Galilean Moons Of Jupiter Research Articles

The nature of the Laplace resonance between the Galilean moons

The Laplace resonance is a mean-motion resonance that involves the three inner Galilean moons of Jupiter. However, its true nature is in part unclear; in particular, different views can be found in the literature on whether the Laplace resonance is a pure three-body resonance or a mere superposition of two-body resonances. To settle this question, we conduct a thorough analysis of the many resonances involved, starting from the two-body 2:1 commensurabilities of the couples Io–Europa and Europa–Ganymede, and ending with the three-body 4:2:1 commensurability between the three moons. By artificially varying the parameters of the system and monitoring its fundamental frequencies, we cartography all resonances involved and their interactions. From the analysis of the individual 2:1 commensurabilities, we find that despite the oscillation of the resonant angles they are not genuine resonances, as the trajectory of the system in the phase space is not enclosed by separatrices. On the contrary, as suggested by previous works, we show that the only current true mean-motion resonance is the pure three-body resonance between all three satellites. Moreover, we find that the current values of the moons’ orbital elements make the Laplace resonance sufficiently separated from the individual two-body 2:1 resonances, preventing chaotic effects from appearing.

A Celebration of Kepler’s Third Law: Harmony, Power Laws, and Keplerian Orbits

Kepler’s greatest achievements are contained in his three laws, which today reappear constantly at the cutting edge of modern astrophysics. The modified third law has been the major workhorse of astronomy and astrophysics in determining the mass of objects throughout the universe. Kepler never revealed why he chose the integers, 2 and 3, to test using Tycho’s data. Because of his attachment to Pythagorean ideas and his knowledge of musical theory, I suggest he was guided by the musical interval known as the perfect fifth, for which the ratio of frequencies is 3/2. The perfect fifth is the most consonant of all intervals except the octave, and, as such, is the basis of all the tuning of stringed instruments. If Kepler had recognized the significance of the perfect fifth in analyzing Tycho’s data, it suggests a very pleasing historical parallelism between music and astronomy. In discovering the third law, Kepler also chanced upon the world's first known power law, which is now found in many forms throughout the earth and heavens. In discovering that the Galilean moons of Jupiter also obeyed the third law, Kepler encountered the phenomenon of scale independence, which is responsible for the ubiquity of power laws across the universe. The third law also played a crucial role in Newton’s discovery of the inverse square law of gravity in 1666. Not only did it provide Newton with a crucial mathematical step, but the third law also had the authority of Tyco’s observations. Christopher Wren and Edmund Halley relied similarly upon the third law for their apparent independent discoveries of the inverse square law.

Analytical framework for mutual approximations

Context. The apparent close encounters of two satellites in the plane of the sky, called mutual approximations, have been suggested as a different type of astrometric observation to refine the moons’ ephemerides. The main observables are then the central instants of the close encounters, which have the advantage of being free of any scaling and orientation errors. However, no analytical formulation is available yet for the observation partials of these central instants, leaving numerical approaches or alternative observables (i.e. derivatives of the apparent distance instead of central instants) as options. Aims. Filling that gap, this paper develops an analytical method to include central instants as direct observables in the ephemerides estimation and assesses the quality of the resulting solution. Methods. To this end, the apparent relative position between the two satellites is approximated by a second-order polynomial near the close encounter. This eventually leads to an expression for mutual approximations’ central instants as a function of the apparent relative position, velocity, and acceleration between the two satellites. Results. The resulting analytical expressions for the central instant partials were validated numerically. In addition, we ran a covariance analysis to compare the estimated solutions obtained with the two types of observables (central instants versus alternative observables), using the Galilean moons of Jupiter as a test case. Our analysis shows that alternative observables are almost equivalent to central instants in most cases. Accurate individual weighting of each alternative observable, accounting for the mutual approximation’s characteristics (which are automatically included in the central instants’ definition), is however crucial to obtain consistent solutions between the two observable types. Using central instants still yields a small improvement of 10–20% of the formal errors in the radial and normal directions (RSW frame), compared to the alternative observables’ solution. This improvement increases when mutual approximations with low impact parameters and large impact velocities are included in the estimation. Conclusions. Choosing between the two observables thus requires careful assessment, taking into account the characteristics of the available observations. Using central instants over alternative observables ensures that the state estimation fully benefits from the information encoded in mutual approximations, which might be necessary depending on the application of the ephemeris solution.

On the stability of Laplace resonance for Galilean moons (Io, Europa, Ganymede).

