Non-gravitational Forces Research Articles

Main-belt comets as contributors to the near-Earth objects population

Aims. Most studies of the dynamics of main-belt objects describing the evolution of the bodies in inner Solar System have been carried with models that include weak nongravitational forces, such as the Yarkovsky and YORP effects. Only about 19 objects exhibit cometary-type activity, with sublimation being the principal mechanism. This paper presents a study of the influence of cometary- type nongravitational forces on the dynamics of main-belt comets, and the possible paths and timescales of evolution into other Solar System regions. Methods. We used the standard Marsden model for cometary-type activity. This model was designed for elongated orbits and the continuous ejection of mass, while the main-belt comets exhibit a different mode of activity. For this reason, we propose a simple model of nongravitational force activation that is consistent with observations. The dynamical evolution of objects was studied using a fifteenth-order RADAU integrator implemented in the REBOUND package. Results. The paper presents the dynamical routes of main-belt comets in the inner Solar System when cometary-type nongravitational forces are included in calculations. The forces significantly shorten the time of transition to other regions compared to the Yarkovsky effect, shortening this time to as little as a few thousand years depending on the frequency of the activity and the A1, A2, and A3 Marsden constants. There is a large probability of a transition to near-Earth object(NEO)-type orbits for bodies with A2 < 0, which means that cometary-type nongravitational forces can be a non-negligible mechanism increasing the number of bodies in that population. The forces can also deliver active main-belt objects into mean motion resonances but can equally eject bodies into outer planetary regions on far shorter timescales than the Yarkovsky and YORP effects. Cometary-type nongravitational effects should be included in dynamical studies of individual sublimating active asteroids.

Modeling of Solar Radiation Pressure for BDS-3 MEO Satellites with Inter-Satellite Link Measurements

As the largest non-gravitational force, solar radiation pressure (SRP) causes significant errors in precise orbit determination (POD) of the BeiDou global navigation satellite system (BDS-3) medium Earth orbit (MEO) satellite. This is mainly due to the imperfect modeling of the satellite’s cuboid body. Since the BDS-3’s inter-satellite link (ISL) can enhance the orbit estimation of BDS-3 satellites, the aim of this study is to establish an a priori SRP model for the satellite body using 281-day ISL observations to reduce the systematic errors in the final orbits. The adjustable box wind (ABW) model is employed to refine the optical parameters for the satellite buses. The self-shadow effect caused by the search and rescue (SAR) antenna is considered. Satellite laser ranging (SLR), day-boundary discontinuity (DBD), and overlapping Allan deviation (OADEV) are utilized as indicators to assess the performance of the a priori model. With the a priori model developed by both ISL and ground observation, the slopes of SLR residual for the China Academy of Space Technology (CAST) and Shanghai Engineering Center for Microsatellites (SECM) satellites decrease from −0.097 cm/deg and 0.067 cm/deg to −0.004 cm/deg and −0.009 cm/deg, respectively. The standard deviation decreased by 21.8% and 26.6%, respectively. There are slight enhancements in the average values of DBD and OADEV, and a reduced β-dependent variation is observed in the OADEV of the corresponding clock offset. We also found that considering the SAR antenna only slightly improves the orbit accuracy. These results demonstrate that an a priori model established for the BDS-3 MEO satellite body can reduce the systematic errors in orbits, and the parameters estimated using both ISL and ground observation are superior to those estimated using only ground observation.

Varying water activity and momentum transfer on comet 67P/Churyumov-Gerasimenko from its non-gravitational forces and torques

