Non-gravitational Force Modeling Research Articles

Accurate analytical non-gravitational force model for precise orbit determination of QZS-1, 2, and 4

Accurate analytical non-gravitational force model for precise orbit determination of QZS-1, 2, and 4

Non-gravitational force measurement and correction by a precision inertial sensor of TianQin-1 satellite

Non-gravitational force models are critical not only for the applications of satellite orbit determination and prediction, but also for the studies of gravitational reference sensors in space-based gravitational wave detection missions and accelerometers in gravity satellite missions. In this paper, based on the inertial sensor data from the TianQin-1 (TQ-1) mission, a correction has been made in the non-gravitational force models by applying additional terms related to the orbital periods. After taking into account this correction, about 37 hours of TQ-1 inertial sensor data is calibrated in the sensitive axes, i.e. y- and z-axes, by comparing with the simulated non-gravitational accelerations. It is indicated that the peak-to-peak value of the non-gravitational acceleration correction terms are about 2% and 13% of the measured accelerations in the y- and z-axes, respectively. Within the frequency band below 0.01 Hz, the root mean square of calibration residual errors in y- and z-axes are suppressed from 1.03 × 10−9 and 3.872 × 10−9 m s−2 to 8.14 × 10−10 and 1.343 × 10−9 m s−2, respectively. The bias and scale factor of the inertial sensor are also obtained from the calibration by the method of least-squares fit. Meanwhile, the inertial sensor measurements are validated and their signal compositions are analyzed.

Precovery Observations Confirm the Capture Time of Asteroid 2020 CD3 as Earth’s Minimoon

Abstract Asteroid 2020 CD3 was discovered on 2020 February 15 by the Catalina Sky Survey while it was temporarily captured in a geocentric orbit before escaping Earth’s Hill sphere on 2020 March 7. We searched archival images and found precoveries of 2020 CD3 from the Dark Energy Camera and Catalina Sky survey. The Dark Energy Camera images yielded three observations on 2019 January 17, while the Catalina Sky Survey images yielded four observations on 2019 January 24 from the Mt. Lemmon telescope and four observations on 2018 May 9 from the Mt. Bigelow telescope. These precovery observations allowed us to refine the orbit of 2020 CD3 and determine that it was captured in a geocentric orbit on 2017 September 15 after a close approach to the Moon at a distance of 11,974 ± 10 km. We analyzed the trajectory of 2020 CD3 to look for potential Earth impacts within the next 100 years and find a ≳1% probability of an impact between 2061 and 2120 depending on nongravitational force model assumptions. The small size of 2020 CD3, about 1 to 2 m, makes any potential impact harmless.

Dynamic GPS-based LEO orbit determination with 1 cm precision using the Bernese GNSS Software

The Astronomical Institute of the University of Bern (AIUB) has been performing GPS-based Precise Orbit Determination (POD) for a large variety of Low Earth Orbit (LEO) satellites since two decades. Traditionally, LEO orbits have been generated by a reduced-dynamic POD strategy using the Bernese GNSS Software, replacing an explicit modeling of non-gravitational forces by dedicated empirical orbit parametrizations. This LEO POD strategy can be advanced by two main developments: on the one hand, use is made of the GNSS Observation-Specific Bias (OSB) and clock products provided by the Center for Orbit Determination in Europe (CODE), allowing for the resolution of single-receiver GNSS carrier-phase ambiguities. On the other hand, the main focus of this article, a refined satellite non-gravitational force modeling strategy is constructed to reduce the amount of empirical parameters used to compensate for force modeling deficiencies. LEO POD is first performed for Sentinel-3, a satellite formation currently consists of two identical satellites −3A and −3B, which experience a similar in-flight environment and allow for direct POD performance comparisons. A third satellite Swarm-C, which flies at a lower altitude and has a more sophisticated surface geometry, is selected to validate the robustness of the new POD strategy. As a result, both the internal consistency checks and external orbit validations suggest superior orbit quality obtained for the three satellites for a time span of 1.5 years (7 June, 2018 to 31 December, 2019). The ambiguity resolution adds strong constraints to the orbits and the satellite non-gravitational force modeling leads to more tightly constrained (towards zero) pseudo-stochastic empirical parameters. The final orbit solutions agree with external orbit solutions and independent satellite laser ranging measurements at levels of sub-cm, indicating approximately 20% improvement w.r.t. the nominal reduced-dynamic orbit solutions. This suggests potential benefits to the space geodesy community that always pursues best-possible satellite orbits.

