On the justification of topological derivative for wave-based qualitative imaging of finite-sized defects in bounded media

PurposeThis work contributes to the general problem of justifying the validity of the heuristic that underpins medium imaging using topological derivatives (TDs), which involves the sign and the spatial decay away from the true anomaly of the TD functional. The author considers here the identification of finite-sized (i.e. not necessarily small) anomalies embedded in bounded media and affecting the leading-order term of the acoustic field equation.Design/methodology/approachTD-based imaging functionals are reformulated for analysis using a suitable factorization of the acoustic fields, which is facilitated by a volume integral formulation. The three kinds of TDs (single-measurement, full-measurement and eigenfunction-based) studied in this work are given expressions whose structure allows to establish results on their sign and decay properties. The latter are obtained using analytical methods involving classical identities on Bessel functions and Legendre polynomials, as well as asymptotic approximations predicated on spatial scaling assumptions.FindingsThe sign component of the TD imaging heuristic is found to be valid for multistatic experiments and if the sought anomaly satisfies a bound (on a certain operator norm) involving its geometry, its contrast and the operating frequency. Moreover, upon processing the excitation and data by applying suitably-defined bounded linear operatirs to them, the magnitude component of the TD imaging heuristic is proved under scaling assumptions where the anomaly is small relative to the probing region, the latter being itself small relative to the propagation domain. The author additionally validates both components of the TD imaging heuristic when the probing excitation is taken as an eigenfunction of the source-to-measurement operator, with a focusing effect analogous to that achieved in time-reversal based methods taking place. These findings extend those of earlier studies to the case of finite-sized anomalies embedded in bounded media.Originality/valueThe originality of the paper lies in the theoretical justifications of the TD-based imaging heuristic for finite-sized anomalies embedded in bounded media.

CMMSE: Study of a new symmetric anomaly in the elliptic, hyperbolic and parabolic Keplerian motion

In the present work, we define a new anomaly, $\Psi$, termed semifocal anomaly. It is determined by the mean between the true anomaly, $f$, and the antifocal anomaly, $f^{\prime}$; Fukushima defined $f^{\prime}$ as the angle between the periapsis and the secondary around the empty focus. In this first part of the paper, we take an approach to the study of the semifocal anomaly in the hyperbolic motion and in the limit case correspoding to the parabolic movement. From here we find a relation beetween the semifocal anomaly and the true anomaly that holds independently of the movement type. We focus on the study of the two-body problem when this new anomaly is used as the temporal variable.\\ In the second part, we show the use of this anomaly —combined with numerical integration methods— to improve integration errors in one revolution. Finally, we analyze the errors committed in the integration process —depending on several values of the eccentricity— for the elliptic, parabolic and hyperbolic cases in the apsidal region.

Increasing the Accuracy of Orbital Elements for a Satellite in a Low Earth Orbit under the Influence of Atmospheric Drag Using Adams-Bashforth Method

The perturbed equation of motion can be solved by using many numerical methods. Most of these solutions were inaccurate; the fourth order Adams-Bashforth method is a good numerical integration method, which was used in this research to study the variation of orbital elements under atmospheric drag influence. A satellite in a Low Earth Orbit (LEO), with altitude form perigee = 200 km, was selected during 1300 revolutions (84.23 days) and ASat / MSat value of 5.1 m2/ 900 kg. The equations of converting state vectors into orbital elements were applied. Also, various orbital elements were evaluated and analyzed. The results showed that, for the semi-major axis, eccentricity and inclination have a secular falling discrepancy, Longitude of Ascending Node is periodic, Argument of Perigee has a secular increasing variation, while true anomaly grows linearly from 0 to 360°. Furthermore, all orbital elements, excluding Longitude of Ascending Node, Argument of Perigee, and true anomaly, were more affected by drag than other orbital elements, through their falling as the time passes. The results illustrate a high correlation as compared with literature reviews in this field.

On normal coordinates in the vicinity of the Lagrangian libration points of the restricted elliptic three-body problem

A planar restricted elliptic three-body problem is considered. The motions close to the triangular libration points are studied. The problem parameters (the eccentricity of the orbit of the main attracting bodies and the ratio of their masses) are assumed to lie inside the linear stability region of the libration points. The magnitude of eccentricity is considered small. A linear canonical, periodic in true anomaly transformation is obtained analytically up to the second degree of eccentricity inclusive that reduces the Hamiltonian function of the linearized equations of perturbed motion to real normal form in the vicinity of the libration points. This form corresponds to two harmonic oscillators not connected to one another, with frequencies depending on the problem parameters. In constructing the normalizing canonical transformation, the Depri-Hori method of the perturbation theory of Hamiltonian systems is used. Its implementation in the problem under study relies heavily on computer systems of analytical calculations.

