Non-gravitational Accelerations Research Articles

Tailored accelerometer calibration by POD for thermospheric density retrieval with GRACE and GRACE-FO

The density of the upper atmosphere can be determined by orbit and accelerometer data from low Earth orbit satellites as insitu measurements along the orbit. One main challenge therein is the estimation of physical accelerometer calibration parameters, meaning that these parameters should not absorb other effects and model deficiencies in the Precise Orbit Determination (POD) process. The accelerometers of all geodetic satellites like GRACE and GRACE-FO are affected by time dependent bias and scale factors. Therefore a calibration of the data is indispensable.A dynamic POD based physical accelerometer calibration is developed for the complete GRACE and GRACE-FO missions. We investigate different parametrization strategies and utilize different observation data, as the accurate inter-satellite ranging additionally to GPS orbit data. For the estimation parameters we distinguish between offset and scale, furthermore, cross-track and radial directions are significantly less sensitive than along-track and require a different evaluation. For the offset, constant and time dependent parameters are investigated. Furthermore, a continuous offset calibration over arc boundaries is implemented and tested. The sensitivity of the scale factor is lower, although, in contrast to the offset, it increases with higher total accelerations. This means that it needs to be estimated over longer time periods. We investigate periods between three hours and one month as well as results from Gravity Field Recovery (GFR). Monthly scale factors give valuable results, at least for x-axis and when the Solar activity is not very low. Nevertheless, we also estimate weighted constant scale factors from the monthly results and use these in a subsequent POD, giving more realistic offset results for most periods and cross-track and radial directions.From the used background models in the POD, Earth’s gravitational model has a noticeable influence on the estimated calibration parameters, especially the scale factors. We utilized several different models. Results with monthly ITSG solutions are distinctly better than the ones with the time dependent GOCO06s model.We show that the validation with usual metrics, like post-fit POD residuals, is not able to reflect the quality of the different estimated calibration parameters. For a quantitative validation we introduce an approach based on the modeled non-gravitational accelerations. Therefore, the uncertainty of the models is evaluated first. The influence of main error sources in the models is assessed and propagated to the results.We compare our scale parameters to available references and the complete calibration to TU Delft’s latest results. Finally we show the effect of different calibration options on the retrieved density.The estimated calibration parameters and non-gravitational accelerations for the whole GRACE and GRACE-FO missions are available on our data server www.zarm.uni-bremen.de/zarm_daten.

The dynamical origins of the dark comets and a proposed evolutionary track

So-called ‘dark comets’ are small, morphologically inactive near-Earth objects (NEOs) that exhibit nongravitational accelerations inconsistent with radiative effects. These objects exhibit short rotational periods (minutes to hours), where measured. We find that the strengths required to prevent catastrophic disintegration are consistent with those measured in cometary nuclei and expected in rubble pile objects. We hypothesize that these dark comets are the end result of a rotational fragmentation cascade, which is consistent with their measured physical properties. We calculate the predicted size-frequency distribution for objects evolving under this model. Using dynamical simulations, we further demonstrate that the majority of these bodies originated from the ν6 resonance, implying the existence of volatiles in the current inner main belt. Moreover, one of the dark comets, (523599) 2003 RM, likely originated from the outer main belt, although a JFC origin is also plausible. These results provide strong evidence that volatiles from a reservoir in the inner main belt are present in the near-Earth environment.

Measurability of the Heliocentric Momentum Enhancement from a Kinetic Impact: The Double Asteroid Redirection Test (DART) Mission

