Semi-Analytical Estimates for the Orbital Stability of Earth’s Satellites

Normal form stability estimates are a basic tool of Celestial Mechanics for characterizing the long-term stability of the orbits of natural and artificial bodies. Using high-order normal form constructions, we provide three different estimates for the orbital stability of point-mass satellites orbiting around the Earth. (i) We demonstrate the long-term stability of the semimajor axis within the framework of the $$J_2$$ J 2 problem, by a normal form construction eliminating the fast angle in the corresponding Hamiltonian and obtaining $${\mathcal {H}}_{J_2}$$ H J 2 . (ii) We demonstrate the stability of the eccentricity and inclination in a secular Hamiltonian model including lunisolar perturbations (the ‘geolunisolar’ Hamiltonian $${\mathcal {H}}_\mathrm{gls}$$ H gls ), after a suitable reduction of the Hamiltonian to the Laplace plane. (iii) We numerically examine the convexity and steepness properties of the integrable part of the secular Hamiltonian in both the $${\mathcal {H}}_{J_2}$$ H J 2 and $${\mathcal {H}}_\mathrm{gls}$$ H gls models, which reflect necessary conditions for the holding of Nekhoroshev’s theorem on the exponential stability of the orbits. We find that the $${\mathcal {H}}_{J_2}$$ H J 2 model is non-convex, but satisfies a ‘three-jet’ condition, while the $${\mathcal {H}}_\mathrm{gls}$$ H gls model restores quasi-convexity by adding lunisolar terms in the Hamiltonian’s integrable part.

Why NASA may be legally required to sterilize Mars samples to protect Earth's biosphere - 19 years minimum until ready to receive unsterilized samples with existing laws - advantages of orbits above GEO for preliminary telerobotic study instead

NASA plans to return a sample from Mars in the 2020s. However they have not yet started on the legal process to return such a sample safely. There are many laws that already exist that protect Earth’s biosphere. Previous sample return studies have shown that we need to build a sample receiving facility to prevent adverse changes to the environment of Earth from a sample return. This paper examines the timescale based on an end to end requirement, that NASA are required to know what it is they need to build before approving funds for the build. This will not be known until the end of the legal process.We find that it is not possible, with current laws and technology, to have a facility ready to receive unsterilized samples on this timescale. However we find that it is possible to sterilize the samples sufficiently for planetary protection requirements while preserving both astrobiological and geological interest. We also propose as an alternative to return the sample to an orbit in the Laplace plane above GEO, as optimal for protection of Earth, the Moon, and other satellites. This will not delay the geological studies as sterilized subsamples can be returned immediately, and it will permit study of unsterilized material in situ telerobotically. We also look at particular worst case scenarios, which have not been considered in detail before, such as the return of a mirror life blue-green algae, capable of living on Mars and almost anywhere on Earth. We suggest that it is a high priority to determine whether Martian life can be safely mixed into the terrestrial biosphere, and to learn what safety protocols are needed to return it safely. We find that there could be life on Mars that can never be mixed into Earth’s biosphere safely. Finding the answers to this should be a top priority for both scientists and space colonization enthusiasts as the future possibilities, and opportunities, that are open to us depend on whether there is life on Mars and what its nature is.

Cassini state of Galilean Moons: Influence of a subsurface ocean

<p>Large moons such as the Galilean satellites are thought to be in an equilibrium rotation state, called a Cassini state (Peale, 1969). This state is characterized by a synchronous rotation and a precession rate of the rotation axis that is equal to the precession rate of the normal to its orbit. It also implies that the spin axis, the normal to the orbit and the normal to the Laplace plane are coplanar with a (nearly) constant obliquity.</p><p>For rigid bodies, up to 4 possible Cassini states exist, but not all of them are stable. It is generally assumed that the Galilean satellites are in Cassini State I for which the obliquity is close to zero (see e.g. Baland et al. 2012). However, it is also theoretically possible that these satellites occupy or occupied another Cassini state.</p><p>We here investigate how the interior structure, and in particular the presence of a subsurface ocean, influences the existence and stability of the different possible Cassini states.</p><p><em>References :</em></p><p>Baland, R.M., Yseboodt, M. and Van Hoolst, T. (2012). Obliquity of the Galilean satellites: The influence of a global internal liquid layer. Icarus 220, 435-448.</p><p>Peale, S. (1969). Generalized Cassini’s laws. Astron. J. 74 (3), 483-489.</p>