Analysis of Tiangong-2 orbit determination and prediction using onboard dual-frequency GNSS data

Tiangong-2 is the first Chinese real space laboratory, launched into earth orbit with an altitude of approximately 393 km on September 15, 2016. Precise orbit determination (POD) is one of the essential conditions for conducting onboard scientific research. The precise orbit of Tiangong-2 is mainly determined by the reduced-dynamic method using space-borne global navigation satellite system (GNSS) data, which are collected by an onboard dual-frequency GNSS receiver. The in-flight performance of the receiver is first assessed in terms of tracking ability, code multipath errors and noise levels of code and carrier phase observations. Then, the effects of refined non-gravitational force models and GNSS antenna phase center variations (PCVs) on the POD are analyzed. The estimated empirical accelerations are substantially reduced by 45% in the along-track direction using a macro-model compared to that using a cannonball model for drag computation. The application of antenna PCVs correction leads to better consistency between reduced-dynamic and kinematic orbit solutions. Satellite laser ranging validation shows that the accuracy of Tiangong-2 precise orbits is 1.7 cm after using the improved reduced-dynamic method. Based on the orbit determination results, the quality of Tiangong-2 orbit predictions is assessed for periods without and with the refined non-gravitational force models. The use of the macro-model and high-quality density models for drag computation is shown to help improve orbit prediction quality.

GRACE accelerometer calibration by high precision non-gravitational force modeling

The precise modeling and knowledge of non-gravitational forces acting on satellites is of big interest to many scientific tasks and missions. Since 2002, the twin GRACE satellites have measured these forces in a low Earth orbit with highly precise accelerometers, for about 15 years. Besides the significance for the GRACE mission, these measurement data allow the evaluation of modeling approaches and the improvement of force models. Unfortunately, before any scientific usage, the accelerometer measurements need to be calibrated, namely scale factor and bias have to be regularly estimated.In this study we demonstrate an accelerometer calibration approach, solely based on high precision non-gravitational force modeling without any use of empirically or stochastically estimated parameters, using our in-house developed satellite simulation tool XHPS. The aim of this work is twofold, first we use the accelerometer data and the residuals resulting from the calibration to quantitatively analyze and validate different non-gravitational force model approaches. In a second step, we compare the calibration results to three different calibration methods from different authors, based on gravity field recovery, GPS-based precise orbit determination, and based on modeled accelerations.We consider atmospheric drag forces and winds, as well as radiation forces due to solar radiation pressure, albedo, Earth infrared and thermal radiation (TRP) of the satellite itself. For TRP, we investigate different transient temperature calculation approaches for the satellite surfaces with absorbed power from the aforementioned radiation sources. A detailed finite element model of the satellite is utilized for every force, considering orientation, material properties and shadowing conditions for each element.For cross-track and radial direction, which are mainly affected by the radiative forces, our calibration residuals are quite small when drag is not super dominant (1–3 nm/s2 for total accelerations around ±50 nm/s2). For these directions the calibration seems to perform better than the other compared methods, where some bigger differences were found. For the drag dominated along-track direction it is vice versa, here our method is not sensitive enough because the difference between modeled and measured drag is bigger (e.g. residuals around 10 nm/s2 for total accelerations around ±70 nm/s2 for low solar activity). In along-track direction the orbit determination based methods are more sensitive and produce more reliable results. Results for the complete GRACE mission time span from 2003 to 2017 are shown, covering different seasonal environmental conditions.

