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The semi-empirical atmospheric density models widely used by the space community were mainly developed taking into account satellite drag measurements and other observations, either in situ and ground based, acquired at relatively low altitudes, mostly below 500-600 km, and in general below 1000 km. The launch of the Italian geodetic satellite LARES, in 2012, at the altitude of about 1450 km and with an inclination of 70 degrees, offered however the rare possibility of probing the atmosphere at such height. This spherical satellite, fully covered with corner-cube laser retro-reflectors, has the highest area-to-mass ratio of any artificial object launched so far, being therefore not well suited for detecting small non-gravitational forces, like atmospheric drag. However, the very high accuracy of its orbit determinations, made possible by the laser tracking technique, more than compensated its unfavorable area-to-mass ratio, and the signature of atmospheric drag was extremely evident in the measured semi-major axis decay. Such decay, observed since 2012, was therefore used to infer the neutral atmosphere drag at the height of LARES during a 7-year span of solar cycle 24, covering the solar maximum, the declining phase and the beginning of the minimum. These measurements were compared with the predictions of six semi-empirical density models (JR-71, MSIS-86, MSISE-90, NRLMSISE-00, GOST-2004, and JB2008), employed well outside of their typical application ranges. In general, their predictions resulted quite satisfactory, with uncertainties not so far from those already known at lower altitudes. This study was also supplemented by the simultaneous analysis of another spherical geodetic satellite, the Japanese Ajisai, just 50 km higher, but with an area-to-mass ratio nearly 20 times greater than that of LARES and a smaller inclination of 50 degrees. An attempt was also made to estimate the physical drag coefficients of both satellites, in order to derive the mean density biases of the models. None of them could be considered unconditionally the best, the specific outcome depending on solar activity and on the regions of the atmosphere crossed by the satellites. Moreover, during solar maximum conditions, an additional density bias, probably linked to the different high latitudes overflown by the satellites, was detected.

HY-2A (Haiyang 2A) is the first altimetry satellite in China, and it was designed to be in a repeated ground track orbit to achieve the mission targets. Maneuvers are necessary to keep the satellite on the designed orbit according to the dynamic precise orbital prediction. Atmospheric density models are essential for predicting the low Earth orbit (LEO) satellites, such as HY-2A. Nevertheless, it is a complex process to determine the optimal atmospheric density model for orbit prediction. In this paper, short-term and long-term orbit predictions based on the dynamic method using three different atmospheric density models are tested. Detailed comparisons and evaluation of the accuracy of the predicted results are performed. Furthermore, to assess the results for the ground tracking of the satellite, the interpolation method especially for a spherical surface is introduced. The results show that among the three models, the Jacchia 1971 model is in the closest agreement with Multi-Mission Ground Segment for Altimetry precise positioning and Orbitography (SSALTO) precise orbits. The root-mean-squares (RMSs) of radial orbit differences between the predicted and precise orbits are 0.016 m, 0.091 m, 0.176 m, 0.573 m, and 1.421 m for predicted 1-h, 12-h, 1-day, 3-day, and 7-day arcs, respectively.

The radar imaging satellite mission TerraSAR-X requires precisely determined satellite orbits for validating geodetic remote sensing techniques. Since the achieved quality of the operationally derived, reduced-dynamic (RD) orbit solutions limits the capabilities of the synthetic aperture radar (SAR) validation, an effort is made to improve the estimated orbit solutions. This paper discusses the benefits of refined dynamical models on orbit accuracy as well as estimated empirical accelerations and compares different dynamic models in a RD orbit determination. Modeling aspects discussed in the paper include the use of a macro-model for drag and radiation pressure computation, the use of high-quality atmospheric density and wind models as well as the benefit of high-fidelity gravity and ocean tide models. The Sun-synchronous dusk–dawn orbit geometry of TerraSAR-X results in a particular high correlation of solar radiation pressure modeling and estimated normal-direction positions. Furthermore, this mission offers a unique suite of independent sensors for orbit validation. Several parameters serve as quality indicators for the estimated satellite orbit solutions. These include the magnitude of the estimated empirical accelerations, satellite laser ranging (SLR) residuals, and SLR-based orbit corrections. Moreover, the radargrammetric distance measurements of the SAR instrument are selected for assessing the quality of the orbit solutions and compared to the SLR analysis. The use of high-fidelity satellite dynamics models in the RD approach is shown to clearly improve the orbit quality compared to simplified models and loosely constrained empirical accelerations. The estimated empirical accelerations are substantially reduced by 30% in tangential direction when working with the refined dynamical models. Likewise the SLR residuals are reduced from $$-3\,\pm \,17$$ to $$2\,\pm \,13$$ mm, and the SLR-derived normal-direction position corrections are reduced from 15 to 6 mm, obtained from the 2012–2014 period. The radar range bias is reduced from $$-10.3$$ to $$-6.1$$ mm with the updated orbit solutions, which coincides with the reduced standard deviation of the SLR residuals. The improvements are mainly driven by the satellite macro-model for the purpose of solar radiation pressure modeling, improved atmospheric density models, and the use of state-of-the-art gravity field models.

