The precessions of the Keplerian orbital elements are calculated for several tidal-type accelerations due to the presence of a distant 3rd body: Newtonian, post-Newtonian gravitoelectric, and post-Newtonian gravitomagnetic. The calculation is made, first, in a kinematically and dynamically non-rotating frame. Then, it is repeated in a dynamically non-rotating and kinematically rotating frame accounting for the de Sitter–Fokker and Pugh–Schiff precessions of its axes.

The physics and chemistry underpinning the origins of the Universe, stars, elements, and molecules is described in this chapter. It begins with outlining our understanding of the Big Bang, and how gravity subsequently facilitated the emergence of order and complexity in the Universe. This is followed by a brief exposition of star formation, stellar evolution of low- and high-mass stars, and the multiple pathways responsible for the production of elements in stars (i.e., stellar nucleosynthesis) such as the triple alpha process. The chapter concludes with an introduction to the broad subject of astrochemistry. The emphasis is on delineating the sites of molecule formation (e.g., molecular clouds), as well as the processes involved in gas-phase chemistry and grain-surface chemistry that drive the synthesis of molecules.

The theme of how life and its environment have coevolved together for about four billion years on Earth is explored in this chapter. The major evolutionary events that unfolded in the Archean eon (4 to 2.5 billion years ago), Proterozoic eon (2.5 to 0.539 billion years ago), and the Phanerozoic eon (0.539 billion years ago to present) are outlined, such as the origin(s) of multicellularity, eukaryotes, complex multicellular organisms, and humans. By drawing on this evolutionary timeline, theoretical paradigms for understanding and grouping the notable evolutionary events are sketched (e.g., major transitions in evolution). The next part of the chapter illustrates the intricate interplay between life and its environment by chronicling the rise in molecular oxygen levels, its possible causes and profound consequences, and its potential connections with key geological changes like the putative Snowball Earth episodes. Lastly, the ‘Big Five’ mass extinctions that transpired in the Phanerozoic, along with their triggers and ramifications, are described.

Life-as-we-know-it harnesses carbon for the scaffolding in biomolecules and liquid water as the solvent. This chapter delineates the beneficial properties of carbon and water, and then investigates whether viable alternatives to this duo exist (i.e., ‘exotic’ life). With regard to the latter, the likes of ammonia, sulfuric acid, and liquid hydrocarbons are expected to have some physical and/or chemical advantages relative to water, while also exhibiting certain downsides. In contrast, it is suggested that few options appear feasible aside from carbon, with silicon representing a partial exception. The chapter subsequently delves into the habitability of the clouds of Venus and the lakes of Titan, because the alternative solvents sulfuric acid and liquid hydrocarbons (methane and ethane) are, respectively, documented therein. Both these environments might be conducive to hosting exotic life, but it is cautioned that they are likely subjected to severe challenges.

The impact of the 1pN gravitomagnetic Lense–Thirring acceleration, generalized also to the case of two massive spinning bodies of comparable masses and angular momenta, is calculated for different types of observation-related quantities (Keplerian orbital elements, anomalistic, draconitic, and sidereal orbital periods, two-body range and range rate, radial velocity curve and radial velocity semiamplitude of spectroscopic binaries, astrometric angles RA and dec., times of arrival of binary pulsars, characteristic timescales of transiting exoplanets, and their sky-projected spin-orbit angle). The results are applied to a test particle orbiting a primary, a Sun–Jupiter exoplanet system, and an S star in Sgr A*.

The impact of the Newtonian quadrupolar acceleration, generalized also to the case of two bodies of comparable masses and quadrupole moments, is calculated for different types of observation-related quantities (Keplerian orbital elements, anomalistic, draconitic and sidereal orbital periods, two-body range and range rate, radial velocity curve and radial velocity semiamplitude of spectroscopic binaries, astrometric angles RA and dec., times of arrival of binary pulsars, characteristic timescales of transiting exoplanets and their sky-projected spin-orbit angle). The results are applied to a test particle orbiting a primary, a Sun-Jupiter exoplanet system, and to a S star in Sgr A*.

The first part of this chapter introduces and defines key concepts that are commonly encountered in this subject: astrobiology, habitability, and life; in doing so, it also clarifies the ambiguities inherent in these terms. The second part briefly chronicles the lengthy and rich history of speculations about the plurality of worlds and extraterrestrial life in myriad societies across different epochs. It concludes with a summary of developments in astrobiology in the early- and mid-twentieth century, and describes how the future of this field looks optimistic.

This chapter elucidates the physical and chemical mechanisms involved in the formation of planets, the conventional abodes of life. The first part is devoted to protoplanetary discs, wherein planet formation unfolds. The topics covered include the minimum mass required for assembling the solar system (minimum mass solar nebula), the thermal and density structure of protoplanetary discs, and the rich chemistry that occurs in these settings. The second delves into the many stages of planet formation starting from the coagulation of dust to the hurdles encountered (e.g., metre barrier) in forming kilometre-sized planetesimals and subsequently to collisions between planetesimals engendering planetary cores and eventually terrestrial planets; a brief description of how giant planets are assembled is also delineated. The final part outlines how interactions between a given planet and its neighbouring gas or planetesimals can contribute to the migration of the former, as well as influence the delivery of water and other volatiles to the planet.