Reduced dynamic and kinematic precise orbit determination for the Swarm mission from 4 years of GPS tracking

Precise science orbits for the first 4 years of the Swarm mission have been generated from onboard GPS measurements in a systematic reprocessing using refined models and processing techniques. Key enhancements relate to the introduction of macro-models for a more elaborate non-gravitational force modeling (solar radiation pressure, atmospheric drag and lift, earth albedo), as well as carrier phase ambiguity fixing. Validation using satellite laser ranging demonstrates a 30% improvement in the precision of the reduced dynamic orbits with resulting errors at the 0.5–1 cm level (1D RMS). A notable performance improvement is likewise achieved for the kinematic orbits, which benefit most from the ambiguity fixing and show a 50% error reduction in terms of SLR residuals while differences with respect to reduced dynamic ephemerides amount to only 1.7 cm (median of daily 3D RMS). Compared to the past kinematic science orbits based on float-ambiguity estimates, the new kinematic position solutions exhibit a factor of reduction of two to three in Allan deviation at time scales of 1000s and higher, and promise an improved recovery of low-degree and -order gravity field coefficients in Swarm gravity field analyses.

Time-variable gravity fields and ocean mass change from 37 months of kinematic Swarm orbits

Abstract. Measuring the spatiotemporal variation of ocean mass allows for partitioning of volumetric sea level change, sampled by radar altimeters, into mass-driven and steric parts. The latter is related to ocean heat change and the current Earth's energy imbalance. Since 2002, the Gravity Recovery and Climate Experiment (GRACE) mission has provided monthly snapshots of the Earth's time-variable gravity field, from which one can derive ocean mass variability. However, GRACE has reached the end of its lifetime with data degradation and several gaps occurred during the last years, and there will be a prolonged gap until the launch of the follow-on mission GRACE-FO. Therefore, efforts focus on generating a long and consistent ocean mass time series by analyzing kinematic orbits from other low-flying satellites, i.e. extending the GRACE time series. Here we utilize data from the European Space Agency's (ESA) Swarm Earth Explorer satellites to derive and investigate ocean mass variations. For this aim, we use the integral equation approach with short arcs (Mayer-Gürr, 2006) to compute more than 500 time-variable gravity fields with different parameterizations from kinematic orbits. We investigate the potential to bridge the gap between the GRACE and the GRACE-FO mission and to substitute missing monthly solutions with Swarm results of significantly lower resolution. Our monthly Swarm solutions have a root mean square error (RMSE) of 4.0 mm with respect to GRACE, whereas directly estimating constant, trend, annual, and semiannual (CTAS) signal terms leads to an RMSE of only 1.7 mm. Concerning monthly gaps, our CTAS Swarm solution appears better than interpolating existing GRACE data in 13.5 % of all cases, when artificially removing one solution. In the case of an 18-month artificial gap, 80.0 % of all CTAS Swarm solutions were found closer to the observed GRACE data compared to interpolated GRACE data. Furthermore, we show that precise modeling of non-gravitational forces acting on the Swarm satellites is the key for reaching these accuracies. Our results have implications for sea level budget studies, but they may also guide further research in gravity field analysis schemes, including satellites not dedicated to gravity field studies.

Use of long-term nongravitational force models for fitting astrometric observations of comet Encke

Based on the equations derived in (Usanin et al., 2016) a new solution combining the observations of 30 apparitions of the comet Encke from 1911 to 2010 is obtained. For the first time in the worldwide practice the solution is obtained by using converging differential correction of all 60 observed returns of the comet, however, the deviations are still unsatisfactory. The single solution has allowed to draw some preliminary conclusions. The contributions of planetary and nongravitational perturbations to the change of the elements of the orbit during the entire period of observation are determined. The extrapolation of the solution shows that for the past two thousand years the elements of the orbit orientation could change for a half of turnover, which should be taken into account when identifying the comet and associated meteor showers in ancient records. The predictions made by Z. Sekanina and I. Ferrín about oncoming termination of the comet activity are confirmed.

