Non-gravitational Perturbations Research Articles

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 Lense–Thirring effect measurement and LAGEOS satellites orbit analysis with the new gravity field model from the CHAMP mission

The Lense–Thirring effect – one of the main predictions of Einstein’s theory of gravitation in the limit of weak field and slow motion – represents a tiny relativistic precession of the orbital plane of a satellite produced by the angular momentum of the primary. In the present work, we estimated an updated error budget for the Lense–Thirring effect measurement through the accurate analysis of the orbit of the passive laser-ranged LAGEOS satellites. This error budget has been estimated over a 9 years time span. The error estimate has been performed on a nodes-only combination of the satellites orbital residuals. The advantage is the smaller impact of the non-gravitational perturbations with respect to a combination involving also LAGEOS II argument of perigee. The recent gravity model EIGEN-2 for the Earth’s gravity field has been considered. Indeed, with the nodes-only combination the error budget from the non-gravitational perturbation is about a few parts of % of the relativistic effect (48.1 mas/yr), while the error from the full covariance matrix of the EIGEN-2 solution is about 17.8%. Therefore, taking into consideration these two sources of error, we obtained an error budget less than 18% for the Lense–Thirring effect measurement (computed in a root–sum–square fashion). The contribution from other gravitational error sources has been considered, as solid and oceans tides, odd zonal harmonics, and secular variations in the even zonal harmonics. All these perturbations are responsible, with the exception of the secular variations in the even zonal harmonics, of systematic effects smaller than those estimated for the non-gravitational perturbations. The open problems related with a full calibration of the errors from the new gravity field models are outlined.

On the use of Ajisai and Jason-1 satellites for tests of general relativity

In this paper we analyze in detail some aspects of the proposed use of Ajisai and Jason-1, together with the LAGEOS satellites, to measure the general relativistic Lense–Thirring effect in the gravitational field of the Earth. A linear combination of the nodes of such satellites is the proposed observable. The systematic error due to the mismodelling in the uncancelled even zonal harmonics would be ∼1% according to the latest present-day CHAMP/GRACE-based Earth gravity models. In regard to the non-gravitational perturbations especially affecting Jason-1, only relatively high-frequency harmonic perturbations should occur: neither semisecular nor secular bias of non-gravitational origin should affect the proposed combination: their maximum impact is evaluated to ∼4% over 2 years. Our estimation of the root-sum-square total error is about 4–5% over at least 3 years of data analysis required to average out the uncancelled tidal perturbations.

The Non-Gravitational Perturbations impact on the BepiColombo Radio Science Experiment and the key rôle of the ISA accelerometer: direct solar radiation and albedo effects

The paper is focused on the estimate of the impact of the non-gravitational perturbations on the orbit of the Mercury Planetary Orbiter (MPO), one of the two spacecrafts that will be placed in orbit around the innermost planet of the solar system by the BepiColombo space mission. The key role of the Italian Spring Accelerometer (ISA), that has been selected by the European Space Agency (ESA) to fly on-board the MPO, is outlined. In the first part of the paper, through a numerical simulation and analysis we have estimated, over a time span of several years, the long-period behaviours of the disturbing accelerations produced by the incoming direct solar radiation pressure, and the indirect effects produced by Mercury’s albedo. The variations in the orbital parameters of the spacecraft, together with their spectral contents, have been estimated over the analysed period. The direct solar radiation pressure represents the strongest non-gravitational perturbation on the MPO in the very complex radiation environment of Mercury. The order-of-magnitude of this acceleration is quite high, about 10−6 m/s2, because of the proximity to the Sun and the large area-to-mass ratio of the spacecraft. In the second part of the paper, we concentrated upon the short-period effects of direct solar radiation pressure and Mercury’s albedo. In particular, the disturbing accelerations have been compared with the ISA measurement error and the advantages of an on-board accelerometer are highlighted with respect to the best modelling of the non-gravitational perturbations in the strong radiation environment of Mercury. The readings from ISA, with an intrinsic noise level of about \(10^{-9}\,m/s^{2}/\sqrt{Hz}\) in the frequency band of 3·10−5–10−1 Hz, guarantees a very significant reduction of the non-gravitational accelerations impact on the space mission accuracy, especially of the dominant direct solar radiation pressure.

