This study aims to evaluate and analyze the orbit predictions of selected satellites: geodetic, Global Navigational Satellite Systems (GNSS), and scientific low-orbiting, which are tracked by laser stations. The possibility of conducting satellite laser ranging (SLR) to artificial satellites depends on the access to high-quality predictions of satellite orbits. The predictions provide information to laser stations where to aim the telescope in search of a satellite to get the returns from the retroreflectors installed onboard. If the orbit predictions are very imprecise, SLR stations must spend more time to correct the telescope pointing, and thus the number of collected observations is small or, in an extreme case, there are none of them at all. Currently, there are about 120 satellites equipped with laser retroreflectors orbiting the Earth. Therefore, the necessity to determine the quality of predictions provided by various analysis centers is important in the context of the increasing number of satellites tracked by SLR stations. We compare the orbit predictions to final GNSS orbits, precise orbits of geodetic satellites based on SLR measurements determined in postprocessing, and kinematic orbits of low-orbiting satellites based on GPS data. We assess the quality degradation of the orbit predictions over time depending on the type of orbit and the satellite being analyzed. We estimate the time of usefulness of prediction files, and indicate those centers which publish most accurate predictions of the satellites’ trajectories. The best-quality predictions for geodetic satellites and Galileo reach the mean error of 0.5–1 m for the whole 5-day prediction file (for all three components), while the worst ones can reach values of up to several thousand meters during the first day of the prediction.

LARES-2 is a new geodetic satellite designed for high-accuracy satellite laser ranging. The orbit altitude of LARES-2 is similar to that of LAGEOS-1, whereas the inclination angle of 70° complements the LAGEOS-1 inclination of 110°; hence, both satellites form the butterfly configuration for the verification of the Lense–Thirring effect. Although the major objective of LARES-2 is testing general relativity, LARES-2 substantially contributes to geodesy in terms of the realization of terrestrial reference frames, recovery of the geocenter motion, pole coordinates, length-of-day, and low-degree gravity field coefficients. We analyze the first 1.5 years of LARES-2 data and test different empirical orbit models for LARES-2 with and without co-estimating low-degree gravity field coefficients to find the best combination strategy with LAGEOS satellites. We found that LARES-2 orbit determination is more accurate than that of LAGEOS-1/2 due to a different satellite construction consisting of a solid sphere with no inner structure. Neither the correction for D ₀ nor the empirical once-per-revolution along-track accelerations S _C/S _S have to be estimated for LARES-2 when co-estimating gravity field coefficients. The only empirical parameter needed for LARES-2 is the constant along-track acceleration S ₀ to compensate for the Yarkovsky–Schach effect. On the contrary, for LAGEOS-1/2, the non-gravitational perturbations affect C ₃₀ and Z geocenter estimates when once-per-revolution parameters are not estimated. LARES-2 does not face this issue. LARES-2 improves the formal errors of the Z geocenter component by up to 59% and C ₂₀ by up to 40% compared to the combined LAGEOS-1/2 solutions and provides C ₃₀ estimates unaffected by thermal orbit modeling issues.

Satellite laser ranging (SLR) measurements play a key role in determining global geodetic parameters, such as station coordinates, geocenter motion, low‐degree Earth's gravity field parameters, and Earth rotation parameters. Observations to two LAser GEOdynamics Satellites (LAGEOS) and two Etalon satellites provide operational standard products and contribute to the realization of the scale and the origin of the International Terrestrial Reference Frame (ITRF). Currently, an extension of the ITRF realizations is being considered with the inclusion of the Laser Relativity Satellite (LARES). In July 2022, the LARES‐2 satellite was launched with the main purpose to verify fundamental physics, especially the Lense‐Thirring effect emerging from General Relativity. We simulate orbits and observations for the LARES‐2 satellite, as well as the LARES‐like satellites, which complement the current constellation of LAGEOS‐1/‐2 and LARES‐1/‐2 using the butterfly configuration. We assess the impact of the observations to satellites with different orbital parameters on the determination of global geodetic parameters. We show that placing a satellite in a retrograde orbit (against the Earth's rotation), can improve the quality of the global geodetic parameters. The solution based on LAGEOS‐1/‐2 + LARES‐1/‐2 + a satellite supplementary to LAGEOS‐2 in a retrograde orbit achieves the 3D mean error at the level of 1.62 mm for the station coordinates, and mean errors of 0.7, 0.7, and 1.3 mm for theX,Y, andZgeocenter components, respectively, bringing us closer to fulfilling the requirements established by the Global Geodetic Observations System (GGOS) of 1 mm accuracy for the reference frame stability.