Impact of the Atmospheric Drag on Starlette, Stella, Ajisai, and Lares Orbits

Abstract The high-quality satellite orbits of geodetic satellites, which are determined using Satellite Laser Ranging (SLR) observations, play a crucial role in providing, e.g., low-degree coefficients of the Earth's gravity field including geocenter coordinates, Earth rotation parameters, as well as the SLR station coordinates. The appropriate modeling of non-gravitational forces is essential for the orbit determination of artificial Earth satellites. The atmospheric drag is a dominating perturbing force for satellites at low altitudes up to about 700-1000 km. This article addresses the impact of the atmospheric drag on mean semi-major axes and orbital eccentricities of geodetic spherical satellites: Starlette, Stella, AJISAI, and LARES. Atmospheric drag causes the semi-major axis decays amounting to about ▲a = -1.2, -.12, -.14, and -.30 m/year for LARES, AJISAI, Starlette, and Stella, respectively. The density of the upper atmosphere strongly depends on the solar and geomagnetic activity. The atmospheric drag affects the along-track orbit component to the largest extent, and the out-of-plane to a small extent, whereas the radial component is almost unaffected by the atmospheric drag.

Performance of GPS-based accelerometry: A simulation experiment

Recent studies have shown that with the availability of high-quality CHAMP and GRACE gravity field models, it is feasible to determine accurate non-gravitational accelerations for low Earth orbiting satellites indirectly from precise GPS satellite-to-satellite observations. Possible applications of this so-called GPS-based accelerometry approach consist of accelerometer calibration and atmospheric density and wind computations. With the growing number of high-quality space-borne GPS receivers, this method could be applied to a large range of satellites. In this paper an extensive simulation study has been carried out, based on real accelerometer data from the GRACE mission, in order to determine the optimal processing strategy and the resulting accuracy of the estimated non-gravitational accelerations. It is shown that the optimal processing strategy consists of a piecewise linear parameterization of the estimated empirical accelerations, together with short 6-h orbit arcs. The GPS-based accelerometry approach makes use of triple-differenced GPS observations and the impact of considering the correlated observation noise was found to be marginal in the presence of other error sources such as GPS ephemeris errors. Using a priori non-gravitational force models improves the recovery of low temporal resolution accelerations, except during huge geomagnetic storms. With this strategy, non-gravitational accelerations can be recovered during high solar activity with an accuracy of better than 10% of the total signal in along-track direction and around 25–40% in cross-track direction, at time resolutions of around 8–20 min. During solar minimum conditions, the relative recovery error will increase to approximately 50% in along-track direction and around 60–70% in cross-track direction, due to the reduced atmospheric drag signal. Unfortunately, GPS-based accelerometry is hardly sensitive in the radial direction.

Non-gravitational forces and masses of some long-period comets. The cases of Hale-Bopp and Hyakutake

AbstractBy means of a simple non-gravitational force model of the cometary nucleus, which relies on the observed light curves assumed to be a good representation of the water sublimation rate, we estimate the masses of a sample of long-period comets (LPCs).A critical issue of our method is the assumption of a correlation between visual heliocentric magnitudes and water production rates. This is a necessary assumption because of the sparse observational data of gas production rates (with the exception of very few comets like Hale-Bopp or Hyakutake). In this regard we present here a new correlation for LPCs. We also present the preliminary results for the masses of comets Hale-Bopp and Hyakutake.

CHAMP and GRACE accelerometer calibration by GPS-based orbit determination

Current and planned Earth observation missions are equipped with highly sensitive accelerometers. Before using the data, the instrument has to be calibrated by determining scale and bias parameters for each axis. Here, the accelerometer measurements are used in a GPS-based reduced-dynamic orbit determination approach, replacing the non-gravitational force models, and nominally daily calibration parameters are estimated. Additional empirical accelerations are estimated to account for deficiencies in the applied force models. This method is applied to 5 years of CHAMP and GRACE data, resulting in an orbit precision at the level of a few centimeters. In along-track direction the calibration parameters can be estimated freely, scale factors of 0.96 ± 0.014 and 0.95 ± 0.015 are obtained for GRACE A and B, and 0.85 ± 0.024 for CHAMP. A constant scale factor results in the smoothest bias series, with clear trends and occasional jumps. In radial and cross-track direction tight constraints to a priori biases have to be applied. Furthermore, the determined orbits are analyzed with respect to reference trajectories, and SLR, phase and KBR residuals are presented.