An assessment of the measurement of the Lense–Thirring effect in the Earth gravity field, in reply to: “On the measurement of the Lense–Thirring effect using the nodes of the LAGEOS satellites, in reply to “On the reliability of the so far performed tests for measuring the Lense–Thirring effect with the LAGEOS satellites” by L. Iorio,” by I. Ciufolini and E.

In this paper we reply to recent claims by Ciufolini and Pavlis about certain aspects of the measurement of the general relativistic Lense–Thirring effect in the gravitational field of the Earth. (I) The proposal by such authors of using the existing satellites endowed with some active mechanism of compensation of the non-gravitational perturbations as an alternative strategy to improve the currently ongoing Lense–Thirring tests is unfeasible because of the impact of the uncancelled even zonal harmonics of the geopotential and of some time-dependent tidal perturbations. (II) It is shown that their criticisms about the possibility of using the existing altimeter Jason-1 and laser-ranged Ajisai satellites are groundless. (III) Ciufolini and Pavlis also claimed that we would have explicitly proposed to use the mean anomaly of the LAGEOS satellites in order to improve the accuracy of the Lense–Thirring tests. We prove that it is false. In regard to the mean anomaly of the LAGEOS satellites, Ciufolini himself did use such an orbital element in some previously published tests. About the latest test performed with the LAGEOS satellites, (IV) we discuss the cross-coupling between the inclination errors and the first even zonal harmonic as another possible source of systematic error affecting it with an additional 9% bias. (V) Finally, we stress the weak points of the claims about the origin of the two-nodes LAGEOS–LAGEOS II combination used in that test.

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 LAGEOS satellites orbital residuals determination and the Lense–Thirring effect measurement

The method applied since 1996 for the analysis of the orbital residuals of the LAGEOS satellites in order to measure the Lense–Thirring effect has been the subject of the present work. This method, based on the difference between the orbital elements of consecutive arcs, is explained and analysed also from the analytical point of view. It is proved that this “difference method” works well for the determination of the secular effects, as in the case of the relativistic precession induced by the Earth's angular momentum, but also very useful for the determination and study of the long-term periodic effects. Indeed, the only limitation in the determination of the periodic effects is the possibility of the reduction of their amplitude by a factor which depends from the periodicity of the given perturbation and from the orbital arc length chosen for the satellite during the data analysis. In the case of the Yarkovsky–Schach effect, the main non-gravitational perturbation seen in the LAGEOS satellites orbital residuals, in particular in its perigee rate and eccentricity vector excitation residuals, we show that the “difference method” is quite good also for the determination of the long-period perturbations induced by this subtle non-conservative force.

New Dust Belts of Uranus: One Ring, Two Ring, Red Ring, Blue Ring

We compared near-infrared observations of the recently discovered outer rings of Uranus with Hubble Space Telescope results. We find that the inner ring, R/2003 U 2, is red, whereas the outer ring, R/2003 U 1, is very blue. Blue is an unusual color for rings; Saturn's enigmatic E ring is the only other known example. By analogy to the E ring, R/2003 U 1 is probably produced by impacts into the embedded moon Mab, which apparently orbits at a location where nongravitational perturbations favor the survival and spreading of submicron-sized dust. R/2003 U 2 more closely resembles Saturn's G ring, which is red, a typical color for dusty rings.