Helios spacecraft data revisited: detection of cometary meteoroid trails by following in situ dust impacts

Context. Cometary meteoroid trails exist in the vicinity of comets, forming a fine structure of the interplanetary dust cloud. The trails consist predominantly of the largest cometary particles (with sizes of approximately 0.1 mm–1 cm), which are ejected at low speeds and remain very close to the comet orbit for several revolutions around the Sun. In the 1970s, two Helios spacecraft were launched towards the inner Solar System. The spacecraft were equipped with in situ dust sensors which measured the distribution of interplanetary dust in the inner Solar System for the first time. Recently, when re-analysing the Helios data, a clustering of seven impacts was found, detected by Helios in a very narrow region of space at a true anomaly angle of 135 ± 1°, which the authors considered as potential cometary trail particles. However, at the time, this hypothesis could not be studied further. Aims. We re-analyse these candidate cometary trail particles in the Helios dust data to investigate the possibility that some or all of them indeed originate from cometary trails and we constrain their source comets. Methods. The Interplanetary Meteoroid Environment for eXploration (IMEX) dust streams in space model is a new and recently published universal model for cometary meteoroid streams in the inner Solar System. We use IMEX to study the traverses of cometary trails made by Helios. Results. During ten revolutions around the Sun, the Helios spacecraft intersected 13 cometary trails. For the majority of these traverses the predicted dust fluxes are very low. In the narrow region of space where Helios detected the candidate dust particles, the spacecraft repeatedly traversed the trails of comets 45P/Honda-Mrkos-Pajdušáková and 72P/Denning-Fujikawa with relatively high predicted dust fluxes. The analysis of the detection times and particle impact directions shows that four detected particles are compatible with an origin from these two comets. By combining measurements and simulations we find a dust spatial density in these trails of approximately 10−8–10−7 m−3. Conclusions. The identification of potential cometary trail particles in the Helios data greatly benefited from the clustering of trail traverses in a rather narrow region of space. The in situ detection and analysis of meteoroid trail particles which can be traced back to their source bodies by spacecraft-based dust analysers provides a new opportunity for remote compositional analysis of comets and asteroids without the necessity to fly a spacecraft to or even land on those celestial bodies. This provides new science opportunities for future missions like DESTINY+ (Demonstration and Experiment of Space Technology for INterplanetary voYage with Phaethon fLyby and dUst Science), Europa Clipper, and the Interstellar Mapping and Acceleration Probe.

Exospheric Na distributions along the Mercury orbit with the THEMIS telescope

<p>The variability of Na exosphere of Mercury shows time scales from less than one hour to seasonal variations. While the faster variations, accounting of about 10-20% of fluctuations are probably linked to the planetary response to solar wind and Interplanetary Magnetic Field variability, the seasonal variations (up to about 80%) should be explained by complex mechanisms involving different surface release processes, loss, source and migrations of the exospheric Na atoms. Eventually, a Na annual cycle can be identified. In the past, ground-based observations and equatorial density from MESSENGER data have been analysed. In this study, for a better investigation of the exospheric Na features, we have studied the local time and latitudinal distributions of the exospheric Na column density as a function of the True Anomaly Angle (TAA) of Mercury by means of the extended dataset of images, collected from 2009 to 2013, by the THEMIS solar telescope. Our results show that the THEMIS images, in agreement with previous results, registered a strong general increase at aphelion and a dawn ward emission predominance with respect to dusk ward and subsolar region between 90° and 150° TAA. Unlikely other analyses, ours evidences a predominance of subsolar column density along the rest of Mercury’s orbit. An unexpected relationship between Northward or Southward peak emission and both TAA and local time is also evidenced by our analysis. This result seems to contradict previous results obtained from different data sets and it is not easily explained, thus it requires further investigations.</p>

Controlling the Perturbations of Solar Radiation Pressure on the Lorentz Spacecraft