Chaos in the inert Oort cloud

Context. Distant trans-Neptunian objects are subject to planetary perturbations and galactic tides. The former decrease with the distance, while the latter increase. In the intermediate regime where they have the same order of magnitude (the “inert Oort cloud”), both are weak, resulting in very long evolution timescales. To date, three observed objects can be considered to belong to this category. Aims. We aim to provide a clear understanding of where this transition occurs, and to characterise the long-term dynamics of small bodies in the intermediate regime: relevant resonances, chaotic zones (if any), and timescales at play. Methods. The different regimes are explored analytically and numerically. We also monitored the behaviour of swarms of particles during 4.5 Gyrs in order to identify which of the dynamical features are discernible in a realistic amount of time. Results. There exists a tilted equilibrium plane (Laplace plane) about which orbits precess. The dynamics is integrable in the low and high semi-major axis regimes, but mostly chaotic in between. From about 800 to 1100 astronomical units (au), the chaos covers almost all the eccentricity range. The diffusion timescales are large, but not to the point of being indiscernible in a 4.5 Gyrs duration: the perihelion distance can actually vary from tens to hundreds of au. Orbital variations are damped near the ecliptic (where previous studies focussed), but favoured in specific ranges of inclination corresponding to well-defined resonances. Moreover, starting from uniform distributions, the orbital angles cluster after 4.5 Gyrs for semi-major axes larger than 500 au, because of a very slow differential precession. Conclusions. Even if it is characterised by very long timescales, the inert Oort cloud mostly features chaotic regions; it is therefore much less inert than it appears. Orbits can be considered inert over 4.5 Gyrs only in small portions of the space of orbital elements, which include (90377) Sedna and 2012VP113. Effects of the galactic tides are discernible down to semi-major axes of about 500 au. We advocate including the galactic tides in simulations of distant trans-Neptunian objects, especially when studying the formation of detached bodies or the clustering of orbital elements.

Strong tidal energy dissipation in Saturn at Titan’s frequency as an explanation for Iapetus orbit

Context. Natural satellite systems present a large variety of orbital configurations in the solar system. While some are clearly the result of known processes, others still have largely unexplained eccentricity and inclination values. Iapetus, the furthest of Saturn’s main satellites, has a still unexplained 3% orbital eccentricity and its orbital plane is tilted with respect to its local Laplace plane (8° of free inclination). On the other hand, astrometric measurements of saturnian moons have revealed high tidal migration rates, corresponding to a quality factor Q of Saturn of around 1600 for the mid-sized icy moons. Aims. We show how a past crossing of the 5:1 mean motion resonance between Titan and Iapetus may be a plausible scenario to explain Iapetus’ orbit. Methods. We have carried out numerical simulations of the resonance crossing using an N-body code as well as using averaged equations of motion. A large span of migration rates were explored for Titan and Iapetus was started on its local Laplace plane (15° with respect to the equatorial plane) with a circular orbit. Results. The resonance crossing can trigger a chaotic evolution of the eccentricity and the inclination of Iapetus. The outcome of the resonance is highly dependent on the migration rate (or equivalently on Q). For a quality factor Q of over around 2000, the chaotic evolution of Iapetus in the resonance leads in most cases to its ejection, while simulations with a quality factor between 100 and 2000 show a departure from the resonance with post-resonant eccentricities spanning from 0 up to 15%, and free inclinations capable of reaching 11°. Usually high inclinations come with high eccentricities but some simulations (less than 1%) show elements compatible with Iapetus’ current orbit Conclusions. In the context of high tidal energy dissipation in Saturn, a quality factor between 100 and 2000 at the frequency of Titan would bring Titan and Iapetus into a 5:1 resonance, which would perturb Iapetus’ eccentricity and inclination to values observed today. Such rapid tidal migration would have avoided Iapetus’ ejection around 40–800 million years ago.