Determination of frame-dragging using Earth gravity models from CHAMP and GRACE

Using the new generation Earth’s gravity field models EIGEN-2S, GGM01S and EIGEN-GRACE02S generated by the space missions CHAMP and GRACE, we have obtained an accurate measurement of the Lense–Thirring effect with the LAGEOS and LAGEOS II satellites analyzing about 10 years of data with the EIGEN-2S and GGM01S models and about 11 years of data with EIGEN-GRACE02S. This new analysis is in agreement with our previous measurements of the Lense–Thirring effect using the LAGEOS satellites and obtained with the JGM-3 and EGM96 Earth’s models. However, the new determinations are more accurate and, especially, more robust than our previous measurements. In the present analysis we are only using the nodal rates of the two satellites, making no use of the perigee rate, as in our previous analyses. The perigee is affected by a number of non-gravitational perturbations difficult to be modelled and whose impact in the total error budget is not easy to assess. Using the EIGEN-2S model, we obtain a total error budget between 18% and 36% of the Lense–Thirring effect due to all the error sources. Specifically, by using EIGEN-2S, we obtain: μ=0.85, with a total error between ±0.18 and ±0.36, with GGM01S we get μ=1.06 with a total error between ±0.19 and ±0.24 and with EIGEN-GRACE02S we obtain μ=0.99, with a total error between ±0.05 and ±0.1, i.e., between 5% and 10% of the general relativistic predicted value of the Lense–Thirring effect. In addition to the analyses using EIGEN-2S, GGM01S and EIGEN-GRACE02S without the use of the perigee, we have also performed an analysis using the older model EGM96 with our previous method of combining the nodes of the LAGEOS satellites with the perigee of LAGEOS II. However, this analysis was performed over a period of about 10 years, i.e. about 2.5 times longer than any our previous analysis. The result using EGM96 over this longer period of observation agrees with our previous results over much shorter periods and with the EIGEN-2S, GGM01S and EIGEN-GRACE02S measurements of μ. In addition to the accurate determination of frame-dragging and in agreement with our previous analyses of the orbits of the LAGEOS satellites, we have observed, since 1998, an anomalous change in the Earth quadrupole coefficient, J2 which agrees with recent findings of other authors. This anomalous variation of J2 is accurately observed both on the node of LAGEOS and LAGEOS II and it is independent of the model used, i.e., it is observed by using the model EGM96 or by using EIGEN-2S, GGM01S or EIGEN-GRACE02S. However, this anomalous variation of the Earth quadrupole coefficient does not affect at all our determination of the Lense–Thirring effect thanks to the total elimination of the J2-induced errors with our especially devised estimation technique.

ISA (Italian Spring Accelerometer): A new configuration for the Radio Science Experiment

We describe the accelerometer to be used in the Radio Science Experiment conceived for the BepiColombo space mission to Mercury. The key rôle of the ISA is outlined in order to remove from the list of unknowns the strong non-gravitational perturbations acting on the satellite. The main characteristics of the three-axis accelerometer are given, with particular emphasis on its configuration inside the planned spacecraft and to the attenuation of the thermal perturbing effects that represent one of the major difficulties in a gravimetry experiment.

Non-gravitational forces acting on small bodies

Non-gravitational perturbations, regardless being many orders of magnitude weaker than gravity, hold keys to fully understand the evolution of small Solar System bodies. This is because individual bodies, or their entire groups, manifest traces of a long-term accumulated changes by these effects.For meteoroids and small asteroids in the 10 cm–10 km size range, the principal non-gravitational force and torque arise from an anisotropic thermal emission of the absorbed solar radiation. Related perturbations of the orbital and rotational motion are called the Yarkovsky and YORP effects.We review the most important Yarkovsky- and YORP-driven processes, in the Main Asteroid Belt. These include: steady and size-dependent semimajor axis drift, secular changes of rotational period and obliquity, efficient transport towards low-order resonances, interaction with weaker higher-order resonances, captures in secular and spin-orbit resonances.Many independent observations can be naturally interpreted in the framework of Yarkov-sky/YORP models, like cosmic ray exposure ages of meteorites, current population and size-distribution of near-Earth objects, the existence of unstable resonant asteroids or the structure of asteroid families.

The impact of the new Earth gravity models on the measurement of the Lense–Thirring effect with a new satellite

In this paper we investigate the opportunities offered by the new Earth gravity models from the dedicated CHAMP and, especially, GRACE missions to the project of measuring the general relativistic Lense–Thirring effect with a new Earth’s artificial satellite. It turns out that it would be possible to abandon the stringent, and expensive, requirements on the orbital geometry of the originally prosed LARES mission (same semimajor axis a = 12,270 km of the existing LAGEOS and inclination i = 70°) by inserting the new spacecraft in a relatively low, and cheaper, orbit ( a = 7500–8000 km, i ∼ 70°) and suitably combining its node Ω with those of LAGEOS and LAGEOS II in order to cancel out the first two even zonal harmonic coefficients of the multipolar expansion of the terrestrial gravitational potential J 2, J 4 along with their temporal variations J ˙ 2 , J ˙ 4 . The total systematic error due to the mismodelling in the remaining even zonal harmonics would amount to ∼1% and would be insensitive to departures of the inclination from the originally proposed value of many degrees. No semisecular long-period perturbations would be introduced because the period of the node, which is also the period of the solar K 1 tidal perturbation, would amount to ∼10 2 days. Since the coefficient of the node of the new satellite would be smaller than 0.1 for such low altitudes, the impact of the non-gravitational perturbations of it on the proposed combination would be negligible. Then, a particular financial and technological effort for suitably building the satellite in order to minimize the non-conservative accelerations would be unnecessary.