The NASA Double Asteroid Redirection Test (DART) has demonstrated the capability of successfully conducting kinetic impact-based asteroid deflection missions. The changes in the Didymos–Dimorphos mutual orbit as a result of the DART impact have already been measured. To fully assess the heliocentric outcome of deflection missions, the heliocentric momentum enhancement parameter, β ⊙, needs to be determined and disentangled from other nongravitational phenomena such as the Yarkovsky effect. Here we explore the measurability of β ⊙ resulting from DART, which we estimate simultaneously with nongravitational accelerations using a least-squares filter. Results show that successful stellar occultation measurements of the Didymos system in the second half of 2024 in addition to the ones in the 2022–2023 campaigns can achieve a statistically significant estimate of β ⊙, with an uncertainty slightly above 20% for an assumed β ⊙ = 3. Adding additional occultation measurements and pseudorange measurements from the Hera spacecraft operations at Didymos starting in 2027 decreases this relative uncertainty to under 6%. We find that pre-impact occultation observations combined with post-impact occultations would have yielded substantially higher signal-to-noise ratios on the heliocentric deflection. Additionally, pre-impact occultations would also have enabled a statistically significant β ⊙ estimate using only one additional occultation in 2023 September. Therefore, we conclude that future asteroid deflection missions would greatly benefit from both pre- and post-deflection occultation measurements to help assess the resulting orbital changes.

Seasonally varying outgassing as an explanation for dark comet accelerations

Significant nonradial, nongravitational accelerations with magnitudes incompatible with radiation-driven effects have been reported in seven photometrically inactive near-Earth objects. Two of these objects exhibit large transverse accelerations (i.e., within the orbital plane but orthogonal to the radial direction), and six exhibit significant out-of-plane accelerations. Here, we find that anisotropic outgassing resulting from differential heating on a nucleus with nonzero spin-pole obliquity, averaged over an eccentric orbit, can explain these accelerations for most of the objects. This balanced outgassing model depends on three parameters — the spin pole orientation (R.A. and Dec.) and an acceleration magnitude. For these “dark comets” (excepting 2003 RM), we obtain parameter values that reproduce the observed nongravitational accelerations. We derive formulae for the component accelerations under certain assumptions for the acceleration scaling over heliocentric distance. Although we lack estimates of these objects’ spin axes to confirm our values, this mechanism is nevertheless a plausible explanation for the observed accelerations, and produces accurate perturbations to the heliocentric motions of most of these objects. This model may also be applied to active objects outside of the dark comets group.

X-Rays Trace the Volatile Content of Interstellar Objects

The nondetection of a coma surrounding 1I/‘Oumuamua, the first discovered interstellar object (ISO), has prompted a variety of hypotheses to explain its nongravitational acceleration. Given that forthcoming surveys are poised to identify analogs of this enigmatic object, it is prudent to devise alternative approaches to characterization. In this study, we posit X-ray spectroscopy as a surprisingly effective probe of volatile ISO compositions. Heavily ionized metals in the solar wind interact with outgassed neutrals and emit high-energy photons in a process known as charge exchange, and charge-exchange-induced X-rays from comets and planetary bodies have been observed extensively in our solar system. We develop a model to predict the X-ray flux of an ISO based on its chemical inventory and ephemeris. We find that while standard cometary constituents, such as H2O, CO2, CO, and dust, are best probed via optical or infrared observations, we predict strong X-ray emission generated by charge exchange with extended comae of H2 and N2—species that lack strong infrared fluorescence transitions. We find that XMM-Newton would have been sensitive to charge exchange emission from 1I/‘Oumuamua during the object’s close approach to Earth, and that constraints on composition may have been feasible. We argue for follow-up X-ray observations of newly discovered ISOs with close-in perihelia. Compositional constraints on the general ISO population could reconcile the apparently self-conflicting nature of 1I/‘Oumuamua and provide insight into the earliest stages of planet formation in extrasolar systems.

Oort Cloud comets discovered far from the Sun

Context. Increasingly, Oort Cloud comets are being discovered at great distances from the Sun and tracked over ever wider ranges of heliocentric distances as observational equipment improves. Aims. Our goal is to investigate in detail how the original semimajor axis for near-parabolic comets depends on the selected data arc and the assumed form of the nongravitational (NG) acceleration. Methods. Among currently known Oort Cloud comets with large perihelion distances (q > 3 au), we selected 32 objects observed over the widest ranges of heliocentric distances in orbital legs before and after perihelion. For each of them, we determined a series of orbits using at least three basic types of datasets selected from available positional data (pre- and post-perihelion data and the entire dataset), and a few forms of NG acceleration representing water ice or CO sublimation. Results. We find that the motion of comets is often measurably affected by NG forces at heliocentric distances beyond 5 au from the Sun. The most spectacular example is C/2010 U3 (Boattini), whose perihelion distance is 8.44 au. NG effects are detectable for 19 of the 32 comets within the positional data. For five comets, we find asymmetric effects of NG forces – in three cases significantly greater before perihelion than afterward (C/2017 M4, C/2000 SV75, and C/2015 O1), and in two others the opposite (C/1997 BA6 and C/2006 S3). We also find that the well-known systematic effect of finding more tightly bound original orbits when including the NG acceleration than in purely gravitational solutions may be related to the specific form of the standard g(r) function describing the sublimation of ices.