Aims. We investigate the ability of a simultaneous fitting of comet 67P/Churyumov-Gerasimenko’s non-gravitational forces, torques, and total water-outgassing rate, as observed by Rosetta, to constrain complex thermophysical models of cometary material. Methods. We extend the previous work of fitting geographically defined surface outgassing models to the Rosetta observations by testing the effects of a more detailed geomorphological mapping, the resolution of the shape-model used, self-heating by neighbouring facets on the shape-model, thermal inertia in the outgassing solution, and the variation in the momentum coupling between the gas and the nucleus. We also directly compare the non-gravitational acceleration curves available in the literature. Results. We correct an error in the calculation of pole-orientation in the previous paper. We find that, under the assumptions of the model, non-gravitational forces and torques are driven by water sublimation from the nucleus, thermal inertia and self-heating have only minor effects, spatially uniform activity cannot explain 67P’s non-gravitational dynamics, spatially uniform momentum transfer cannot explain 67P’s non-gravitational dynamics, and different terrain types have different instantaneous responses to insolation. Conclusions. Consolidated terrain facing south on 67P/Churyumov-Gerasimenko has a high outgassing flux, a steep response to insolation, and a large gas momentum transfer coefficient. Instead, that facing north behaves differently, producing little to no water outgassing, and with a lower momentum transfer efficiency. Dusty terrain also has a lower outgassing rate and momentum transfer efficiency, and either depletes its volatile component or is buried in fall-back as the comet approaches the Sun. Momentum transfer appears correlated with insolation, likely due to an increased enhancement in the gas temperature as the dust it flows through is heated.

An application of recurrence relations to central force fields

By generalizing the relationships between auxiliary variables that appear in the works of A.E. Roy, we investigate the dynamics of non-interacting particles under the action of a central force field whose force function is a solution to a certain differential equation. The method used by A.E. Roy, R. Broucke, and later by G. Sitarski, was utilized in such a way that the obtained recursive equations can be used to describe the motion of a particle under such a field. The class of such fields includes both gravitational and non-gravitational force fields. Several numerical and historically essential examples and detailed discussions of various cases are given.

Catalog of Proper Orbits for 1.25 Million Main-belt Asteroids and Discovery of 136 New Collisional Families

The proper elements of asteroids are obtained from the instantaneous orbital elements by removing periodic oscillations produced by gravitational interactions with planets. They are unchanged in time, at least if chaotic dynamics and nongravitational forces could be ignored, and can therefore be used to identify fragments of major collisions (asteroid families) that happened eons ago. Here we present a new catalog of proper elements for 1.25 × 106 main-belt asteroids. We explain the methodology, evaluate uncertainties, and discuss how the new catalog can be used to identify asteroid families. A systematic search for families yielded 153 cases not reported in Nesvorný et al.—17 of these cases were identified in various other publications, and 136 cases are new discoveries. There are now 274 families in the asteroid belt in total (plus a handful of families in the resonant Hilda population). We analyzed several compact families in detail. The new family around the middle-belt asteroid (9332) 1990SB1 (nine members) is the youngest family found so far (estimated formation only 16–17 kyr ago). The new families (1217) Maximiliana, (6084) Bascom, (10164) Akusekijima, and (70208) 1999RX33 all formed 0.5–2.5 Myr ago. The (2110) Moore–Sitterly family is a close pair of relatively large bodies, 2110 and 44612, and 15 small members all located sunward from 2110 and 44612, presumably a consequence of the Yarkovsky drift over the estimated family age (1.2–1.5 Myr). A systematic characterization of the new asteroid families is left for future work.

Charge monitoring of test masses in gravitational waves interferometers

The sensitivity of gravitational waves (GWs) detectors is impacted by several sources of noise. One such source is related to the deposition of charge on the test masses (TMs), since its interaction with the surrounding electrical fields introduces an unwanted non-gravitational force on the TM. The charging process is still not completely understood and the charge deposition has historically never been consistently monitored, therefore we propose to implement a real-time monitoring system to overcome these limitations. In particular, in our work we explored 32 candidate sensor locations. Using simulation, we considered more than 100,000 different Gaussian-distributed charge located on either the front or back face of the TM. Utilizing dimensional reduction theories, like the PCA, we established sensor selection criteria to individuate the most relevant sensors. Exploiting Neural Networks (NNs), trained on the simulations, we determined the charge distributions.

