t in years. All entries in arcseconds.
T0 is the constant term, T1 the linear and T2 the quadratic coefficient.

T0 | T1 | T2 | |
---|---|---|---|

Sun (ΔL_{0})_{α} |
-0.05±0.01 | -0.28±0.01 | 1.42±0.04 |

Sun (ΔL_{0})_{δ} |
-0.28±0.01 | +0.02±0.02 | 1.51±0.10 |

Mercury (ΔL)_{α} |
-0.80±0.03 | -0.89±0.10 | 4.51±0.41 |

Venus (ΔL)_{α} |
-0.20±0.01 | -0.30±0.03 | 2.78±0.15 |

Since

ΔE=(ΔL_{0} )_{δ}-(ΔL_{0 })_{α}

at the epoch J2000.0: -0.10 ±0.01 arcs and *d(ΔE*)/dT= + 0.30 ±0.03 arcs
/cy

Figure 2a

Figure 2b

The dependence of the trends on mean motions provides evidence that some acceleration
factor affects the comparison results. The Expanding Spacetime (EST) theory (formerly
Scale Expanding Cosmos theory) by Masreliez (2000) predicts accelerations of the
planets in the Solar system according to the relation *dn/dt=3n/T* Hubble time).
For Mercury, Venus and the Earth the predicted secular accelerations are 5.7, 2.3,
and 1.4 *arcs/cy ^{2}*, i.e. of the same order as the actually detected
quadratic terms presented in Table 1 if the

__Fig. 1a and b.__ Secular variation of corrections to the mean longitudes of
the Earth as derived from observations of Mercury (P1), Venus (P2) and the Sun (P3)
in right ascension (a) and declination (b) in the interval 1900-2000.

__Fig. 2 a and b.__ Secular variation of corrections to the mean longitudes of
Mercury (a) and Venus (b) as derived from observations in right ascension in the
interval 1900-2000. Error bars indicate the formal errors of the normal points in
bins.

Residual rotation of proper motion systems of the principal compiled catalogues
of the 19^{th} and 20^{th} centuries was investigated by their direct
comparison with Hipparcos motions. The results are given in Table 2.

**Table 2.** Estimation of the residual rotation *Δε* and correction
to adopted precession constant (*Δ*p_{1}) of historical compiled
catalogues from their direct comparison with Hipparcos proper motions in the equatorial
zone. All estimates are in arcs ec/cy.

Direct comparison with Hipparcos of the catalogues constructed before the FK5 indicate
(*Δ*p_{1})_{δ} correction to Newcomb's precession
close to Fricke¹s correction 1.11 arcs/cy. As for the FK5 and N70E they give nearly
zero values. This result is in evident confrontation with an independent determination
of the precession constant from LLR and VLBI (Charlot et.al. 1995). If LLR and VLBI
results are to be believed, a conclusion follows: in the global sense Hipparcos
system is not absolutely independent from the input catalogue (which is FK5-based).
Otherwise LLR and VLBI determinations are to be revised. As a result the systems
of Hipparcos and N70E (after rigid rotation) should not be considered as rotation
free, the systematic difference Δd_{α} in proper motions due to
the old precession constant, which is by 0.3 arcs/cy larger than its actual value,
can affect the results of secular variation of the longitude of the Sun and produce
a linear trend equivalent to the value 0.3 arcs/cy just obtained. If this interpretation
is accepted the linear trend should be considered rather as a correction to Fricke's
precession *Δ*p_{1}=-0.30 arcs/cy than a drift of the origin of
right ascensions with respect to dynamical equinox.

An attempt to interpret the complex character of the secular variations of the longitudes
was made. The Expanding Spacetime theory presumes violation of the Kepler¹s law
and explains the positive quadratic trends in the 20^{th} century. The residual
rotation of the Hipparcos based system with respect to dynamical equinox +0.30 arcs
±0.03 arcs/cy is explained by the fact that Hipparcos proper motion system is not
independent from the FK5 system.

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