This paper presents the application of recent ansatz for estimation of stability of the Laplace resonance for Galilean moons (Io, Europa, Ganymede). We estimate over time the eccentricity + semi-major axis in a binary system experiencing the net tidal friction, including the additional tidal heating which comes from the transformation of net transfer of angular momentum between the Galilean moons of Jupiter (due to dynamical features of the Laplace resonance). Presumably, there should be a net transfer of angular momentum between Io and Europa (for the reason that tidal heating on Ganymede seems to be negligible with respect to Io and Europa). We established the fact that Laplace resonance should be valid and stable on a timescale of centuries in the future, but there might be chaotic perturbations less than 0.1\% for the accuracy of such phenomenon. Moreover, the presented ansatz can be used to predict a scheme for optimizing the maneuvers of spacecrafts in the vicinity of Ganymede (due to absence of net transfer of angular momentum between Ganymede and other Galilean moons). The main conclusion stems from previously suggested approach (\cite{ershkov2017tidal.

Observations of the Galilean Moons of Jupiter at Pulkovo in 2018

We present the results of observations of the Galilean moons of Jupiter carried out at the Normal Astrograph of the Pulkovo Observatory in 2018. We obtained 452 positions of the Galilean moons of Jupiter in the Gaia DR1 catalog system (ICRF, J2000.0) and 671 differential coordinates of the satellites relative to each other. The obtained mean errors in the satellites’ normal positions on the right ascension and declination, which demonstrate the intrinsic convergence of the observational results, are eα = 0.003′′ and eδ = 0.003′′, respectively, for the entire observational period. The errors of one difference are σα = 0.070′′, and σδ = 0.067′′, respectively. The equatorial coordinates of the moons were compared to eight motion theories of planets and satellites. On average, the (O–C) residuals in the both coordinates relative to the motion theories are 0.014′′. The best agreement with observations is achieved by combination of all four motion theories of satellites with the planetary theory EPM2017, which yields average (O–C) residuals of approximately 0.01′′ for each of them. The new results were compared to those of the 2016−2017 observational season. As in the past, peculiarities in the behavior of the (O–C) residuals for Io and Ganymede have been noticed.

A Galilean dance 1:2:4 resonant periodic motions and their librations of Jupiter and his Galilean moons

The four Galilean moons of Jupiter were discovered by Galileo in the early 17th century, and their motion was first seen as a miniature solar system. Around 1800 Laplace discovered that the Galilean motion is subjected to an orbital \begin{document}$ 1{:}2{:}4 $\end{document} -resonance of the inner three moons Io, Europa and Ganymedes. In the early 20th century De Sitter gave a mathematical explanation for this in a Newtonian framework. In fact, he found a family of stable periodic solutions by using the seminal work of Poincare, which at the time was quite new. In this paper we review and summarize recent results of Broer, Hansmann and Zhao on the motion of the entire Galilean system, so including the fourth moon Callisto. To this purpose we use a version of parametrised Kolmogorov-Arnol'd-Moser theory where a family of multi-periodic isotropic invariant three-dimensional tori is found that combines the periodic motions of De Sitter and Callisto. The \begin{document}$ 3 $\end{document} -tori are normally elliptic and excite a family of invariant Lagrangean \begin{document}$ 8 $\end{document} -tori that project down to librational motions. Both the \begin{document}$ 3 $\end{document} - and the \begin{document}$ 8 $\end{document} -tori occur for an almost full Hausdorff measure set in the product of corresponding dimension in phase space and a parameter space, where the external parameters are given by the masses of the moons.

Proposed landing on europa: instruments, radiation shielding, planetary protection, and mission

Europa is a moon of the planet Jupiter. Slightly smaller than Earth's own moon, it is the smallest of the four Galilean moons of Jupiter but the sixth largest moon in our solar system. Its primary feature is its highly reflective surface; preliminary indications are that it may have a massive ocean underneath its icy crust. In 2013, the Hubble Space Telescope detected indications of water-vapor plumes [1]. Furthermore, Europa's variegated shell may be the result of geological activity, like Earth's plate tectonics. In 2015, NASA reported that sea salt may coat some surface features on Europa [2]. Outside of Earth, Europa is the most promising body in the solar system for supporting life. Europa might support a base for human habitation while performing interplanetary exploration.