Climate change in hell: Long-term variation in transits of the evaporating planet K2-22b

Rocky planets on ultra-short period orbits can have surface magma oceans and rock-vapour atmospheres in which dust can condense. Observations of that dust can inform us about the composition and surface conditions on these objects. We constrained the properties and long-term (decade) behaviour of the transiting dust cloud from the evaporating planet K2-22b. We observed K2-22b around 40 predicted transits with MuSCAT ground-based multi-optical channel imagers, and complemented these data with long-term monitoring by the ground-based ATLAS (2018-2024) and space-based (2021-2023) surveys. We detected signals during 7 transits, none of which showed significant wavelength dependence. The expected number of MuSCAT-detected transits is $ indicating a decline in mean transit depth since the discovery observations in 2014. The lack of a significant wavelength dependence indicates that dust grains are large or the cloud is optically thick. Long-term trends of depth could be due to a magnetic cycle on the host star or to overturn of the planet's dayside surface magma ocean. The possibility that K2-22b is disappearing altogether is ruled out by the stability of the transit ephemeris against non-gravitational forces, which constrains the mass to be at least comparable to Ceres.

A statistical analysis of over three thousand meteors and their spectra

ABSTRACT In this article, over three thousand meteor spectra recorded in Saitama, Japan, between 2018 and 2021 are analysed. We performed a principal component analysis of the intensity of the sodium and magnesium lines and the iron band of each meteor in combination with the orbital elements and the kinematic parameters such as the geocentric velocity and the initial and final altitudes to determine the relative importance of each of these variables in the composition of a meteor’s spectrum. We found that for meteor showers such as GEM, LEO, QUA, and PER, the orbital elements or kinematic parameters are important parameters that determine the intensity of these spectral lines, which could indicate the influence of gravitational and/or non-gravitational forces in distinguishing the composition or variations in the strength of the meteoroid material in each meteor shower. The normal spectral type in our sample ranges from 39.5 per cent to 96.8 per cent, corresponding to GEM and PER, respectively. The COM meteors have a similar sodium content to the components of the LEO and PER showers, suggesting a comet as a possible parent body. The sodium and magnesium content of the iron-class meteoroids is the lowest of all our samples, but it is not zero, suggesting that there are no pure iron meteoroids. The sodium content of the GEM meteor shower shows temporal variations in 2021 compared to the 2019 and 2020 observing seasons. We found no correlation between the sodium content and the perihelion distance for other meteor showers.

Influence of non-gravitational forces on the co-orbital motion

ABSTRACT In the Solar system, there exist many non-gravitational perturbations for co-orbital objects, such as the solar radiation pressure, Yarkovsky effect, and so forth. Their effects play important roles in the dynamics of co-orbital objects as they lead to long-term perturbations accumulating. The motivation of this paper is to investigate the general mechanism of the non-gravitational force on the co-orbital motion in the circular restricted three-body problem. We propose an effective method for perturbed co-orbital motions by analysing the locus of the co-orbital objects in a two-dimensional map. Several expressions derived uncover how the non-gravitational force acts on orbital parameters. Taking the Sun–Jupiter system as an example, we implement numerical computations to demonstrate the validity of our results. Numerical computation shows that most of loci of co-orbital motions are in agreement with our conclusions. Some interesting phenomena of perturbed co-orbital motion, such as the co-orbital transition and escape, are found and explained. The results obtained from this paper provide an efficient approach to analyse the evolution of perturbed co-orbital motions.

Thermospheric Mass Density Modelling during Geomagnetic Quiet and Weakly Disturbed Time