Long-period comets with non-gravitational effects

The influence of non-gravitational effects on the motion of long-period comets is analyzed. Investigations were performed for about 60 nearly-parabolic comets discovered during the last thirty years. All three non-gravitational parameters were detected in the motion of 19 comets on the basis of positional observations only. For these comets the standard g(r) function as well as some of its modifications were used to model the ice sublimation from the cometary nucleus. For 14 of 19 comets the orientation of spin axes of the nucleus were also determined. Finally, the magnitude of the non-gravitational effects derived for the long-period comets have been compared with observed the non-gravitational perturbations on periodic comets.

Space-wise approach to satellite gravity field determination in the presence of coloured noise

For many years, the gravity field of the Earth was only seen by satellite geodesy as the main factor affecting the orbit and consequently it was retrieved together with a number of other orbital perturbations. Since the advent of a new generation of accelerometers, non-gravitational perturbations can be separated from the gravity effects and a new era of gravity field estimates from space has been born. During preparatory data analysis for new missions performed by the geodetic community, three approaches have been proposed and numerically tested: the brute force method (direct approach), the semi-analytical (time-wise) method and the space-wise method. In particular, the time-wise method takes advantage of the incoming time flow of data and, after performing a Fourier transform of the observation equations, exploits the prevailing block diagonal structure of the normal equations to estimate the spherical harmonic coefficients of the gravity field. Complementary to this is the space-wise approach, which goes back to the traditional computation of the harmonic coefficients by an integration technique or by least-squares collocation. Some advantages and disadvantages are peculiar to both methods, particularly the space-wise approach, which has for a long time ignored the marked signature of the noise spectrum due to the specific measuring conditions of space-borne accelerometers. The application of a proper Wiener filter, exploiting the correlation along the orbit, embedded into an iterative scheme, seems to be the answer. The solution to this major problem of the space-wise approach is illustrated and simulation results are discussed.

LAGEOS asymmetric reflectivity and corner cube reflectors

Accurate laser tracking of LAGEOS satellites, allows investigation together with gravitational effects, a number of fine nongravitational perturbations in their orbit. Several of these forces are reasonably interpreted in terms of known physical phenomena. Postulated asymmetry in reflectivity of LAGEOS hemispheres is an exception. Here we show that in spite of a recent suggestion, this empirical effect cannot be explained by differential sunlight reflection on germanium and fused silica corner cube reflectors. The true nature of this effect remains puzzling.

Non-gravitational perturbations and evolution of the asteroid main belt

Gravity is the most important force to affect the motion of bodies in the Solar system. At small sizes, however, additional forces must be taken into account to explain fine details of their translational and rotational motion, as well as parameters of their populations. This is because the strength of the non-gravitational perturbations typically increases as . The principal perturbation acting on macroscopic main-belt bodies (sizes up to several kilometers for timescales of about billion years) is due to the anisotropic thermal re-radiation of the absorbed sunlight. In orbital dynamics this is known as the Yarkovsky effect, while in rotational dynamics the same physical phenomenon is called the YORP (Yarkovsky-O'Keefe-Radzievskii-Paddack) effect. We review the main observational implications of the Yarkovsky/YORP effects as understood and evidenced today.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

2003 EH1Is the Quadrantid Shower Parent Comet

The Quadrantid meteor shower in early January is our most intense annual shower. Until now, the parent was thought to have evolved away from the observable part of an old, widely dispersed meteoroid stream. A few years ago, it was found from a small dispersion in a new set of precisely reduced Quadrantid orbits that the stream was only about 500 years old. It was predicted that the parent was still to be found among the meteoroids. I now find that the shower originated from 2003 EH1, a minor planet discovered by LONEOS on March 6, currently passing 0.213 AU outside of Earth orbit in a high-inclination, comet-like orbit with a Tisserand invariant with respect to Jupiter of only 2.064. The orbit agrees with that of the Quadrantids. Small discrepancies in node (~03) and perihelion distance (~0.23 AU) are consistent with the differential evolution of comet and debris that was released from 2003 EH1 about 500 years ago into slightly longer orbits. I conclude that object 2003 EH1 is an intermittently active comet. The large total mass in the shower (~1013 kg) is only consistent with a young age if the meteoroids were shed during a breakup. Comet C/1490 Y1 was observed in about the right time frame for such a breakup and might be a prior sighting when the Quadrantid meteoroid stream was created, but efforts to construct a common orbit that links 2003 EH1 and comet C/1490 Y1 show that nongravitational perturbations or close encounters with Earth may need to be considered.