Astrometric Observations of the Galilean Moons of Jupiter at the Pulkovo Normal Astrograph in 2016−2017

We present the results of observations of the Galilean moons of Jupiter carried out at the Normal Astrograph of the Pulkovo Observatory in 2016−2017. We obtained 761 positions of the Galilean moons of Jupiter in the system of the Gaia DR1 catalog (ICRF, J2000.0) and 854 differential coordinates of the satellites relative to each other. The mean errors in the satellites’ normal places and the corresponding root-mean-square deviations are eα = 0.0020′′, eδ = 0.0027′′, σα = 0.0546′′, and σδ = 0.0757′′. The equatorial coordinates of the moons are compared to the motion theories of planets and satellites. On average, the (O–C) residuals in the both coordinates relative to the motion theories are less than 0.031′′. The best agreement with observations is achieved by a combination of the EPM2015 and V. Lainey-V.2.0|V1.1 motion theories, which yields the average (O–C) residuals of approximately 0.02″. Peculiarities in the behavior of the (O–C) residuals and error values in Ganymede have been noticed.

Band Formation and Ocean‐Surface Interaction on Europa and Ganymede

AbstractGeologic activity in the outer H2O ice shells of Europa and Ganymede, Galilean moons of Jupiter, may facilitate material exchange between global water oceans and the icy surface, fundamentally affecting potential habitability and the future search for life. Spacecraft imagery reveals surfaces rich with tectonic bands, predominantly attributed to the extension of brittle ice overlaying a convecting ice layer. However, the details of band‐forming processes and links to potential ocean‐surface exchange have remained elusive. We simulate ice shell faulting and convection with two‐dimensional numerical models and track the movement of “fossil” ocean material frozen into the base of the ice shell and deformed through geologic time. We find that distinct band types form within a spectrum of extensional terrains correlated to lithosphere strength, governed by lithosphere thickness and cohesion. Furthermore, we find that smooth bands formed in weak lithosphere promote exposure of fossil ocean material at the surface.

An Impacting Descent Probe for Europa and the Other Galilean Moons of Jupiter

We present a study of an impacting descent probe that increases the science return of spacecraft orbiting or passing an atmosphere-less planetary body of the solar system, such as the Galilean moons of Jupiter. The descent probe is a carry-on small spacecraft (< 100 kg), to be deployed by the mother spacecraft, that brings itself onto a collisional trajectory with the targeted planetary body in a simple manner. A possible science payload includes instruments for surface imaging, characterisation of the neutral exosphere, and magnetic field and plasma measurement near the target body down to very low-altitudes (~1 km), during the probe's fast (~km/s) descent to the surface until impact. The science goals and the concept of operation are discussed with particular reference to Europa, including options for flying through water plumes and after-impact retrieval of very-low altitude science data. All in all, it is demonstrated how the descent probe has the potential to provide a high science return to a mission at a low extra level of complexity, engineering effort, and risk. This study builds upon earlier studies for a Callisto Descent Probe (CDP) for the former Europa-Jupiter System Mission (EJSM) of ESA and NASA, and extends them with a detailed assessment of a descent probe designed to be an additional science payload for the NASA Europa Mission.

Ground-based observations of the [SII] 6731 Å emission lines of the Io plasma torus

AbstractThe Io Plasma Torus (IPT) is a doughnut-shaped structure of charged particles, composed mainly of sulfur and oxygen ions. The main source of the IPT is the moon Io, the most volcanically active object in the Solar System. Io is the innermost of the Galilean moons of Jupiter, the main source of the magnetospheric plasma and responsible for injecting nearly 1 ton/s of ions into Jupiter's magnetosphere. In this work ground-based observations of the [SII] 6731 Å emission lines are observed, obtained at the MacMath-Pierce Solar Telescope. The results shown here were obtained in late 1997 and occurred shortly after a period of important eruptions observed by the Galileo mission (1996-2003). Several outbursts were observed and periods of intense volcanic activity are important to correlate with periods of brightness enhancements observed at the IPT. The time of response between an eruption and enhancement at IPT is still not well understood.

Observations of the Galilean moons of Jupiter in 2013–2015 at Pulkovo

Observational results are presented for Jupiter and its Galilean moons from the Normal Astrograph at Pulkovo Observatory in 2013–2015. The following data are obtained: 154 positions of the Galilean satellites and 47 calculated positions of Jupiter in the system of the UCAC4 (ICRS, J2000.0) catalogue; the differential coordinates of the satellites relative to one another are determined. The mean errors of the satellites’ normal places in right ascension and declination over the entire observational period are, respectively: eα = 0.0065″ and eδ = 0.0068″, and their standard deviations are σα = 0.0804″ and σδ = 0.0845″. The equatorial coordinates are compared with planetary and satellite motion theories. The average (O–C) residuals in the two coordinates relative to the motion theories are 0.05″ or less. The best agreement with the observations is achieved by a combination of the EPM2011m and V. Lainey-V.2.0|V1.1 motion theories; the average (O–C) residuals are 0.03″ or less. The (O–C) residuals for the features of the positions of Io and Ganymede are comparable with measurement errors. Jupiter’s positions calculated from the observations of the satellites and their theoretical jovicentric coordinates are in good agreement with the motion theories. The (О–С) residuals for Jupiter’s coordinates are, on average, 0.027″ and–0.025″ in the two coordinates.

