Abstract
The characteristics of the geopotential coefficient J2 in different periods are analyzed using satellite laser ranging data spanning the last 27 years. The satellites used in the analysis are Lageos1 and Lageos2. The variations in J2 are obtained by determining the dynamic orbit. The results show that there are strong seasonal and long-term variations. For different data spans, the seasonal variations agree well in terms of both amplitude and phase. Using all the data, the amplitude and phase of the annual term are 2.5 × 10−10 and 127°, respectively, while the amplitude and phase of the semiannual term are 0.94 × 10−10 and 213°, respectively. In the case of long-term variation, the secular variation in J2\(\left( {\dot J_2 } \right)\) is −2.2 × 10−11 a−1 from 1984 to 2010. \(\dot J_2\) differs for the different periods because of interannual variations, such as the “1998 anomaly”. Another anomaly may have taken place during 2007–2010. Although the cause of the anomaly is unknown, it is an important observational constraint on the shape of the Earth.
Highlights
The Earth is a complex dynamic system that has a mobile atmosphere and oceans, a varying global distribution of ice, snow and water, and a fluid core that is undergoing some type of hydromagnetic motion
J 2 differs for the different periods because of interannual variations, such as the “1998 anomaly”
These processes redistribute the Earth’s mass and affect the Earth’s rotation and its gravitational field over time and space. These variations can be embodied by harmonics coefficients
Summary
Computations are made for an arc length of 15 days using the SHORDE program developed by Shanghai Astronomical Observatory. The precise satellite ephemeris and the partial derivatives of estimated parameters with respect to satellite position are obtained by first determining the dynamic orbit. The estimated parameters are the state vector (position and velocity), the low-degree zonal coefficients, the radiation pressure coefficient per 15 days and the estimated along-track acceleration coefficient per 3 days. Here, n = 2 π / P is the orbital mean motion, P is the orbit period and Re is the Earth’s radius. For Lageos satellites, the inclination factor f4 0.37 is large enough that the magnitude of J4 relative to J2 must be considered. In this paper, the estimated low-degree zonal coefficients are J2 , J3 and J4. Satellite COSPAR ID Launch data RRA Diameter (cm) Shape Reflectors Orbit Inclination (°) Eccentricity Perigee (km) Period (min) Weight (kg)
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