Atmospheric drag stands out as the predominant non-gravitational force acting on satellites in Low Earth Orbit (LEO), with altitudes below 2000 km. This drag exhibits a strong dependence on the thermospheric mass density (TMD), a parameter of vital significance in the realms of orbit determination, prediction, collision avoidance, and re-entry forecasting. A multitude of empirical TMD models have been developed, incorporating contemporary data sources, including TMD measurements obtained through onboard accelerometers on LEO satellites. This paper delves into three different TMD modelling techniques, specifically, Fourier series, spherical harmonics, and artificial neural networks (ANNs), during periods of geomagnetic quiescence. The TMD data utilised for modelling and evaluation are derived from three distinct LEO satellites: GOCE (at an altitude of approximately 250 km), CHAMP (around 400 km), and GRACE (around 500 km), spanning the years 2002 to 2013. The consistent utilisation of these TMD data sets allows for a clear performance assessment of the different modelling approaches. Subsequent research will shift its focus to TMD modelling during geomagnetic disturbances, while the present work can serve as a foundation for disentangling TMD variations stemming from geomagnetic activity. Furthermore, this study undertakes precise TMD modelling during geomagnetic quiescence using data obtained from the GRACE (at an altitude of approximately 500 km), CHAMP (around 400 km), and GOCE (roughly 250 km) satellites, covering the period from 2002 to 2013. It employs three distinct methods, namely Fourier analysis, spherical harmonics (SH) analysis, and the artificial neural network (ANN) technique, which are subsequently compared to identify the most suitable methodology for TMD modelling. Additionally, various combinations of time and coordinate representations are scrutinised within the context of TMD modelling. Our results show that the precision of low-order Fourier-based models can be enhanced by up to 10 % through the utilisation of geocentric solar magnetic coordinates. Both the Fourier- and SH-based models exhibit limitations in approximating the vertical gradient of TMD. Conversely, the ANN-based model possesses the capacity to capture vertical TMD variability without manifesting sensitivity to variations in time and coordinate inputs.

Characterisation of chaos and mean-motion resonances in meteoroid streams

Context. Dynamically linking a meteor shower with its parent body is challenging, and chaos in the dynamics of meteoroid streams may contribute to this challenge. For a robust identification of parent bodies, it is therefore necessary to quantify the amount of chaos involved in the evolution of meteoroid streams. Aims. Characterising chaos in meteoroid streams through the aid of chaos maps is still a new field of study. Thus, we examine two very different meteoroid streams, the Draconids and the Leonids, in order to obtain a general view of this topic. Methods. We used the method developed in a previous paper dedicated to Geminids, drawing chaos maps with the orthogonal fast Lyapunov indicator. We chose four particle size ranges to investigate the effect of non-gravitational forces. As the dynamics are structured by mean-motion resonances with planets, we computed the locations and widths of the resonances at play. We used semi-analytical formulas valid for any eccentricity and inclination and an arbitrary number of planets. Results. We pinpoint which mean-motion resonances with Jupiter play a major role in the dynamics of each meteoroid stream. We show how those resonances tend to trap mostly large particles, preventing them from meeting with Jupiter. We also study particles that manage to escape those resonances, for example, due to the gravitational perturbation of Saturn. Finally, we explain why non-gravitational forces do not disturb the dynamics much, contrary to what is observed for the Geminids.

A detailed analysis of stochastic models applied to temporal gravity field recovery with GRACE observations

Summary In this study, we analyzed the impacts of errors in background force models and observed non-gravitational forces on the pseudo-observations (pre-fits) during gravity field recovery based on the GRACE satellite gravity mission. To reduce these effects, we introduced the stochastic parameters into the functional model of the variational equation integration approach to absorb this type of noise contribution. Simultaneously, the prior variances of observed orbits and K-Band range rates used in traditional method are re-estimated with least-square variance component estimation (LS-VCE) after considering these stochastic parameters. To improve the computing efficiency, a modified method of the calculation of sensitivity matrices related to the introduced stochastic parameters is proposed. Compared to the method of variation of constants widely used in the precise orbit determination and gravity field recovery, the modified method decreases the computational time of these matrices by about four times. Furthermore, an efficient LS-VCE algorithm is derived in a more generalized case. The efficient algorithm only costs 1% of the time of the unoptimized method. With the GRACE data, we analyzed the benefits of these refinements in gravity field recovery, and the results show that these improvements can mitigate the impacts of errors in background force models and accelerometer data on recovered gravity field models, especially in the high degree signals. Furthermore, the quality of results has less dependence on parameterization.