Calibration of high accuracy accelerometers for ESA missions BepiColombo and JUICE at INRIM

High sensitive triaxial accelerometers are used in several space missions to measure the non-gravitational accelerations acting on the spacecraft. Among these, the capacitive accelerometers developed for ESA missions Jupiter Icy moons Explorer (JUICE) and BepiColombo were designed to measure accelerations of the order of 3 · 10−6 m s−2 with an accuracy level of 300 ppm in the frequency range (3 · 10−5–0.1) Hz. Despite the signal to be measured is of the same order of magnitude of the seismic noise on the earth, an accurate on-ground calibration is needed. The facility set-up at INRIM to this purpose is based on a simple principle: the base of the accelerometer is dynamically tilted by an angle α so that the sensor undergoes a component of the gravitational acceleration g proportional to angle α. In practice, several issues have to be addressed by the calibration facility, such as the seismic noise limiting the signal-to-noise ratio, the generation and the accurate measurement of the tilt angle. Furthermore, the calibration was performed taking into account different on-flight conditions such as different operating temperatures and possible deformation of the accelerometers during the launch. The experimental set-up and the calibration procedure are described in the paper. The measurement results and the uncertainty budget show that a relative accuracy of 240 ppm has been achieved.

Splitting of Long-period Comet C/2018 F4 (PANSTARRS)

Long-period comet C/2018 F4 (PANSTARRS) was observed to show duplicity of its inner region in 2020 September, suggestive of a splitting event. We here present analyses of our observations of the comet taken from the LCO Outbursting Objects Key project and the University of Hawaii 2.2 m telescope after the discovery of the splitting. The two fragments Components A and B, estimated to be ∼60 m to 4 km in radius, remained highly similar to each other in terms of brightness, color, and dust morphology throughout our observing campaign from 2020 September to 2021 December. Our fragmentation model yielded that the two components split at a relative speed of 3.00 ± 0.18 m s−1 in 2020 late April, implying a specific energy change of J kg−1, and that Component B was subjected to a stronger nongravitational acceleration than Component A in both the radial and normal directions of the orbit. The obtained splitting time is broadly consistent with the result from the dust morphology analysis, which further suggested that the dominant dust grains were millimeter-sized and ejected at a speed of ∼2 m s−1. We postulate that the pre-split nucleus of the comet consisted of two lobes resembling that of 67P, or that the comet used to be a binary system like main-belt comet 288P. Regardless, we highlight the possibility of using observations of split comets as a feasible manner to study the bilobate shape or binarity fraction of cometary nuclei.

Implications of Evaporative Cooling by H2 for 1I/‘Oumuamua

The first interstellar object observed in our solar system, 1I/‘Oumuamua, exhibited several peculiar properties, including extreme elongation and nongravitational acceleration. Bergner & Seligman (hereafter BS23) proposed that evaporation of trapped H2 created by cosmic rays can explain the nongravitational acceleration. However, their modeling of the thermal structure of 1I/‘Oumuamua ignored the crucial cooling effect of evaporating H2. By taking into account the cooling by H2 evaporation, we show that the surface temperature of H2-water ice is a factor of 9 lower than the case without evaporative cooling. As a result, the thermal speed of outgassing H2 is decreased by a factor of 3. Our one-dimensional thermal modeling that takes into account evaporative cooling for two chosen values of thermal conductivity of κ = 0.01 and 0.1 WK−1 m−1 shows that the water ice volume available for H2 sublimation at T > 30 K would be reduced by a factor of 9 and 5 compared to the results of BS23, not enabling enough hydrogen to propel 1I/‘Oumuamua.