GPS based orbit determination using accelerometer data

Ongoing and future geopotential space missions are equipped with one or more accelerometers. In order to use these observations, the accelerometer measurements have to be calibrated before processing them. In this paper they are introduced in the GPS based precise orbit determination, by replacing the non-gravitational force models for atmospheric drag and solar radiation pressure. Empirical accelerations are still estimated to account for deficiencies in the applied conservative force models. The in-orbit calibrated accelerometer observations are used to validate the accelerations determined by force modeling. In along-track direction they show the best agreement. During days of high solar activity the benefit of using accelerometer observations is clearly visible. The observations during these days show high frequency fluctuations which the modeled and empirical accelerations cannot follow. A long period of GRACE (second half of 2003) and of CHAMP (2004) data is processed. This results for GRACE in a mean orbit fit of a few centimeters with respect to high-quality JPL reference orbits, showing a slightly better consistency compared to the case when using force models, which is also supported by SLR residual analysis. The daily calibration factors determined with this technique show a small variation. When not including empirical accelerations in the estimation procedure, the calibration factors in radial and cross-track direction show a bigger spread, with an orbit fit below the decimeter level.

Nucleus properties of Comet 9P/Tempel 1 estimated from non-gravitational force modeling

The nucleus mass and bulk density of Comet 9P/Tempel 1 have been estimated by utilizing the non-gravitational force modeling technique. Here, the water production rates and non-gravitational perturbations of the orbit are calculated for a large number of model nuclei with different surface ice distribution patterns. By requiring that the empirical water production rate curve is reproduced, a subset of model nuclei are selected, for which masses are calculated by demanding that empirical non-gravitational changes of the orbital period and in the longitude of perihelion (per revolution) are reproduced. We obtain a mass M = 5.8 ( ± 1.6 ) × 10 13 kg , and a bulk density ρ bulk = 450 ± 250 kg m −3 , which compares very well with measurements made by the Deep Impact Science Team. The main goal of the current work is therefore to demonstrate functionality of an indirect method, i.e., mass estimation through non-gravitational force modeling, by comparing such results to ground truth data. Furthermore, the thermal inertia of active areas is estimated as 30–100 MKS, using a comparatively realistic thermophysical model (although a value in the range 100–350 MKS is obtained with a more simple model). An active area fraction of ∼ 3 % is predicted, and these areas are probably confined to the northern hemisphere, being located close to the cometary equator.

Nucleus properties of Comet 9P/Tempel 1 estimated from non-gravitational force modeling

The nucleus mass and bulk density of Comet 9P/Tempel 1 have been estimated by utilizing the non-gravitational force modeling technique. Here, the water production rates and non-gravitational perturbations of the orbit are calculated for a large number of model nuclei with different surface ice distribution patterns. By requiring that the empirical water production rate curve is reproduced, a subset of model nuclei are selected, for which masses are calculated by demanding that empirical non-gravitational changes of the orbital period and in the longitude of perihelion (per revolution) are reproduced. We obtain a mass M = 5.8 ( ± 1.6 ) × 10 13 kg , and a bulk density ρ bulk = 450 ± 250 kg m −3 , which compares very well with measurements made by the Deep Impact Science Team. The main goal of the current work is therefore to demonstrate functionality of an indirect method, i.e., mass estimation through non-gravitational force modeling, by comparing such results to ground truth data. Furthermore, the thermal inertia of active areas is estimated as 30–100 MKS, using a comparatively realistic thermophysical model (although a value in the range 100–350 MKS is obtained with a more simple model). An active area fraction of ∼ 3 % is predicted, and these areas are probably confined to the northern hemisphere, being located close to the cometary equator.