The satellite Cosmos 1025 was chosen as the test object for the IADC re-entry campaign 2007-1. This presentation compares the re-entry predictions carried out at ISTI/CNR using four different atmospheric density models, namely JR-71, MSIS-86, MSISE-90, NRLMSISE-00.

In order to highlight the performances of the JR-71 and MSISE-90 atmospheric density models and also to investigate whether the use of the E 10.7 index, instead of the F 10.7 cm solar radio flux, improves the trajectory modeling of low Earth objects, the orbital decay of 11 spherical satellites was analyzed. The data were distributed over a full solar activity cycle and covered altitudes in between 150 and 1500 km. The observed evolution of the mean semi-major axis was obtained by processing the historical two-line elements record. For each satellite, environmental condition, atmospheric model and solar flux proxy, a drag coefficient was computed by fitting the observed semi-major axis decay, comparing the results with the theoretical estimates. Below 400 km, both models overestimated the atmosphere density, independently on the solar flux proxy and environmental conditions. MSISE-90, with F 10.7 , proved to be the best model to compute the air density, in low solar activity conditions. JR-71, with F 10.7 , was generally more accurate over the maximum of the 23rd solar cycle, while MSISE-90 revealed to be the best model in the increasing phase of the solar flux, when using E 10.7 . Between 750 and 850 km, the average accuracy of the models was generally better than 15% and the choice of the atmospheric density model was relatively inconsequential, both in conditions of low and high solar activity. A quite large uncertainty was instead observed in moderate conditions, when using E 10.7 in both models. At 1500 km, both models underestimated the air density by more than 35%, in low solar activity conditions. For high solar fluxes, the density was well represented by JR-71, both using F 10.7 and E 10.7 , while it resulted to be underestimated, by about 25%, when using MSISE-90, both with E 10.7 and F 10.7 . In general, more accurate orbital decay fits were obtained with E 10.7 , which seems able to better describe the atmosphere density changes induced by a varying solar activity. In conclusion, none of the models analyzed was able to accurately describe the atmosphere density in all orbital regimes and environmental conditions, independently on the solar flux proxy.

In January 2002, the Inter-Agency Space Debris Coordination Committee (IADC) promoted a fourth reentry test campaign, choosing an old Russian upper stage as a study case. As in the past, ISTI – formerly CNUCE – was involved, acting as the Italian Space Agency (ASI) technical contact, in the modeling aspects of the reentry predictions, while other IADC members, namely NASA, Rosaviakosmos and ESA, also provided periodic orbits determinations based on ground sensor data. The test campaign took place in a period of high solar activity, during the second peak of the cycle 23 maximum. This was a good opportunity to investigate the behavior of the models available or developed at ISTI, in terms of atmospheric density description, extreme ultraviolet radiation input, ballistic parameter estimation and orbit propagation. In order to evaluate the intrinsic reentry prediction uncertainties, the orbital decay of the test object was fitted, and predictions were made for it, using three different thermospheric density models and two independent sets of orbit determinations (American and Russian two-line elements). The results obtained were compared in order to provide a quantitative assessment of the level of accuracy that may be expected in similar situations.

In order to estimate the intrinsic accuracy of satellite reentry predictions, the residual lifetimes of eleven spacecraft and five rocket bodies, covering a broad range of inclinations and decaying from orbit in a period of high solar activity, were determined using three different atmospheric density models: JR-71, TD-88 and MSIS-86. For each object, the ballistic coefficient applicable to a specific phase of the flight was obtained by fitting an appropriate set of two-line orbital elements, while the reentry predictions were computed approximately one month, one week and one day before the final orbital decay. No clear correlation between the residual lifetime errors and the satellite inclination or type (spacecraft or rocket body) emerged. JR-71 and MSIS-86 resulted in good agreement, with comparable reentry prediction errors (~10%), semimajor axis residuals and ballistic coefficient estimations. TD-88 exhibited a behaviour consistent with the other two models, but was typically characterised by larger reentry prediction errors (~15-25%) and semimajor axis residuals. At low altitudes (< 250 km) TD-88 systematically overestimated the average atmosphere density (by ~25%) with respect to the other two models.