The development of the satellite laser ranging (SLR) technique is essential not only to meet the objectives set by the Global Geodetic Observing System (GGOS) but also to address growing challenges of understanding increasingly frequent processes occurring at the Earth’s surface and to realize the terrestrial reference frames (TRFs). In this study, we search for optimum orbit parameters for future geodetic satellites tracked by SLR stations. We simulate satellites at various inclination angles, ranging from 0 to 180 degrees with a 1-degree interval, across five different altitudes from 1500 to 10,300 km, with 1200 km intervals, in two solution scenarios: (1) optimized for the realization of TRFs and (2) optimized for the recovery of the Earth’s gravitational potential. We found that an optimal satellite altitude for TRF realization is at the height of 3700 km and an inclination between 0–20° or 160–180°, which minimizes the formal errors in the determination of geocenter coordinates and Earth Rotation Parameters (ERPs). On the other hand, a geodetic satellite primarily intended for recovery of the low-degree Earth’s gravitational potential parameters should orbit at an altitude of 1500 km, with inclinations between 30–40° or 135–145°. In the current SLR constellation, none of the existing satellites has optimum orbital parameters for the low-degree gravity field recovery because the lowest inclination angle of Starlette equals 49°. Adding a single satellite with the appropriate inclination to the current constellation of ten geodetic satellites reduces error in determining the Earth’s oblateness term, C₂₀, by one order of magnitude.

Satellite laser ranging (SLR) is one of the space geodetic techniques used to realize the International Terrestrial Reference Frame (ITRF). SLR contributes considerably to geocenter determination and scale realization. The currently being prepared European Space Agency’s (ESA) mission, Genesis, will co-locate all four space geodetic techniques onboard one satellite. However, Genesis’s contribution and impact of single techniques, e.g., SLR, on the geodetic products, i.e., geocenter coordinates, Earth rotation parameters (ERP), or coefficients of Earth’s gravity field, is still unveiled. Another vital question is the impact of Genesis orbit parameters, especially semi-major axis and inclination, on the quality of geodetic parameters. The orbit parameters will substantially affect the number of possible observations collected by SLR stations but also favor different geodetic parameters by decreasing or increasing their estimation error. We study two approaches to processing Genesis data—one with estimating Genesis orbits based on SLR observations and one with fixing the orbital parameters to GNSS-based values. As we do not analyze Genesis as a single satellite but in combination with LAGEOS and LARES, we conclude that the ESA proposition of orbit will ensure good observability. The orbit proposal for Genesis with the inclination angle of 95° and the height of 6000 km might help to reduce the errors of the Z component of the geocenter motion below 1 mm, especially with the GNSS contribution, which is the aim of the Global Geodetic Observing System for the stability of the ITRF realization.

Satellite laser ranging (SLR) is currently one of the four space geodetic techniques that provide a relevant contribution to the International Terrestrial Reference Frame (ITRF) realization as well as to the determination of global geodetic parameters including the low-degree harmonics of the Earth's gravity potential. ITRF realizations are mostly based on the observations to the two LAGEOS and two Etalon satellites, however, the impact of observations to Etalon satellites is marginal when compared to LAGEOS. Currently under consideration is an extension of the ITRF solution to include the LAser RElativity Satellite (LARES) and LARES-2 developed by the Italian Space Agency ASI and launched on July 13, 2022. The contribution of other satellites with retroreflectors is still being investigated.This study aims to verify various approaches to estimating geodetic parameters depending on the number of determined empirical once-per-revolution parameters for satellite orbits and different approaches of parametrization for the Earth rotation parameters (ERP), including piecewise linear and piecewise constant parametrization. We analyze six parametrizations, where three of them are proposed in this study and the other three are used by research centers, such as the Center for Space Research (CSR), the International GNSS Service (IGS), and the International Laser Ranging System (ILRS). For IGS and ILRS, these are the approaches used in determining the ERPs based on GNSS and SLR data, respectively. To the constellation of geodetic satellites such as LAGEOS-1/-2, Etalon-1/-2, and LARES-1/-2, we add hypothetical SLR satellites such as LARES-3/-4 and LARES-5/-6 which supplement the current constellation in the simulation study. We check whether satellite parameters, such as satellite altitudes and inclination angles affect individual global geodetic parameters when using different approaches to ERP parameterization and the set of estimated empirical orbit parameters.The obtained results show that the value of the obtained formal errors may depend not only on the choice of the estimated geodetic parameters but also on the number of satellites or satellite orbit parameters involved in the calculations.