from the aliasing effect of mismodeled trends in AI which would otherwise bias the
solution for i2 and the 18.6-year tide. The application of the Kalman smoother to the
derivation of the excitation time series is discussed in detail in Eanes (1995).
The success of this procedure requires that the long arc remain close enough to the true
orbit that the linearization of the observation equations and of the dynamics retains
sufficient accuracy. The RMS of the SLR residuals from the Lageos-l10ng arc used here
is about 2 m, and the sufficiency of the linearization procedure is demonstrated by the fact
that the RMS of the short-arc residuals is below 3 cm for almost all arcs after 1987. The
weighted RMS of Lageos-l short-arc residuals over the entire data span is 5 cm. Also, we
depend on the fact that the short period perturbations caused by the temporal variations of
the Stokes coefficients are small. Although successful isolation of the temporal variations
of the short-period perturbations would yield additional observational constraints, these will
be significantly less accurate than the constraints derived from the long-period terms. We
expect these short-period signals to be sub-cm in size and thus feel justified in deferring
attempts to utilize them to future investigations.
In the case of Starlette and Ajisai, a two-step method is used to obtain the excitation time
series. First, 1 cpr accelerations are estimated in 9-day intervals while converging annual
orbital arcs, and the values are used in eq. (4) to compute the 'lip and 'I' time series.
Then, corrections to these time series are computed from short arc or~ital element
adjustments using eq. (3). Anomalous vector excitations are accommodated in the annual
arcs by adjusting mean transverse accelerations in 3-day intervals. The adjustment of the
empirical parameters ensures that the annual Starlette arcs stay close enough to the true
orbit for success of the linearization procedures employed.
SECULAR AND 18.6-YEAR ZONAL HARMONIC VARIATIONS
More than 19 year spans of Lageos-l and Starlette SLR observations are now available,
and these provide adequate separability of the linear (secular) and 18.6-year signals in the
excitation time series. In this section we focus on these signals in Im('¥ Q) and express the
results as constraints useful in geophysical studies involving temporal changes in the
gravitational field.
Relatively large mismodeled non-gravitational signals possibly caused by radiation
pressure and thermal forces exist in the Lageos-l eccentricity excitations and currently limit
their use in constraining the odd degree gravitational changes. These excitations (often
referred to as the Lageos anomaly) are discussed in Tapley et al. (1993) and are also the
subject of recent work on the non-gravitational force models by Martin and Rubincam
(1995) and Metris et al. (1995). Starlette appears not to be significantly affected by this
problem; nonetheless, in this paper we will limit discussion to the constraints derivable
from'll Q.
Several other possible sources of error in the results to follow should be briefly
mentioned. Errors in UTI during the years before the advent of regular VLBI
observations are a potential biasing influence on the secular and 18.6-year results from
Lageos-l, but the effect of UTI errors on the Starlette results should be about 10 times
smaller because of the larger sensitivity of Starlette to gravitational field changes. The SLR
observations before about 1980 are less numerous and less accurate than in later years.
Variable annual signals in the excitations, caused mainly by mass redistribution in the
atmosphere, are parameterized using a single sinusoid, and this results in substantial
temporal correlation in the excitation residuals after the secular and ddal parameter fits.
36
solution for i2 and the 18.6-year tide. The application of the Kalman smoother to the
derivation of the excitation time series is discussed in detail in Eanes (1995).
The success of this procedure requires that the long arc remain close enough to the true
orbit that the linearization of the observation equations and of the dynamics retains
sufficient accuracy. The RMS of the SLR residuals from the Lageos-l10ng arc used here
is about 2 m, and the sufficiency of the linearization procedure is demonstrated by the fact
that the RMS of the short-arc residuals is below 3 cm for almost all arcs after 1987. The
weighted RMS of Lageos-l short-arc residuals over the entire data span is 5 cm. Also, we
depend on the fact that the short period perturbations caused by the temporal variations of
the Stokes coefficients are small. Although successful isolation of the temporal variations
of the short-period perturbations would yield additional observational constraints, these will
be significantly less accurate than the constraints derived from the long-period terms. We
expect these short-period signals to be sub-cm in size and thus feel justified in deferring
attempts to utilize them to future investigations.
In the case of Starlette and Ajisai, a two-step method is used to obtain the excitation time
series. First, 1 cpr accelerations are estimated in 9-day intervals while converging annual
orbital arcs, and the values are used in eq. (4) to compute the 'lip and 'I' time series.
Then, corrections to these time series are computed from short arc or~ital element
adjustments using eq. (3). Anomalous vector excitations are accommodated in the annual
arcs by adjusting mean transverse accelerations in 3-day intervals. The adjustment of the
empirical parameters ensures that the annual Starlette arcs stay close enough to the true
orbit for success of the linearization procedures employed.
SECULAR AND 18.6-YEAR ZONAL HARMONIC VARIATIONS
More than 19 year spans of Lageos-l and Starlette SLR observations are now available,
and these provide adequate separability of the linear (secular) and 18.6-year signals in the
excitation time series. In this section we focus on these signals in Im('¥ Q) and express the
results as constraints useful in geophysical studies involving temporal changes in the
gravitational field.
Relatively large mismodeled non-gravitational signals possibly caused by radiation
pressure and thermal forces exist in the Lageos-l eccentricity excitations and currently limit
their use in constraining the odd degree gravitational changes. These excitations (often
referred to as the Lageos anomaly) are discussed in Tapley et al. (1993) and are also the
subject of recent work on the non-gravitational force models by Martin and Rubincam
(1995) and Metris et al. (1995). Starlette appears not to be significantly affected by this
problem; nonetheless, in this paper we will limit discussion to the constraints derivable
from'll Q.
Several other possible sources of error in the results to follow should be briefly
mentioned. Errors in UTI during the years before the advent of regular VLBI
observations are a potential biasing influence on the secular and 18.6-year results from
Lageos-l, but the effect of UTI errors on the Starlette results should be about 10 times
smaller because of the larger sensitivity of Starlette to gravitational field changes. The SLR
observations before about 1980 are less numerous and less accurate than in later years.
Variable annual signals in the excitations, caused mainly by mass redistribution in the
atmosphere, are parameterized using a single sinusoid, and this results in substantial
temporal correlation in the excitation residuals after the secular and ddal parameter fits.
36