Mercury is locked in an unusual 3:2 spin-orbit resonance and as such is expected to be in a state of equilibrium called Cassini state. In that state, the angle between the spin axis and orbit normal, called obliquity, remains almost constant while the spin axis remains almost in the plane, also called Cassini plane, defined by the normal to the Laplace plane and the normal to the orbital plane. The spin axis and the orbit normal precess together with a period of about 300 kyr. The orientation of the spin axis of Mercury has been estimated using different approaches: (i) Earth-based radar observations, (ii) Messenger images and altimeter data, and (iii) Messenger radio tracking data. The different estimates all tend to confirm that Mercury occupies the Cassini state. The observed obliquity is small and close to 2 arcmin. It indicates a normalized polar moment of inertia of about 0.34. This information, combined with the existence of a liquid iron core, as evidenced by the librations, allows to constrain the interior structure of Mercury. However, the different estimates of the orientation of the spin axis locate the spin axis somewhat behind or ahead of the Cassini plane, and it is difficult to reconcile and interpret them coherently in terms of detailed interior properties. We review recent models for the obliquity and spin orientation of Mercury, which include the effects of complex orbital dynamics, tidal deformations and associated dissipation, and internal couplings related to the presence of fluid and solid cores. We discuss some implications regarding the interpretations of the orientation estimates in term of interior properties.

In the context of a perturbed two body problem, in which the Keplerian motion of the small object (the satellite) is perturbed by the oblateness of the central body (the asteroid) and the attraction of a third body (the Sun), we discuss the long-term evolution of the orbital elements of a satellite orbiting an oblate body, with a particular focus on the behavior of the inclination and the longitude of the ascending node. We derive analytically the position of the Laplace plane as a function of several parameters and use this solution to analyse the long-term evolution of distant circular orbits. The analytical study is complemented by numerical tests, performed in the context of both Cartesian and Hamiltonian frameworks. The results give a description of the orbital dynamical environment of asteroids and reveal the parameters that play a key role in the long-term stability of distant circular orbits.

Like our Moon, the large icy satellites of Jupiter are thought to be in a Cassini State, an equilibrium rotation state characterized by a synchronous rotation rate and a precession rate of the rotation axis equal to that of the normal to the orbit. In these equilibrium states (up to four Cassini States are possible for a solid and rigid satellite), the spin axis of the satellite, the normal to its orbit and the normal to the inertial plane remain coplanar with an obliquity that remains theoretically constant. However, as the gravitational torque exerted on the satellite shows small periodic variations, the orientation of the rotation axis will also vary with time and nutations in obliquity will appear.

Here we present a dynamical model for the study of the Cassini States. This model includes the coupling between the polar motion and the spin axis precession/nutation which is neglected in the classical studies. We study the influence of the triaxiality of Ganymede on its four possible Cassini States, use a Toy model of the Moon to illustrate the nutations in obliquity obtained with the dynamical model, and investigate the influence of the presence of a subsurface ocean on the Cassini State I of Europa.

Our climate future depends on the delicate, fine balance of earth processes first elaborated on by James Croll, born 200 years ago in 1821. A childhood victim of the Scottish clearances, Croll, after following various indifferent occupations, managed to remove to the then rapidly industrialising city of Glasgow and eventually to Scotland's capital, Edinburgh. He blossomed as a most original, outside-the-box, thinker of great intellectual strength and modesty. He carried out scores of studies across a broad range of research topics, many related to the physical causes of climate change. He is well known for his astronomical theory of the ice ages, but should be much better regarded for his incisive physical insights into the central importance of feedbacks in the Earth system. Although humble, Croll was an ardent controversialist who strongly, perhaps over-strongly, always defended his corner. As well as his many accomplishments as a man of science, Croll was committed to exploring philosophical questions of theism and determinism, topics which occupied his earliest and last publications. A ‘top ten’ selection out of the varied subject areas that Croll tackled are explored herein, along with a brisk survey of their legacy to contemporary modelling studies and to Earth's climate future: (1) causes of climate change (1864); (2) ice-cap melt and sea-level rise (1865); (3) predicting future climates using eccentricity (1866); (4) combining orbital precession, eccentricity and obliquity (1867); (5) geological time and the date of the glacial epochs (1868); (6) geological time and denudation rates (1868); (7) ocean currents and the hemispherical temperature difference (1869); (8) feedbacks – a remarkable circumstance which led to changes of climate (1875); (9) temperature of space and its bearing on terrestrial physics (1880); (10) the causes of mild polar climates (1884).