Shape models and spin states of Jupiter Trojans

The leading theory for the origin of Jupiter Trojans (JTs) assumes that JTs were captured to their orbits near the Lagrangian points of Jupiter during the early reconfiguration of the giant planets. The natural source region for the majority of JTs would then be the population of planetesimals born in a massive trans-Neptunian disk. If true, JTs represent the most accessible stable population of small Solar System bodies that formed in the outer regions of the Solar System. For this work, we compiled photometric datasets for about 1000 JTs and applied the convex inversion technique in order to assess their shapes and spin states. We obtained full solutions for 79 JTs, and partial solutions for an additional 31 JTs. We found that the observed distribution of the pole obliquities of JTs is broadly consistent with expectations from the streaming instability, which is the leading mechanism for the formation of planetesimals in the trans-Neptunian disk. The observed JTs’ pole distribution has a slightly smaller prograde vs. retrograde asymmetry (excess of obliquities >130°) than what is expected from the existing streaming instability simulations. However, this discrepancy can be plausibly reconciled by the effects of the post-formation collisional activity. Our numerical simulations of the post-capture spin evolution indicate that the JTs’ pole distribution is not significantly affected by dynamical processes such as the eccentricity excitation in resonances, close encounters with planets, or the effects of nongravitational forces. However, a few JTs exhibit large latitude variations of the rotation pole and may even temporarily transition between prograde- and retrograde-rotating categories.

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

Characterisation of chaos in meteoroid streams

Context. Dynamically linking a meteor shower with its parent body can be challenging. This is in part due to the limits of the tools available today (such as D-criteria) but is also due to the complex dynamics of meteoroid streams. Aims. We choose a method to study chaos in meteoroid streams and apply it to the Geminid meteoroid stream. Methods. We decided to draw chaos maps. Amongst the chaos indicators we studied, we show that the orthogonal fast Lyapunov indicator is particularly well suited to our problem. The maps are drawn for three bin sizes, ranging from 10−1 to 10−4 m. Results. We show the influence of mean-motion resonances with the Earth and with Venus, which tend to trap the largest particles. The chaos maps present three distinct regimes in eccentricity, reflecting close encounters with the planets. We also study the effect of non-gravitational forces. We determine a first approximation of the particle size rlim needed to counterbalance the resonances with the diffusion due to the non-gravitational forces. We find that, for the Geminids, rlim lies in the range [3; 8] × 10−4 m. However, rlim depends on the orbital phase space.

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.

Can the Gravitational Effect of Planet X be Detected in Current-era Tracking of the Known Major and Minor Planets?

Using Fisher information matrices, we forecast the uncertainties σ M on the measurement of a “Planet X” at heliocentric distance d X via its tidal gravitational field’s action on the known planets. Using planetary measurements currently in hand, including ranging from the Juno, Cassini, and Mars-orbiting spacecraft, we forecast a median uncertainty (over all sky positions) of A 5σ detection of a 5 M ⊕ Planet X at d X = 400 au should be possible over the full sky but over only 5% of the sky at d X = 800 au. The gravity of an undiscovered Earth- or Mars-mass object should be detectable over 90% of the sky to a distance of 260 or 120 au, respectively. Upcoming Mars ranging improves these limits only slightly. We also investigate the power of high-precision astrometry of ≈8000 Jovian Trojans over the 2023–2035 period from the upcoming Legacy Survey of Space and Time (LSST). We find that the dominant systematic errors in optical Trojan astrometry (photocenter motion, nongravitational forces, and differential chromatic refraction) can be solved internally with minimal loss of information. The Trojan data allow cross-checks with Juno/Cassini/Mars ranging, but do not significantly improve the best achievable σ M values until they are ≳10× more accurate than expected from LSST. The ultimate limiting factor in searches for a Planet X tidal field is confusion with the tidal field created by the fluctuating quadrupole moment of the Kuiper Belt as its members orbit. This background will not, however, become the dominant source of uncertainty until the data get substantially better than they are today.