The Interstellar Interlopers

Interstellar interlopers are bodies formed outside of the Solar System but observed passing through it. The first two identified interlopers, 1I/‘Oumuamua and 2I/Borisov, exhibited unexpectedly different physical properties. 1I/‘Oumuamua appeared unresolved and asteroid-like, whereas 2I/Borisov was a more comet-like source of both gas and dust. Both objects moved under the action of nongravitational acceleration. These interlopers and their divergent properties provide our only window so far onto an enormous and previously unknown galactic population. The number density of such objects is ∼0.1 AU−3 which, if uniform across the galactic disk, would imply 1025 to 1026 similar objects in the Milky Way. The interlopers likely formed in, and were ejected from, the protoplanetary disks of young stars. However, we currently possess too little data to firmly reject other explanations.▪1I/‘Oumuamua and 2I/Borisov are both gravitationally unbound, subkilometer bodies showing nongravitational acceleration.▪The acceleration of 1I/‘Oumuamua in the absence of measurable mass loss requires either a strained explanation in terms of recoil from sublimating supervolatiles or the action of radiation pressure on a nucleus with an ultralow mass column density, ∼1 kg m−2.▪2I/Borisov is a strong source of CO and H2O, which together account for its activity and nongravitational acceleration.▪The interlopers are most likely planetesimals from the protoplanetary disks of other stars, ejected by gravitational scattering from planets. 1I/‘Oumuamua and 2I/Borisov have dynamical ages ∼108 and ∼109 years, respectively.▪Forthcoming observatories should detect interstellar interlopers every year, which will provide a rapid boost to our knowledge of the population.

Adaptive Precise Attitude Estimation Using Unscented Kalman Filter in High Dynamics Environments

In this paper, a novel adaptive scaled unscented Kalman filter (ASUKF) algorithm is developed using low-cost micro-electro-mechanical system (MEMS) triaxial gyroscope and accelerometer. The body non-gravitational accelerations are estimated and used to compensate the accelerometers measurements. The estimated external acceleration is used to adapt the acceleration measurement noise covariance matrix to achieve robustness during harsh environments. The proposed ASUKF uses the adapted covariance matrix and the compensated accelerometer measurements to precisely estimate the body attitude angles. The achieved accuracies for the proposed model are discussed and compared with other state-of-the-art algorithms through a laboratory and field tests. The results show that the proposed algorithm achieves an outstanding level accuracy in high dynamics environments in comparison to other attitude estimators.

Calibration and validation of a space electrostatic accelerometer onboard Tianzhou-1 cargo spacecraft using GNSS and attitude data

The first Chinese cargo spacecraft, named Tianzhou-1, provides a very quiet and stable environment to test space accelerometers. In this study, the high-precision electrostatic accelerometer with a resolution of 3×10−10m/s2/Hz1/2 onboard Tianzhou-1 is calibrated and validated by in-orbit measurements. In our analysis, we employ 14.5 hours of accelerometer, Global Navigations Satellite Systems (GNSS), and attitude measurements. Non-gravitational linear accelerations of the spacecraft are estimated from GNSS observables by reduced dynamic orbit determination, and centrifugal accelerations are estimated from the spacecraft attitude data and the center of mass offset. The spacecraft microgravity reaches a level of 1×10−6m/s2/Hz1/2 within the bandwidth of 1×10−4 to 1×10−2 Hz revealed from accelerometer measurements, which agrees well with our estimation of the non-gravitational and centrifugal accelerations. The results show that the centrifugal forces are the dominant signal at the frequencies above 3 cycle per revolution (cpr, 1 cpr ≈1.8×10−4 Hz) while non-gravitational forces occupy the lower frequency band. Furthermore, the bias and scale factor of the accelerometer are obtained by calibration with the estimated non-gravitational and centrifugal accelerations, using the method of least-squares linear fit. Based on the data covering the whole test period (00:33:20-15:02:43, 3 June, 2017, Beijing time), the estimated biases are −(5.31±0.04)×10−5, −(1.75±0.02)×10−6 and (2.65±0.01)×10−6m/s2 for the x, y and z axes, respectively, and the estimated scale factors are 1.001±0.008, 0.999±0.003 and 1.018±0.003 for the x, y and z axes, respectively.

