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Concept: Celestial mechanics


The spin and orbital magnetic moments, as well as the magnetic anisotropy energy (MAE), of small 4d transition metal ™ clusters are systematically studied by using the spin-orbit coupling (SOC) implementation of the density-functional theory (DFT). The effects of spin-orbit interactions on geometrical structures and spin moments are too weak to alternate relative stabilities of different low-lying isomers. Remarkable orbital contributions to cluster magnetic moments are identified in Ru, Rh, and Pd clusters, in contrast to immediate quenching of the atomic orbital moment at the dimer size in other elemental clusters. More interestingly, there is always collinearity between total spin and orbital moments (antiferromagnetic or ferromagnetic coupling depends on the constituent atoms whose 4d subshell is less or more than half-filled). The clusters preserve the validity of Hund’s rules for the sign of orbital moment. The calculations on MAEs reveal the complicated changes of the easy axes in different structures. The perturbation theory and the first-principles calculations are compared to emphasize how MAEs evolve with cluster size. Finally, large orbital moments combined with strong spin-orbit coupling are proposed to account for large MAEs in Ru, Rh, and Pd clusters.

Concepts: Quantum mechanics, Angular momentum, Fundamental physics concepts, Atom, Magnetism, Celestial mechanics, Magnetic anisotropy, Electron shell


When speed is of the essence: After photoisomerization to its metastable cis form, an azo dye must undergo fast thermal isomerization back to the trans form to be suitable for real-time information transmission. The azopyrimidine shown has a relaxation time, τ, of just 40 ns under physiological conditions as well as high biocompatibility, as determined by Escherichia coli growth in its presence.

Concepts: Time, Escherichia coli, Dye, Azo compound, Azo compounds, Celestial mechanics, Azo dyes, Azobenzene


A measurement of Newton’s gravitational constant G has been made with a cryogenic torsion pendulum operating below 4 K in a dynamic mode in which G is determined from the change in torsional period when a field source mass is moved between two orientations. The source mass was a pair of copper rings that produced an extremely uniform gravitational field gradient, whereas the pendulum was a thin fused silica plate, a combination that minimized the measurement’s sensitivity to error in pendulum placement. The measurement was made using an as-drawn CuBe torsion fibre, a heat-treated CuBe fibre, and an as-drawn Al5056 fibre. The pendulum operated with a set of different large torsional amplitudes. The three fibres yielded high Q-values: 82 000, 120 000 and 164 000, minimizing experimental bias from fibre anelasticity. G-values found with the three fibres are, respectively: {6.67435(10),6.67408(15),6.67455(13)}×10(-11) m(3) kg(-1) s(-2), with corresponding uncertainties 14, 22 and 20 ppm. Relative to the CODATA2010 G-value, these are higher by 77, 37 and 107 ppm, respectively. The unweighted average of the three G-values, with the unweighted average of their uncertainties, is 6.67433(13)×10(-11) m(3) kg(-1) s(-2) (19 ppm).

Concepts: General relativity, Mass, Gravitation, Celestial mechanics, Prime number, Gravitational constant, Standard gravity, Newton's law of universal gravitation


The origin of the Moon’s large-scale topography is important for understanding lunar geology, lunar orbital evolution and the Moon’s orientation in the sky. Previous hypotheses for its origin have included late accretion events, large impacts, tidal effects and convection processes. However, testing these hypotheses and quantifying the Moon’s topography is complicated by the large basins that have formed since the crust crystallized. Here we estimate the large-scale lunar topography and gravity spherical harmonics outside these basins and show that the bulk of the spherical harmonic degree-2 topography is consistent with a crust-building process controlled by early tidal heating throughout the Moon. The remainder of the degree-2 topography is consistent with a frozen tidal-rotational bulge that formed later, at a semi-major axis of about 32 Earth radii. The probability of the degree-2 shape having both tidal-heating and frozen shape characteristics by chance is less than 1%. We also infer that internal density contrasts eventually reoriented the Moon’s polar axis by 36 ± 4°, to the configuration we observe today. Together, these results link the geology of the near and far sides, and resolve long-standing questions about the Moon’s large-scale shape, gravity and history of polar wander.

Concepts: Earth, Moon, Celestial mechanics, Crust, Tide, Tidal force, Orbital period


Saturn’s moon Enceladus emits a plume of water vapour and micrometre-sized ice particles from a series of warm fissures located near its south pole. This geological activity could be powered or controlled by variations in the tidal stresses experienced by Enceladus as it moves around its slightly eccentric orbit. The specific mechanisms by which these varying stresses are converted into heat, however, are still being debated. Furthermore, it has proved difficult to find a clear correlation between the predicted tidal forces and measured temporal variations in the plume’s gas content or the particle flux from individual sources. Here we report that the plume’s horizontally integrated brightness is several times greater when Enceladus is near the point in its eccentric orbit where it is furthest from Saturn (apocentre) than it is when near the point of closest approach to the planet (pericentre). More material therefore seems to be escaping from beneath Enceladus' surface at times when geophysical models predict its fissures should be under tension and therefore may be wider open.

