TEMPORAL VARIABILITY OF EARTH'S GRAVITATIONAL
FIELD FROM SATELLITE LASER RANGING
Richard J. Eanes and Srinivas V. Bettadpur
University of Texas Center for Space Research
University of Texas at Austin, Austin, Texas 78712 USA
INTRODUCTION
Satellite laser ranging (SLR) observations of geodetic satellites (Degnan, 1993) have long
been used to study the temporal variations of the Earth's external potential through the
long-period orbital perturbations they produce (Yoder et al., 1983; Rubincam, 1984; Cheng
et al., 1989; Tapley et al., 1993; Gegout and Cazenave, 1993; Nerem et al., 1993; Chao and
Eanes, 1995; Nerem and Klosko, 1995.) Secular and long period variations in the zonal
Stokes coefficients and nearly diurnal and semidiurnal tidal variations in the order 1 and 2
coefficients can be monitored with this approach. In this paper we analyze SLR
observations of Lageos-l and Starlette and present new results for constraints on the
secular and 18.6-year variations in the zonal harmonics. These results provide important
information for improving geophysical models of glacial rebound, ice··sheet changes, and
mantle anelasticity.
Our approach uses analytical results for the evolution of orbital elements in combination
with estimates derived from both long and short spans of tracking data. This treatment has
its origins in early papers on the subject of estimating tidal parameters from satellite
tracking data using the evolution of mean elements and using the differences between long
and short-arc orbit fits (Douglas et al., 1973; Lambeck et al., 1974; Felsentreger et al.,
1978, Goad and Douglas, 1978). The accuracy required for our application is significantly
more stringent than that obtained in these pioneering investigations, and our success is a
testament to the excellent quality of the SLR data and the general improvement in the
fidelity of the necessary dynamical models.
First we outline a semi-analytical approach that uses 3 complex non-singular orbital
vectors whose evolution is forced by 3 complex excitation time serif~s to be determined
using the SLR observations. Then we present equations relating these excitations to
general satellite accelerations and to variations in the Earth's external potential. Finally, we
discuss the geophysical applications of the orbital excitation time series including the
constraints they imply for the secular variation of the even-degree zonal Stokes coefficients
and the solid Earth's anelastic response to the 18.6-year second degree zonal tide.
NON-SINGULAR ORBITAL VECTORS AND THEIR EXCITATIONS
The reference orbit for the analytical treatment of orbital excitations is a numerically
integrated trajectory, best-fit to the SLR data over a duration depending on the satellite
30
FIELD FROM SATELLITE LASER RANGING
Richard J. Eanes and Srinivas V. Bettadpur
University of Texas Center for Space Research
University of Texas at Austin, Austin, Texas 78712 USA
INTRODUCTION
Satellite laser ranging (SLR) observations of geodetic satellites (Degnan, 1993) have long
been used to study the temporal variations of the Earth's external potential through the
long-period orbital perturbations they produce (Yoder et al., 1983; Rubincam, 1984; Cheng
et al., 1989; Tapley et al., 1993; Gegout and Cazenave, 1993; Nerem et al., 1993; Chao and
Eanes, 1995; Nerem and Klosko, 1995.) Secular and long period variations in the zonal
Stokes coefficients and nearly diurnal and semidiurnal tidal variations in the order 1 and 2
coefficients can be monitored with this approach. In this paper we analyze SLR
observations of Lageos-l and Starlette and present new results for constraints on the
secular and 18.6-year variations in the zonal harmonics. These results provide important
information for improving geophysical models of glacial rebound, ice··sheet changes, and
mantle anelasticity.
Our approach uses analytical results for the evolution of orbital elements in combination
with estimates derived from both long and short spans of tracking data. This treatment has
its origins in early papers on the subject of estimating tidal parameters from satellite
tracking data using the evolution of mean elements and using the differences between long
and short-arc orbit fits (Douglas et al., 1973; Lambeck et al., 1974; Felsentreger et al.,
1978, Goad and Douglas, 1978). The accuracy required for our application is significantly
more stringent than that obtained in these pioneering investigations, and our success is a
testament to the excellent quality of the SLR data and the general improvement in the
fidelity of the necessary dynamical models.
First we outline a semi-analytical approach that uses 3 complex non-singular orbital
vectors whose evolution is forced by 3 complex excitation time serif~s to be determined
using the SLR observations. Then we present equations relating these excitations to
general satellite accelerations and to variations in the Earth's external potential. Finally, we
discuss the geophysical applications of the orbital excitation time series including the
constraints they imply for the secular variation of the even-degree zonal Stokes coefficients
and the solid Earth's anelastic response to the 18.6-year second degree zonal tide.
NON-SINGULAR ORBITAL VECTORS AND THEIR EXCITATIONS
The reference orbit for the analytical treatment of orbital excitations is a numerically
integrated trajectory, best-fit to the SLR data over a duration depending on the satellite
30