Dark Comets? Unexpectedly Large Nongravitational Accelerations on a Sample of Small Asteroids

We report statistically significant detections of nonradial, nongravitational accelerations based on astrometric data in the photometrically inactive objects 1998 KY26, 2005 VL1, 2016 NJ33, 2010 VL65, 2016 RH120, and 2010 RF12. The magnitudes of the nongravitational accelerations are greater than those typically induced by the Yarkovsky effect, and there is no radiation-based, nonradial effect that can be so large. Therefore, we hypothesize that the accelerations are driven by outgassing and calculate implied H2O production rates for each object. We attempt to reconcile outgassing-induced acceleration with the lack of visible comae or photometric activity via the absence of surface dust and low levels of gas production. Although these objects are small, and some are rapidly rotating, the surface cohesive forces are stronger than the rotational forces, and rapid rotation alone cannot explain the lack of surface debris. It is possible that surface dust was removed previously, perhaps via outgassing activity that increased the rotation rates to their present-day value. We calculate dust production rates of order ∼10−4 g s−1 in each object, assuming that the nuclei are bare, within the upper limits of dust production from a sample stacked image of 1998 KY26 of g s−1. This production corresponds to brightness variations of order ∼0.0025%, which are undetectable in extant photometric data. We assess the future observability of each of these targets and find that the orbit of 1998 KY26—which is also the target of the extended Hayabusa2 mission—exhibits favorable viewing geometry before 2025.

(523599) 2003 RM: The Asteroid that Wanted to be a Comet

We report a statistically significant detection of nongravitational acceleration on the subkilometer near-Earth asteroid (523599) 2003 RM. Due to its orbit, 2003 RM experiences favorable observing apparitions every 5 yr. Thus, since its discovery, 2003 RM has been extensively tracked with ground-based optical facilities in 2003, 2008, 2013, and 2018. We find that the observed plane-of-sky positions cannot be explained with a purely gravity-driven trajectory. Including a transverse nongravitational acceleration allows us to match all observational data, but its magnitude is inconsistent with perturbations typical of asteroids such as the Yarkovsky effect or solar radiation pressure. After ruling out that the orbital deviations are due to a close approach or collision with another asteroid, we hypothesize that this anomalous acceleration is caused by unseen cometary outgassing. A detailed search for evidence of cometary activity with archival and deep observations from the Panoramic Survey Telescope and Rapid Response System and the Very Large Telescope does not reveal any detectable dust production. However, the best-fitting H2O sublimation model allows for brightening due to activity consistent with the scatter of the data. We estimate the production rate required for H2O outgassing to power the acceleration and find that, assuming a diameter of 300 m, 2003 RM would require Q(H2O) ∼ 1023 molec s−1 at perihelion. We investigate the recent dynamical history of 2003 RM and find that the object most likely originated in the mid-to-outer main belt (∼86% probability) as opposed to from the Jupiter-family comet region (∼11% probability). Further observations, especially in the infrared, could shed light on the nature of this anomalous acceleration.

Yarkovsky effect detection from ground-based astrometric data for near-Earth asteroid (469219) Kamo’oalewa