The aim of the present paper is to analyze the viability of using Lorentz Force (LF) acting on a charged spacecraft to neutralize the effects of Solar Radiation Pressure (SRP) on the longitude of the ascending node and the argument of perigee of the spacecraft’s orbit. In this setting, the Gauss planetary equations for LF and SRP are presented and averaged over the true anomaly. The averaged variations for the longitude of the ascending node (h) and the argument of perigee (g) are invariant under the symmetry (i,g)⟶(−i,−g) due to Lorentz Force. The sum of change rates due to both perturbing forces of LF and SRP is assigned by zero to estimate the charge amount to balance the variation for the argument of perigee and longitude of ascending. Numerical investigations have been developed to show the evolution of the charge quantity for different orbital parameters at both Low Earth and Geosynchronous Orbits.

The use of Kepler solver in numerical integrations of quasi-Keplerian orbits

ABSTRACT A Kepler solver is an analytical method used to solve a two-body problem. In this paper, we propose a new correction method by slightly modifying the Kepler solver. The only change to the analytical solutions is that the obtainment of the eccentric anomaly relies on the true anomaly that is associated with a unit radial vector calculated by an integrator. This scheme rigorously conserves all integrals and orbital elements except the mean longitude. However, the Kepler energy, angular momentum vector, and Laplace–Runge–Lenz vector for perturbed Kepler problems are slowly varying quantities. However, their integral invariant relations give the quantities high-precision values that directly govern five slowly varying orbital elements. These elements combined with the eccentric anomaly determine the desired numerical solutions. The newly proposed method can considerably reduce various errors for a post-Newtonian two-body problem compared with an uncorrected integrator, making it suitable for a dissipative two-body problem. Spurious secular changes of some elements or quasi-integrals in the outer Solar system may be caused by short integration times of the fourth-order Runge–Kutta algorithm. However, they can be eliminated in a long integration time of 108 yr by the proposed method, similar to Wisdom–Holman second-order symplectic integrator. The proposed method has an advantage over the symplectic algorithm in the accuracy but gives a larger slope to the phase error growth.

Exospheric Na distributions along the Mercury orbit with the THEMIS telescope

<p>The variability of Na exosphere of Mercury shows time scales from less than one hour to seasonal variations. While the faster variations, accounting of about 10-20% of fluctuations are probably linked to the planet response to solar wind and IMF variability, the seasonal variations (up to about 80%) should be explained by a complex mechanisms involving different surface release processes, loss, source and migrations of the exospheric Na atoms. Eventually, a Na annual cycle can be identified. In the past, integrated disk emission from ground-based observations and equatorial density from MESSENGER have been analysed. In this study, for a better investigation of the exospheric Na features, we have studied the local time and latitudinal distributions of the exospheric Na column density as a function of the True Anomaly Angle (TAA) of Mercury by means of the extended dataset of images, collected from 2009 to 2013, by the THEMIS solar telescope. In particular, THEMIS images, in agreement with previous results, registered a strong general increase at aphelion and a dawn ward emission predominance with respect to dusk ward and subsolar region between 90° and 150° TAA. We find a predominance of subsolar column density along the rest of the Mercury orbit. Also an unexpected relation between Northward or Southward peak emission and both TAA and local time is evidenced by our analysis requiring further investigations. Possible relationship with distance from the dust disk or IMF polarity is being considering.</p>

Velocity field of image points in satellite imagery of planet’s surface

This paper derives a formula for calculating the velocity of arbitrary point in the field of view of the satellite camera in the process of orbital imagery of the planet's surface. The formula describes the velocity as a function of the point coordinates in the image fixation plane, the focal length of the imaging camera, the orbital parameters of the satellite, the angular velocity of the planet’s rotation, the coordinates of the satellite’s true anomaly in the orbit, the orientation angles of the imaging camera relative to the orbit, and the angular velocity of the camera. The paper also provides examples of the formula use for calculating the velocity field of image points for different sets of imagery parameters.The formula is derived under the assumption that the planet is a homogeneous absolutely solid body, shaped as a ball, and rotating at a constant angular velocity; as a result, the satellite moves in a Keplerian orbit, with the planet located at one of the orbit’s foci. Despite this idealization, the derived formula can be used in developing algorithms for remote sensing of the Earth, for building and optimizing the image blurring compensators, for solving the problem of blurred image recovery, and for a number of other problems related to satellite imagery preparation, execution, and processing the results.