Concepts: Scientific method, Water, Earth, Planet, Moon, Celestial mechanics, Saturn, Tide


Cometary outgassing can produce torques that change the spin state of the cometary nucleus, which in turn influences the evolution and lifetime of the comet. If these torques increase the rate of rotation to the extent that centripetal forces exceed the material strength of the nucleus, the comet can fragment. Torques that slow down the rotation can cause the spin state to become unstable, but if the torques persist the nucleus can eventually reorient itself and the rotation rate can increase again. Simulations predict that most comets go through a short phase of rapid changes in spin state, after which changes occur gradually over longer times. Here we report observations of comet 41P/Tuttle-Giacobini-Kresák during its close approach to Earth (0.142 astronomical units, approximately 21 million kilometres, on 1 April 2017) that reveal a rapid decrease in rotation rate. Between March and May 2017, the apparent rotation period of the nucleus increased from 20 hours to more than 46 hours-a rate of change of more than an order of magnitude larger than has hitherto been measured. This phenomenon must have been caused by the gas emission from the comet aligning in such a way that it produced an anomalously strong torque that slowed the spin rate of the nucleus. The behaviour of comet 41P/Tuttle-Giacobini-Kresák suggests that it is in a distinct evolutionary state and that its rotation may be approaching the point of instability.

Concepts: Fundamental physics concepts, Torque, Moon, Rotation, Celestial mechanics, Jupiter, Comet, Comets


Many exoplanetary systems containing hot Jupiters are observed to have highly misaligned orbital axes relative to the stellar spin axes. Kozai-Lidov oscillations of orbital eccentricity and inclination induced by a binary companion, in conjunction with tidal dissipation, constitute a major channel for the production of hot Jupiters. We demonstrate that gravitational interaction between the planet and its oblate host star can lead to chaotic evolution of the stellar spin axis during Kozai cycles. As parameters such as the planet mass and stellar rotation period are varied, periodic islands can appear in an ocean of chaos, in a manner reminiscent of other dynamical systems. In the presence of tidal dissipation, the complex spin evolution can leave an imprint on the final spin-orbit misalignment angles.

Concepts: Chaos theory, Moon, Celestial mechanics, Star, Jupiter, Neptune, Pluto


Asteroid 21 Lutetia was approached by the Rosetta spacecraft on 10 July 2010. The additional Doppler shift of the spacecraft radio signals imposed by 21 Lutetia’s gravitational perturbation on the flyby trajectory were used to determine the mass of the asteroid. Calibrating and correcting for all Doppler contributions not associated with Lutetia, a least-squares fit to the residual frequency observations from 4 hours before to 6 hours after closest approach yields a mass of (1.700 ± 0.017) × 10(18) kilograms. Using the volume model of Lutetia determined by the Rosetta Optical, Spectroscopic, and Infrared Remote Imaging System (OSIRIS) camera, the bulk density, an important parameter for clues to its composition and interior, is (3.4 ± 0.3) × 10(3) kilograms per cubic meter.

Concepts: Fundamental physics concepts, Density, Mars, Kilogram, Celestial mechanics, ORBit, Comet, 21 Lutetia


We have detected in Cassini spacecraft data the signature of the periodic tidal stresses within Titan, driven by the eccentricity (e = 0.028) of its 16-day orbit around Saturn. Precise measurements of the acceleration of Cassini during six close flybys between 2006 and 2011 have revealed that Titan responds to the variable tidal field exerted by Saturn with periodic changes of its quadrupole gravity, at about 4% of the static value. Two independent determinations of the corresponding degree-2 Love number yield k(2) = 0.589 ± 0.150 and k(2) = 0.637 ± 0.224 (2σ). Such a large response to the tidal field requires that Titan’s interior be deformable over time scales of the orbital period, in a way that is consistent with a global ocean at depth.

Concepts: Moon, Celestial mechanics, Jupiter, Neptune, Saturn, Natural satellite, Titan, Cassini–Huygens


The discovery of transiting circumbinary planets by the Kepler mission suggests that planets can form efficiently around binary stars. None of the stellar binaries currently known to host planets has a period shorter than 7 d, despite the large number of eclipsing binaries found in the Kepler target list with periods shorter than a few days. These compact binaries are believed to have evolved from wider orbits into their current configurations via the so-called Lidov-Kozai migration mechanism, in which gravitational perturbations from a distant tertiary companion induce large-amplitude eccentricity oscillations in the binary, followed by orbital decay and circularization due to tidal dissipation in the stars. Here we explore the orbital evolution of planets around binaries undergoing orbital decay by this mechanism. We show that planets may survive and become misaligned from their host binary, or may develop erratic behavior in eccentricity, resulting in their consumption by the stars or ejection from the system as the binary decays. Our results suggest that circumbinary planets around compact binaries could still exist, and we offer predictions as to what their orbital configurations should be like.

Concepts: Planet, White dwarf, Celestial mechanics, Star, Extrasolar planet, Binary star, Multiple star