Context. The Yarkovsky effect is a weak non-gravitational force but may significantly affect sub-kilometre-sized near-Earth asteroids. Yarkovsky-related drift may be detected, in principle, from astrometric or radar datasets of sufficient duration. To date, the asteroid Kamo’oalewa, the most stable of Earth’s quasi-satellites, has an ~18 yr-long arc of ground-based optical astrometry. These data provide an opportunity to detect the Yarkovsky effect acting on the asteroid Kamo’oalewa. Aims. We determined the Yarkovsky-related drift of asteroid Kamo’oalewa from ~18 yr of ground-based optical astrometry. Furthermore, we investigated the influence of the Yarkovsky effect on the orbital evolution of asteroid Kamo’oalewa based on this estimated value, and evaluated the potential improvements in the detection of non-gravitational accelerations (Yarkovsky effect and solar radiation pressure) for the asteroid Kamo’oalewa that could be provided by the future Chinese small-body exploration mission, Tianwen-2. Methods. The Yarkovsky-related drift of asteroid Kamo’oalewa was detected from the orbital fitting of the astrometry measurements. We checked the Yarkovsky effect detection based on both the orbit fitting results and the physical mechanisms of the Yarkovsky effect. Results. We report for the first time the detection of the Yarkovsky effect acting on asteroid Kamo’oalewa based on ~18 yr of ground-based optical astrometry data. The estimated semi-major axis drift is (−6.155 ± 1.758) × 10−3 au Myr−1. In addition, our numerical simulation shows that the Yarkovsky effect has almost no influence on the short-term orbital evolution of the asteroid Kamo’oalewa, but does have a long-term influence, by delaying the entry of the object into the Earth co-orbital region and accelerating its exit from this region, with a more significant signature on the exit than on the entry. In the context of spacecraft tracking data, the Tianwen-2 mission will improve both non-gravitational accelerations (Yarkovsky effect and solar radiation pressure) and predictions of its future ephemeris.

A simplified gravitational reference sensor for satellite geodesy

We describe a Simplified Gravitational Reference Sensor (S-GRS), an ultra-precise inertial sensor for future Earth geodesy missions. These sensors are used to measure or compensate for all non-gravitational accelerations of the host spacecraft so that they can be removed in the data analysis to recover spacecraft motion due to Earth's gravity field, which is the main science observable. Low-low satellite-to-satellite tracking missions like GRACE-FO that utilize laser ranging interferometers are technologically limited by the acceleration noise performance of their electrostatic accelerometers, in addition to temporal aliasing associated with Earth's dynamic gravity field. The S-GRS is estimated to be at least 40 times more sensitive than the GRACE accelerometers and more than 500 times more sensitive if operated on a drag-compensated platform. The improved performance is enabled by increasing the mass of the sensor's test mass, increasing the gap between the test mass and its electrode housing, removing the small grounding wire used in the GRACE accelerometers and replacing them with a UV LED-based charge management system. This level of improvement allows future missions to fully take advantage of the sensitivity of the GRACE-FO laser Ranging Interferometer in the gravity recovery analysis. The S-GRS concept is a simplified version of the flight-proven LISA Pathfinder GRS. Our performance estimates are based on models vetted during the LISA Pathfinder flight and the expected Earth orbiting spacecraft environment based on flight data from GRACE-FO. The relatively low volume, mass, and a power consumption enables use of the S-GRS on ESPA-class microsatellites, reducing launch costs or enabling larger numbers of satellite pairs to be utilized to improve the temporal resolution of Earth gravity field maps.

Destruction of Long-period Comets

We identify a sample of 27 long-period comets for which both nongravitational accelerations and Lyα-based gas production rates are available. Seven of the 27 comets (i.e., ∼25%) did not survive perihelion because of nucleus fragmentation or complete disintegration. Empirically, the latter nuclei have the smallest gas production rates and the largest nongravitational accelerations, which are both indicators of small size. Specifically, the disintegrating nuclei have a median radius of only 0.41 km, one-quarter of the 1.60 km median radius of those surviving perihelion. The disintegrating comets also have a smaller median perihelion distance (0.48 au) than do the survivors (0.99 au). We compare the order-of-magnitude timescale for outgassing torques to change the nucleus spin, τ s , with the time spent by each comet in strong sublimation, Δt, finding that the disrupted comets are those with τ s < Δt. The destruction of near-Sun long-period comets is thus naturally explained as a consequence of rotational breakup. We discuss this process as a contributor to Oort’s long mysterious “fading parameter.”