James Croll was a pioneer in studies of the impact of the slowly changing orbital dynamics of the Earth on climate change. His book Climate and Time in their Geological Relations (1875) was far ahead of its time in seeking correlations between climate change, the occurrence of ice ages and perturbations to the Earth's orbit about the Sun. The astronomical cycles he discovered are now called ‘Milankovitch Cycles’ after the Serbian scientist whose research was first published in the Handbuch der Klimatologie in 1930. The celestial mechanical and astronomical background to Croll's research is the focus of this essay. The development of the understanding of the impact of perturbations of the elliptical planetary orbits by other bodies in the solar system paralleled new mathematical techniques, many of which were developed in association with celestial mechanical problems. The central contributions of many of the major mathematicians of the late 18th and 19th Centuries, including Euler, Lagrange, Laplace and Le Verrier, are highlighted. Although Croll's contributions faded from view for several generations, his pioneering insights have now been demonstrated to have been basically correct.

James Croll's Physical Theory of Secular Changes of Climate emerged during an age of revolution in geology that included the rise of the glacial theory and the search for its underlying causes. According to Croll, periods of high eccentricity are associated with the persistence of long glacial epochs, within which glaciations occur in alternate hemispheres when winter is at aphelion every ~11,000 years; however, astronomical forcing is only able to produce glaciation by means of physical agencies (climate feedbacks) that amplify the small effects of varying seasonal irradiation. Croll understood the importance of interglacial deposits because they provided evidence for the occurrence of multiple glaciations within his long glacial epochs. He was aware of the limitations of the terrestrial record and suggested that deep-sea sediments would contain a continuous succession of glacial-interglacial cycles. Contrary to a widespread view, however, Croll was not envisaging the advent of palaeoceanographic exploration avant la lettre, but instead was drawing attention to the inadequacy of the land record as a testbed of his astronomical theory. Yet, the marine record did eventually deliver a test of astronomical theories almost exactly 100 years after the publication of his 1875 book Climate and Time in their Geological Relations. Here, we provide an historical account of the technological and scientific developments that led to this and a summary of insights on astronomically paced climate changes from marine, terrestrial and ice core records. We finally assess Croll's ideas in the context of our current understanding of the theory of ice ages.

Previous studies have suggested that Marine Isotope Stage (MIS) 13, recognized as atypical in many paleoclimate records, is marked by the development of anomalously strong summer monsoons in the northern tropical areas. To test this hypothesis, we performed a multi-proxy study on three marine records from the tropical Indian Ocean in order to reconstruct and analyse changes in the summer Indian monsoon winds and precipitations during MIS 13. Our data confirm the existence of a low-salinity event during MIS 13 in the equatorial Indian Ocean but we argue that this event should not be considered as “atypical”. Taking only into account a smaller precession does not make it possible to explain such precipitation episode. However, when considering also the larger obliquity in a more complete orbitally driven monsoon “model,” one can successfully explain this event. In addition, our data suggest that intense summer monsoon winds, although not atypical in strength, prevailed during MIS 13 in the western Arabian Sea. These strong monsoon winds, transporting important moisture, together with the effect of insolation and Eurasian ice sheet, are likely one of the factors responsible for the intense monsoon precipitation signal recorded in China loess, as suggested by model simulations.

The large-moon hypothesis states that planetary habitability is enhanced by the presence of a large satellite. This controversial proposal is linked to the equally controversial idea that the axial stability of a planet also enhances habitability. Previous work has shown that, far from encouraging axial stability, large moons actually destabilize obliquity when the effects of tidal drag on the planetary spin rate are taken into account. However, our Moon's mass is remarkably close to the upper limit allowed by axial stability, suggesting that the large-moon hypothesis is actually correct but constrained by an independent requirement for axial stability. This conclusion can be tested by looking at the typical separations between large exo-planets because axial stability is more likely in planetary systems with widely spaced gas giants. Thus, if axial stability really does enhance habitability, Jupiter and Saturn should be unusually widely spaced. This can be tested using data expected from gravitational microlensing planet-search surveys. Unfortunately, in the event of a negative result from this test, it is not possible to distinguish whether this results from large moons and stable axes being unimportant for life or results from large moons and stable axes being widespread.

A three-dimensional general-circulation climate model is used to simulate climates of Earth-like planets with extreme axial tilts (i.e. ‘obliquities’). While no terrestrial-planet analogue exists in the solar system, planets with steeply inclined spin axes may be common around nearby stars. Here we report the results of 12 numerical experiments with Earth-like planets having different obliquities (from 0° to 85°), continental geographies, and levels of the important greenhouse gas, CO2. Our simulations show intense seasonality in surface temperatures for obliquities [ges ]54°, with temperatures reaching 80–100 °C over the largest middle- and high-latitude continents around the summer solstice. Net annual warming at high latitudes is countered by reduced insolation and colder temperatures in the tropics, which maintains the global annual mean temperature of our planets to within a few degrees of 14 °C. Under reduced insolation, seasonal snow covers some land areas near the equator; however no significant net annual accumulation of snow or ice occurs in any of our runs with obliquity exceeding the present value, in contrast to some previous studies. None of our simulated planets were warm enough to develop a runaway greenhouse or cold enough to freeze over completely; therefore, most real Earth-like planets should be hospitable to life at high obliquity.