The impact of accelerometry on CHAMP orbit determination

The contribution of the STAR accelerometer to the CHAMP orbit precision is evaluated and quantified by means of the following results: orbital fit to the satellite laser ranging (SLR) observations, GPS reduced-dynamic vs SLR dynamic orbit comparisons, and comparison of the measured to the modeled non-gravitational accelerations (atmospheric drag in particular). In each of the four test periods in 2001, five CHAMP arcs of 2 days' length were analyzed. The mean RMS-of-fit of the SLR observations of the orbits computed with STAR data or the non-gravitational force model were 11 and 24 cm, respectively. If the accelerometer calibration parameters are not known at least at the few percent level, the SLR orbit fit deteriorates. This was tested by applying a 10% error to the along-track scale factor of the accelerometer, which increased the SLR RMS-of-fit on average to 17 cm. Reference orbits were computed employing the reduced-dynamic technique with GPS tracking data. This technique yields the most accurate orbit positions thanks to the estimation of a large number of empirical accelerations, which compensate for dynamic modeling errors. Comparison of the SLR orbits, computed with STAR data or the non-gravitational force model, to the GPS-based orbits showed that the SLR orbits employing accelerometer observations are twice as accurate. Finally, comparison of measured to modeled accelerations showed that the level of geomagnetic activity is highly correlated with the atmospheric drag model error, and that the largest errors occur around the geomagnetic poles.

Lunar albedo force modeling and its effect on low lunar orbit and gravity field determination

A force model for the lunar albedo effect on low lunar orbiters is developed on the basis of Clementine imagery and absolute albedo measurements. The model, named the Delft Lunar Albedo Model 1 (DLAM-1), is a 15 × 15 spherical harmonics expansion, and is intended for improved force modeling for low satellite orbits as well as to minimise aliasing of non-gravitational force model defects in future lunar gravity solutions. The development of the model from the available lunar albedo data sources is described, followed by a discussion on its calibration using absolute albedo measurements and its correlation with main selenological features. DLAM-1 is next applied in low lunar orbit determination, and results for orbits typical of lunar mapping missions are presented. Finally, the effect of lunar albedo on future gravity solutions is analysed with particular emphasis on gravity mapping from global data sets, i.e. satellite-to-satellite tracking, which is expected to be a core experiment of coming lunar missions. It is shown that albedo-induced orbit perturbations have a magnitude and frequency signature which are non-negligible for precise orbit and gravity modeling. Radial orbit errors for low orbits are in the order of 1–2 m for one week arcs.

Earth rotation from radio interferometric tracking of GPS satellites

Radio-interferometric tracking of the Global Positioning System (GPS) satellites offers a new technique for regular monitoring of variations in the earth's rotation. The observations are sensitive to pole position and length-of-day, at a level of precision which may make this technique competitive with satellite and lunar laser ranging and very long baseline interferometry (VLBI). The present limitations are the number of satellites and tracking stations available and inadequate modeling of non-gravitational forces on the satellites. The potential advantages are rapid turn-around and minimal incremental cost. We have performed a preliminary analysis using six days of observations from a four-station network. Comparison of earth rotation values from our GPS analysis with values obtained by VLBI and laser ranging reveals differences after five days of 0.9 ms in UT1, 0.04″ in x and 0.07″ in y. These differences reflect errors in the GPS determinations due primarily to inadequate modeling of non-gravitational forces.

The intermediate comets and nongravitational effects

The motions of the intermediate-period comets Pons-Brooks, Olbers, Brorsen-Metcalf, and Westphal are investigated over their observed intervals. The three apparitions of comets Pons-Brooks and Olbers were successfully linked, using the now standard nongravitational-force model. The two apparitions of Comet Brorsen-Metcalf were successfully linked without the need for nongravitational effects. For the 1852 and 1913 apparitions of Comet Westphal, complete success was not achieved in modeling the comet's motion either with or without nongravitational effects. However, by including these effects, the comet's astrometric observations could be represented significantly better than if they were assumed inoperative. Comet Westphal's dynamic and photometric behavior suggests its complete disintegration before reaching perihelion in 1913. If the very large radial nongravitational parameter determined for Comet Westphal is due to the comet's disintegration into dust, then the resultant dust-particle size is of the order of 0.8 mm.