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Register a new userOrbits and resonances of the regular moons of Neptune
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We report integrated orbital fits for the inner regular moons of Neptune based on the most complete astrometric data set to date, with observations from Earth-based telescopes, Voyager 2, and the Hubble Space Telescope covering 1981-2016. We summarize the results in terms of state vectors, mean orbital elements, and orbital uncertainties. The estimated masses of the two innermost moons, Naiad and Thalassa, are $GM_{Naiad}$= 0.0080 $pm$ 0.0043 $km^3 s^{-2}$ and $GM_{Thalassa}$=0.0236 $pm$ 0.0064 $km^3 s^{-2}$, corresponding to densities of 0.80 $pm$ 0.48 $g cm^{-3}$ and 1.23 $pm$ 0.43 $g cm^{-3}$, respectively. Our analysis shows that Naiad and Thalassa are locked in an unusual type of orbital resonance. The resonant argument 73 $dot{lambda}_{Thalassa}$-69 $dot{lambda}_{Naiad}$-4 $dot{Omega}_{Naiad}$ $approx$ 0 librates around 180 deg with an average amplitude of ~66 deg and a period of ~1.9 years for the nominal set of masses. This is the first fourth-order resonance discovered between the moons of the outer planets. More high precision astrometry is needed to better constrain the masses of Naiad and Thalassa, and consequently, the amplitude and the period of libration. We also report on a 13:11 near-resonance of Hippocamp and Proteus, which may lead to a mass estimate of Proteus provided that there are future observations of Hippocamp. Our fit yielded a value for Neptunes oblateness coefficient of $J_2$=3409.1$pm$2.9 $times 10^{-6}$.
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Satellites of giant planets thought to form in gaseous circumplanetary disks (CPDs) during the late planet-formation phase, but it was unknown so far whether smaller mass planets, such as the ice giants could form such disks, thus moons there. We combined radiative hydrodynamical simulations with satellite population synthesis to investigate the question in the case of Uranus and Neptune. For both ice giants we found that a gaseous CPD is created at the end of their formation. The population synthesis confirmed that Uranian-like, icy, prograde satellite-system could form in these CPDs within a couple of $10^5$ years. This means that Neptune could have a Uranian-like moon-system originally that was wiped away by the capture of Triton. Furthermore, the current moons of Uranus can be reproduced by our model without the need for planet-planet impact to create a debris disk for the moons to grow. These results highlight that even ice giants -- that among the most common mass-category of exoplanets -- can also form satellites, opening a way to a potentially much larger population of exomoons than previously thought.
The stability of Trojan type orbits around Neptune is studied. As the first part of our investigation, we present in this paper a global view of the stability of Trojans on inclined orbits. Using the frequency analysis method based on the FFT technique, we construct high resolution dynamical maps on the plane of initial semimajor axis $a_0$ versus inclination $i_0$. These maps show three most stable regions, with $i_0$ in the range of $(0^circ,12^circ), (22^circ,36^circ)$ and $(51^circ,59^circ)$ respectively, where the Trojans are most probably expected to be found. The similarity between the maps for the leading and trailing triangular Lagrange points $L_4$ and $L_5$ confirms the dynamical symmetry between these two points. By computing the power spectrum and the proper frequencies of the Trojan motion, we figure out the mechanisms that trigger chaos in the motion. The Kozai resonance found at high inclination varies the eccentricity and inclination of orbits, while the $ u_8$ secular resonance around $i_0sim44^circ$ pumps up the eccentricity. Both mechanisms lead to eccentric orbits and encounters with Uranus that introduce strong perturbation and drive the objects away from the Trojan like orbits. This explains the clearance of Trojan at high inclination ($>60^circ$) and an unstable gap around $44^circ$ on the dynamical map. An empirical theory is derived from the numerical results, with which the main secular resonances are located on the initial plane of $(a_0,i_0)$. The fine structures in the dynamical maps can be explained by these secular resonances.
Aims. Current and upcoming space missions may be able to detect moons of transiting extra-solar planets. In this context it is important to understand if exomoons are expected to exist and what their possible properties are. Methods. Using estimates for the stability of exomoon orbits from numerical studies, a list of 87 known transiting exoplanets is tested for the potential to host large exomoons. Results. For 92% of the sample, moons larger than Luna can be excluded on prograde orbits, unless the parent exoplanets internal structure is very different from the gas-giants of the solar system. Only WASP-24b, OGLE2-TR-L9, CoRoT-3b and CoRoT-9b could have moons above 0.4 moplus, which is within the likely detection capabilities of current observational facilities. Additionally, the range of possible orbital radii of exomoons of the known transiting exoplanets, with two exceptions, is below 8 Jupiter-radii and therefore rather small.
Previously, we have considered the equations of motion of the three-body problem in a Lagrange form (which means a consideration of relative motions of 3-bodies in regard to each other). Analyzing such a system of equations, we considered the case of small-body motion of negligible mass around the 2-nd of two giant-bodies (which are rotating around their common centre of masses on Kepler trajectories), the mass of which is assumed to be less than the mass of central body. In the current development, we have derived a key parameter that determines the character of quasi-circular motion of the small 3-rd body relative to the 2-nd body (Planet). Namely, by making several approximations in the equations of motion of the three-body problem, such the system could be reduced to the key governing Riccati-type ordinary differential equations. Under assumptions of R3BP (restricted three-body problem), we additionally note that Riccati-type ODEs above should have the invariant form if the key governing (dimensionless) parameter remains in the range 0.001-0.01. Such an amazing fact let us evaluate the forbidden zones for Moons orbits in the inner Solar system or the zones of the meanings of distances (between Moon-Planet) for which the motion of small body could be predicted to be unstable according to basic features of the solutions of Riccati-type.
The formation of Uranus regular moons has been suggested to be linked to the origin of its enormous spin axial tilt (~98o). A giant impact between proto-Uranus and a 2-3 M_Earth impactor could lead to a large tilt and to the formation of a debris disc, where prograde and circular satellites are accreted. The most intriguing features of the current regular Uranian satellite system is that it possesses a positive trend in the mass-distance distribution and likely also in the bulk density, implying that viscous spreading of the debris disc after the giant impact plays a crucial role in shaping the architecture of the final system. In this paper, we investigate the formation of Uranus satellites by combining results of SPH simulations for the giant impact, a 1D semi-analytic disc model for viscous spreading of the post-impact debris disc, and N-body simulations for the assembly of satellites from a disc of moonlets. Assuming the condensed rock (i.e., silicate) remains small and available to stick onto the relatively rapid growing condensed water-ice, we find that the best case in reproducing the observed mass and bulk composition of Uranus satellite system is a pure-rocky impactor with 3 M_Earth colliding with the young Uranus with an impact parameter b = 0.75. Such an oblique collision could also naturally explain Uranus large tilt and possibly, its low internal heat flux. The giant impact scenario can naturally explain the key features of Uranus and its regular moons. We therefore suggest that the Uranian satellite system formed as a result of an impact rather than from a circumplanetary disc. Objects beyond the water snow-line could be dominated by rocky objects similar to Pluto and Triton. Future missions to Uranus and its satellite system would further constrain the properties of Uranus and its moons and provide further insight on their formation processes.
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