A VENUS-MASS PLANET ORBITING A BROWN DWARF: A MISSING LINK BETWEEN PLANETS AND MOONS

The co-planarity of solar-system planets led Kant to suggest that they formed from an accretion disk, and the discovery of hundreds of such disks around young stars as well as hundreds of co-planar planetary systems by the Kepler satellite demonstrate that this formation mechanism is extremely widespread. Many moons in the solar system, such as the Galilean moons of Jupiter, also formed out of the accretion disks that coalesced into the giant planets. We report here the discovery of an intermediate system OGLE-2013-BLG-0723LB/Bb composed of a Venus-mass planet orbiting a brown dwarf, which may be viewed either as a scaled down version of a planet plus star or as a scaled up version of a moon plus planet orbiting a star. The latter analogy can be further extended since they orbit in the potential of a larger, stellar body. For ice-rock companions formed in the outer parts of accretion disks, like Uranus and Callisto, the scaled masses and separations of the three types of systems are similar, leading us to suggest that formation processes of companions within accretion disks around stars, brown dwarfs, and planets are similar.

Broad-search algorithms for finding triple-and quadruple-satellite-aided captures at Jupiter from 2020 to 2080

Multiple-satellite-aided capture is a \(\Delta V\)-efficient technique for capturing a spacecraft into orbit at Jupiter. However, finding the times when the Galilean moons of Jupiter align such that three or four of them can be encountered in a single pass is difficult using standard astrodynamics algorithms such as Lambert’s problem. In this paper, we present simple but powerful techniques that simplify the dynamics and geometry of the Galilean satellites so that many of these triple- and quadruple-satellite-aided capture sequences can be found quickly over an extended 60-year time period from 2020 to 2080. The techniques find many low-fidelity trajectories that could be used as initial guesses for future high-fidelity optimization. Results indicate the existence of approximately 3,100 unique triple-satellite-aided capture trajectories and 6 unique quadruple-satellite-aided capture trajectories during the 60-year time period. The entire search takes less than one minute of computational time.

As observações galileanas dos planetas mediceanos de Júpiter e a equivalência do MHS e do MCU

Este trabalho tem como objetivo usar as características orbitais das quatro Luas Galileanas de Júpiter para mostrar a equivalencia do movimento harmônico simples (MHS) com o movimento circular uniforme (MCU). Em nossos cálculos, empregamos os dados obtidos por Galileu Galilei em suas observações pioneiras com o primeiro telescópio da história, realizadas no começo de 1610, e reportadas na obra fundamental Sidereus Nuncius. Comparamos os desenhos de Galileu do Sidereus Nuncius com as imagens da posição de Jupiter e suas luas segundo o Cartes du Ciel, um programa open-source que funciona como efemérides interativa. Com os dados orbitais extraídos dos gráficos de separação angular dos Planetas Mediceanos até Jupiter, obtemos os raios das órbitas assumindo a terceira lei de Kepler.

Layered convection in Io: Implications for short-wavelength surface topography and heat flow

Io, one of the four Galilean moons of Jupiter is remarkable for its extensive volcanism and extreme interior tidal heating. The tidal heating likely yields a very low viscosity asthenosphere and consequently a very high Rayleigh number of O(1012) for convection in the interior. In a state of quasi-steady balance the internally generated heat must be transported from the interior to the base of the Io lithosphere and exhausted to space. The mechanisms whereby the convective radial heat transfer is evacuated involve both conduction and volcanism. Despite Io’s ubiquitous volcanism, only 4% of its mountains (montes) appear to have a volcanic origin and most of the mountainous regions seem to be related to tectonic processes. By employing an original control volume based numerical model we investigate the style of convection in the interior of Io and the correlation of the scale of convection with the Ionian surface heat flux and topography. Our control volume results support the existence of significant asthenospheric heating and demonstrate that short wavelength features of the surface heat flux are well correlated in scale to an expected layered intra-lithospheric style small-scale convection. These numerical analyses suggest that the amplitude of the short wavelength topography of Io is expected to be on the order of a few hundreds of meters. The model results also demonstrate that the Ionian highs cannot be produced by a lithospheric flexure process above the hot upwellings and therefore other tectonic events, such as have previously been suggested; must be responsible for the formation of the high Ionian mountains that reach in excess of 17km in elevation.