LAGEOS II perigee rate and eccentricity vector excitations residuals and the Yarkovsky–Schach effect

We have analysed LAGEOS II perigee rate and eccentricity vector excitation residuals over a period of about 7.8 years, adjusting and computing the satellite orbit with the full set of dynamical models included in the GEODYN II software code. The long-term behaviour of these orbital residuals appears to be characterised by several distinct frequencies which are a clear signature of the Yarkovsky–Schach perturbing effect. This non-gravitational perturbation is not included in the GEODYN II models for the orbit determination and analysis. Through an independent numerical analysis, and using the new LOSSAM model to represent the spin-axis behaviour of the satellite, we propagated the Yarkovsky–Schach effect on LAGEOS II perigee rate and compared the results obtained with the orbital residuals. We have thus been able to satisfactorily fit the amplitude of the Yarkovsky–Schach effect to the observed residuals. Our approach here has proven very successful with very positive results. We have been able to obtain a fractional reduction of about 40% of the post-fit rms with respect to the pre-fit value. When analysing the eccentricity vector residuals, we have been able to obtain a better result in the case of the real component, with a fractional reduction of the post-fit rms of about 49% of the initial value. The analysis of the effect's imaginary component in the eccentricity vector rate is more complicated and deserves additional scrutiny. In this case we need a deeper study which includes the analysis of other unmodelled and mismodelled effects acting on the imaginary component. The study performed in this paper will be of significant relevance not only for the geophysical applications involving LAGEOS II orbit analysis, but also for a refined re-analysis of the general relativistic precession produced by the Earth angular momentum, i.e., the Lense-Thirring effect.

A Dissipative Mapping Technique for theN-Body Problem Incorporating Radiation Pressure, Poynting-Robertson Drag, and Solar Wind Drag

By implementing a version of the dissipative mapping technique introduced by R. Malhotra, we have developed a new integration code for the N-body problem that incorporates the effects of radiation pressure, Poynting-Robertson (P-R) drag, and solar wind drag. The advantage of employing the dissipative mapping technique is that it modifies the basic N-body symplectic integration algorithm developed by Wisdom & Holman to allow certain nongravitational effects to be modeled and therefore retains the speed of execution common to codes based upon this algorithm. To achieve this, we have adapted the dissipative mapping technique to the requirements of the forces being modeled. We present the results of tests that demonstrate the suitability of this new dissipative integration code for investigating the dynamical behavior of micron-sized dust particles in heliocentric orbits in the solar system and, more generally, of particles in exosolar planetary systems where the dominant nongravitational perturbations to the particles' astrocentric orbits are due to the effects of radiation pressure, P-R drag, and solar wind drag.

A model for comet 81P/Wild 2

A model is presented for the nucleus of comet 81P/Wild 2 and its activity, based on analysis of dust coma morphology, water and dust production, and nongravitational perturbations of the orbital motion. A four‐apparition composite light curve is derived from ∼500 magnitude estimates. There appear to be two major outgassing sources on the nucleus: one, near a rotation pole, sustains much of preperihelion activity; the other, on the opposite polar hemisphere and closer to the equatorial plane, accounts for the bulk of postperihelion activity. Both regions are active near perihelion. Their surface areas are estimated at 4.5 and 9.5 km2, respectively. With the nucleus probably 4.0 to 6.3 km across, the total outgassing area makes up 11 to nearly 30% of the nucleus surface, unusually high for a short‐period comet, yet consistent with relatively small perturbations of the orbital motion, driven by the momentum transferred to the nucleus by water sublimation. The absence of a more prominent nongravitational effect may largely be due to high dust mass loading of the gas flow, implying its subsonic initial speed. Indeed, the dustier, polar source appears to be the less efficient of the two in transferring the momentum to the nucleus. The comet's short history in the innermost solar system region could account for the relatively large outgassing fraction of the surface. At the Stardust encounter time, more than three months after perihelion, only the near‐equatorial source (the larger, less dusty one) is expected to be active.