Estimation of the Center of Mass of GRACE-Type Gravity Satellites

One of the key constraints for the accelerometer of GRACE-type gravity satellites to accurately measure the non-gravitational accelerations acting on the satellite is that the center of mass of the satellite and the proof mass of the accelerometer should maintain a coincidence. In addition, the accuracy requirement is that the center of mass offset (CM-offset) in the three directions is less than 100 microns. Since the center of mass (CoM) of the satellite will change with the consumption of cold-gas fuel in the tanks, it is necessary to regularly carry out the CoM calibration maneuver. Firstly, the observation equations consisting of the accelerometer linear acceleration, angular acceleration, and the CM-offset vector are established in order to estimate the amount of CM-offset. Then, according to the estimated CM-offset, the satellite mass trim mechanisms are used to change the satellite’s CoM, so that the satellite’s CoM always approaches the proof mass of the accelerometer, with an accuracy of 100 μm per axis. The CM-offset of the satellite of GRACE-FO is estimated by using the accelerometer, star camera, magnetic torquer, magnetometer, and the precision orbit data during the GRACE-C CM-offset calibration period on 1 February 2020. Four kinds of CM-offset results are obtained by four different angular accelerations as follows: the angular acceleration based on the attitude dynamics (“MTQ angular acceleration”), the accelerometer angular acceleration calibrated by MTQ, the accelerometer angular acceleration, and the angular acceleration calculated by the star camera. By comparing the four kinds of CM-offset results that are estimated by the four different methods, all four of the results are shown to have the same level of accuracy. Based on the accelerometer (calibrated) angular acceleration, the difference with the JPL result is 0.5 μm, while the difference between the conventional method and the JPL result is 6.0 μm. All four of the methods can achieve the requirement of 50 μm accuracy and using four CM-offset estimation methods simultaneously can improve the integrity of the calibration results. Subsequently, the CM-offset results of GRACE-C since its launch are estimated here. The calibration algorithm that is proposed in this paper can be used as a reference in the calibration of gravity satellites carrying an accelerometer payload.

Analysis of Orbital Atmospheric Density from QQ-Satellite Precision Orbits Based on GNSS Observations

Atmospheric drag provides an indirect approach for evaluating atmospheric mass density, which can be derived from the Precise Orbit Determination (POD) of Low Earth Orbit (LEO) satellites. A method was developed to estimate nongravitational acceleration, which includes the drag acceleration of the thermospheric density model and empirical force acceleration in the velocity direction from the centimeter-level reduced-dynamic POD. The main research achievements include the study of atmospheric responses to geomagnetic storms, especially after the launch of the spherical Qiu Qiu (QQ)-Satellite (QQ-Satellite) with the global navigation system satellite (GNSS) receiver onboard tracking the Global Positioning System (GPS) and Beidou System (BDS) data. Using this derivation method, the high-accuracy POD atmospheric density was determined from these data, resulting in better agreement among the QQ-Satellite-derived densities and the NRLMSISE-00 model densities. In addition, the POD-derived density exhibited a more sensitive response to magnetic storms. Improved accuracy of short-term orbit predictions using derived density was one of the aims of this study. Preliminary experiments using densities derived from the QQ-Satellite showed promising and encouraging results in reducing orbit propagation errors within 24 h, especially during periods of geomagnetic activity.

Interstellar objects

ABSTRACT Since 2017, two macroscopic interstellar objects have been discovered in the inner Solar System, both of which are distinct in nature. The first interstellar object, 1I/‘Oumuamua, passed within lunar distances of the Earth, appeared asteroidal lacking detectable levels of gas or dust loss, yet exhibited a nongravitational acceleration. 1I/‘Oumuamua's brief visit left open questions regarding its provenance which has given rise to many theoretical hypotheses, including an icy comet lacking a dust coma, an elongated fragment of a planet or planetesimal that was tidally disrupted, and an ultra-porous fractal aggregate. The second interstellar object, 2I/Borisov, was distinct from 1I/‘Oumuamua in terms of its bulk physical properties and displayed a definitive cometary tail. We review the discoveries of these objects, the subsequent observations and characterisations, and the theoretical hypotheses regarding their origins. We describe 1I/‘Oumuamua and 2I/Borisov in the context of active asteroids and comets in the Solar System. The discovery of these two objects implies a galactic-wide population of similar bodies. Forthcoming observatories should detect many more interstellar planetesimals which may offer new insights into how planetary formation processes vary throughout the Galaxy.