MGA trajectory planning with an ACO-inspired algorithm

Given a set of celestial bodies, the problem of finding an optimal sequence of swing-bys, deep space manoeuvres (DSM) and transfer arcs connecting the elements of the set is combinatorial in nature. The number of possible paths grows exponentially with the number of celestial bodies. Therefore, the design of an optimal multiple gravity assist (MGA) trajectory is a NP-hard mixed combinatorial–continuous problem. Its automated solution would greatly improve the design of future space missions, allowing the assessment of a large number of alternative mission options in a short time. This work proposes to formulate the complete automated design of a multiple gravity assist trajectory as an autonomous planning and scheduling problem. The resulting scheduled plan will provide the optimal planetary sequence and a good estimation of the set of associated optimal trajectories. The trajectory model consists of a sequence of celestial bodies connected by two-dimensional transfer arcs containing one DSM. For each transfer arc, the position of the planet and the spacecraft, at the time of arrival, are matched by varying the pericentre of the preceding swing-by, or the magnitude of the launch excess velocity, for the first arc. For each departure date, this model generates a full tree of possible transfers from the departure to the destination planet. Each leaf of the tree represents a planetary encounter and a possible way to reach that planet. An algorithm inspired by ant colony optimization (ACO) is devised to explore the space of possible plans. The ants explore the tree from departure to destination adding one node at the time: every time an ant is at a node, a probability function is used to select a feasible direction. This approach to automatic trajectory planning is applied to the design of optimal transfers to Saturn and among the Galilean moons of Jupiter. Solutions are compared to those found through more traditional genetic-algorithm techniques.

Using simple harmonic motion to follow the Galilean moons—testing Kepler’s third law ona small system

The motion of the four Galilean moons of Jupiter is studied in this work. The moons hadtheir positions with respect to the centre of the planet measured during one week ofobservation by means of telescopic charge coupled device images. It is shown that theirmovement can be well described as a simple harmonic motion. The revolution period andthe orbital radius of each moon could be extracted from the various images and they wereanalysed in terms of Kepler’s third law and Newton’s law of universal gravitation. Themass of Jupiter could be evaluated within a 2% discrepancy using this simple method.

The adjustment to Taylor's constraint in the presence of an ambient field

The need to satisfy Taylor's constraint is probably the single most important constraint on the dynamics of planetary magnetic fields. We point out that the adjustment to Taylor's constraint is considerably more difficult in the Galilean moons of Jupiter than in the Earth, e.g., simply due to the presence of the ambient Jovian field. In particular, if the ambient field is of sufficient strength, weak field solutions are disallowed. The `default option' of falling back to an Ekman state, if Taylor's constraint cannot be satisfied in any other way, is therefore no longer available. The magnetic field must therefore be in a Taylor state, a model-Z state, or something else entirely, but it cannot be in an Ekman state. In this work, we present a simple model of magnetoconvection specifically designed to explore this adjustment to Taylor's constraint in the limit of vanishing viscosity, in the presence of an ambient field. We find that for a weak imposed thermal wind, the system approaches a Taylor state as the strength of the ambient field is increased. Strong thermal wind solutions behave in a very different manner. Initially, as the ambient field strength is increased, the system exhibits many features, indicating that a Taylor state is being approached. However, it never reaches a Taylor state, evolving instead to a model-Z state as the ambient field strength is increased yet further.

Absence of a magnetic-field signature in plasma-wave observations at Callisto

The galilean moons of Jupiter are substantial bodies—three of them are larger than the Earth's Moon, and one is larger than Mercury—yet little has been known about them until very recently. The discovery of a magnetosphere1 and magnetic field2 associated with Ganymede was surprising, and raised the possibility that other galilean satellites, particularly Callisto (which is the second largest after Ganymede), also might have an internally generated magnetic field. Here we report observations of plasma waves around Callisto, detected during the recent fly-by of the Galileo spacecraft. The nature of the plasma waves indicates that Callisto, unlike Ganymede, does not have a magnetosphere or an internal magnetic field. The electron density near Callisto, however, is substantially higher than that in Jupiter's magnetosphere at this orbital radius, indicating that Callisto is a significant source of locally generated plasma. This plasma most probably comes from a tenuous atmosphere around Callisto, which may be similar to the hydrogen cloud around Ganymede, as the electron densities are somewhat comparable.