SLR Measurement model

Observations. Global quick-look SLR data retrieved from Eurolas Data Center (EDC), and converted to 1 per 20 s normal points, combined with on-site normal points collected from EDC.

Data weighting. Weight sigma of each system is an rss combination of the assumed overall model accuracy (20 cm) and noise level of the system

Troposphere. Marini Murray model.

Geometric correction. Offset of LRR optical centre wrt LRR geometrical centre (6.1 cm), and the LRR geometrical centre offset with respect to the spacecraft nominal centre-of-mass.

Editing. Cutoff elevation = 10 deg. Editing at 3.5 times sigma.

Satellite model

Mass. m = 2377.13 kg.

Position of LRR and CM. According to ESA documents.

Cross-sections. Macro-model, consisting of 8 fixed and 2 rotating panels.

Dynamic model

Gravity model. Joint Gravity Model JGM-2, complete to degree and order 70, including secular C_21 and S_21 and dynamic polar motion. GM = 398600.4415 km3/s2.

Speed of light. c = 299792.458 km/s.

Reference ellipsoid. a_e = 6378.1363 km and 1/f = 298.2564.

Solid Earth tides. Frequency-dependent Wahr model (1981); permanent tide excluded according to IERS Standard (1989).

Ocean tides. JGM-2 ocean tide model.

Third body attraction. Sun, Moon, Mercury, Venus, Mars, Jupiter, Saturn, Neptune, according to JPL DE200 ephemeris.

Atmospheric drag. French Density Model (DTM) with daily F_10.7 values and 3-hourly K_p values from STD (Canspace).

Radiation. Solar radiation pressure at 1 AU = 4.5783e6 N/m2. Umbra, penumbra, and occultation by Moon modeled. Earth albedo modeled. Solar radiation coefficient fixed at C_R=1.0.

Pole tide. Dynamical effect of pole tide applied.

Relativistic effects. included.

Orbit manoeuvres. A priori information according to ESOC predictions. Adjusted during POD.

Reference frame

Station coordinates. LSC(DUT)93L05 9.3-year LAGEOS I solution (epoch 1 Jan 1988), advanced to epoch by 3-dimensional motions incorporated in the coordinate solution.

Reference ellipsoid. GRS80: a_e = 6378.1370 km and 1/f = 298.257.

Earth rotation. Values from IERS Bulletin A at five-day intervals.

CIS. Mean equator and equinox of J2000.0.

Precession. IAU 1976 (Lieske model).

Nutation. IAU 1980 (Wahr model).

Tidal uplift. Love model, including frequency dependent and permanent tides (h_2 = 0.609, l_2 = 0.0852).

Pole tide. Geometrical effect of pole tide accounted for.

Ocean loading. not applied.

Numerical integration

Type. 11th-order Cowell prediction correction method for equations of motion and variational equations.

Step size. 60 seconds.

Estimated parameters

State vector. Position and velocity at epoch.

Drag. Half-dayly drag coefficients (C_D: 11 parameters).

Empirical forces. 1-cpr along-track and cross-track accelerations (4 parameters).

Orbit manoeuvres. in three directions.

Station coordinates. of some (mobile) stations.

Measurement offset. range and timing bias for some stations.

Output ephemeris

Data arcs. Arc length of 5.5 days with an epoch spacing of 3.5 days.

ODR. The position of the satellite's nominal centre-of-mass is given in the Conventional Terrestrial Reference System (CTRS) as latitude, longitude, and height above the GRS80 reference ellipsoid, centred around the mean IERS pole origin. This position is obtained from the Inertial True Of Date (ITOD) coordinates after rotation over the Greenwich hour angle and accounting for polar motion. Time-tagging is in the UTC time scale determined by the USNO master clock.

Step size. 60 seconds.