Implications for the Formation of (155140) 2005 UD from a New Convex Shape Model

(155140) 2005 UD has a similar orbit to (3200) Phaethon, an active asteroid in a highly eccentric orbit thought to be the source of the Geminid meteor shower. Evidence points to a genetic relationship between these two objects, but we have yet to fully understand how 2005 UD and Phaethon could have separated into this associated pair. Presented herein are new observations of 2005 UD from five observatories that were carried out during the 2018, 2019, and 2021 apparitions. We implemented light curve inversion using our new data, as well as dense and sparse archival data from epochs in 2005–2021, to better constrain the rotational period and derive a convex shape model of 2005 UD. We discuss two equally well-fitting pole solutions (λ = 116.°6, β = −53.°6) and (λ = 300.°3, β = −55.°4), the former largely in agreement with previous thermophysical analyses and the latter interesting due to its proximity to Phaethon’s pole orientation. We also present a refined sidereal period of P sid = 5.234246 ± 0.000097 hr. A search for surface color heterogeneity showed no significant rotational variation. An activity search using the deepest stacked image available of 2005 UD near aphelion did not reveal a coma or tail but allowed modeling of an upper limit of 0.04–0.37 kg s−1 for dust production. We then leveraged our spin solutions to help limit the range of formation scenarios and the link to Phaethon in the context of nongravitational forces and timescales associated with the physical evolution of the system.

Activity distribution of comet 67P/Churyumov-Gerasimenko from combined measurements of non-gravitational forces and torques

Aims. Understanding the activity is vital for deciphering the structure, formation, and evolution of comets. We investigate models of cometary activity by comparing them to the dynamics of 67P/Churyumov-Gerasimenko. Methods. We matched simple thermal models of water activity to the combined Rosetta datasets by fitting to the total outgassing rate and four components of the outgassing induced non-gravitational force and torque, with a final manual adjustment of the model parameters to additionally match the other two torque components. We parametrised the thermal model in terms of a distribution of relative activity over the surface of the comet, and attempted to link this to different terrain types. We also tested a more advanced thermal model based on a pebble structure. Results. We confirm a hemispherical dichotomy and non-linear water outgassing response to insolation. The southern hemisphere of the comet and consolidated terrain show enhanced activity relative to the northern hemisphere and dust-covered, unconsolidated terrain types, especially at perihelion. We further find that the non-gravitational torque is especially sensitive to the activity distribution, and to fit the pole-axis orientation in particular, activity must be concentrated (in excess of the already high activity in the southern hemisphere and consolidated terrain) around the south pole and on the body and neck of the comet over its head. This is the case for both the simple thermal model and the pebble-based model. Overall, our results show that water activity cannot be matched by a simple model of sublimating surface ice driven by the insolation alone, regardless of the surface distribution, and that both local spatial and temporal variations are needed to fit the data. Conclusions. Fully reconciling the Rosetta outgassing, torque, and acceleration data requires a thermal model that includes both diurnal and seasonal effects and also structure with depth (dust layers or ice within pebbles). This shows that cometary activity is complex. Nonetheless, non-gravitational dynamics provides a useful tool for distinguishing between different thermophysical models and aids our understanding.

Giga-year dynamical evolution of particles around Mars

Particles of various sizes can exist around Mars. The orbits of large particles are mainly governed by Martian gravity, while those of small particles could be significantly affected by non-gravitational forces. Many of the previous studies of particle dynamics around Mars have focused on relatively small particles (radius of rp≲100μm) for ≲104 years. In this paper, using direct numerical orbital integration and analytical approaches, we consider Martian gravity, Martian J2, the solar radiation pressure (SRP) and the Poynting–Robertson (PR) force to study the giga-year dynamical evolution of particles orbiting near the Martian equatorial plane with radius ranging from micrometer to meter. We also newly study the effect of the planetary shadow upon the particle dynamics. Our results show that small particles (rp≲10μm) initially at ≲8 Martian radii (below the orbit of today’s Deimos) are quickly removed by the SRP due to eccentricity increase, resulting in a collision with Mars at the pericenter distance. The orbits of larger particles (rp>10μm) slowly decay due to the PR forces (timescale of >104 years). The planetary shadow reduces the sunlit area in the orbit and thus the efficiency of the PR drag force is reduced. However, we show that, even including the planetary shadow, particles up to ∼10 cm in radius, initially at ≲8 Martian radii, eventually spiral onto the Martian surface within ∼109 years. Smaller particles require less time to reach Mars, and vice versa. Our results would be important to better understand and constrain the nature of the remaining particle around Mars in a context of giant impact hypothesis for the formation of Phobos and Deimos.