The conditions on early Earth prior to four billion years ago (Hadean Earth), which shaped the origin(s) and early evolution of life, are discussed in this chapter. It begins with a summary of the various sources of internal heat on terrestrial planets and the types of heat transport (e.g., conduction), as these factors influenced the habitability of early Earth and its temporal evolution. This is followed by an exposition of the characteristics of Hadean Earth: the Moon-forming impact, oceans, landmasses, and atmosphere, including the faint young Sun paradox – how did Earth stay unfrozen despite the Sun’s lower luminosity? The chapter concludes with sketching the putative Late Heavy Bombardment (a potential spike in the impactor rate) about four billion years ago, and a general treatment of the positives and downsides of large impacts.

This chapter is devoted to a foundational question in astrobiology: how and where did life originate? The narrative commences with a brief description of the four major categories of biomolecules (proteins, nucleic acids, carbohydrates, and lipids) on Earth and their associated functions. Partly based on this knowledge, biophysical and biochemical constraints on the minimum size of a viable cell are derived. The various origin(s)-of-life hypotheses are discussed next – like the replication-first (e.g., RNA world) and metabolism-first paradigms – along with their attendant strengths and weaknesses. The pathways by which the building blocks of life (e.g., amino acids) could be synthesised through non-biological avenues, such as the famous Miller experiments, are elucidated. Subsequently, the abiotic channels that may facilitate the polymerisation of these molecules to yield biomolecules are delineated. The focus of the chapter is then shifted to the specialised environments that might have enabled the origin(s) of life to readily occur. Two candidates are reviewed in detail (submarine hydrothermal vents and hydrothermal fields), with others mentioned in passing. Finally, the concept of entropy and its subtle connections with living systems are sketched.

The total 1pN gravitoelectric mass quadrupole orbital precessions of the Keplerian orbital elements are calculated in their full generality for an arbitrary orientation of the primary’s spin axis and a general orbital configuration of the test particle. Both the direct effects, due to the 1pN gravitoelectric mass quadrupole acceleration, and the mixed effects, due to the simultaneous action of the 1pN gravitoelectric mass monopole and Newtonian quadrupole accelerations, are calculated.

The impact of a wide range of post-Keplerian perturbing accelerations, of whatever physical origin, on 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 along with their sky-projected spin-orbit angle) is analytically calculated with standard perturbative techniques in a unified and consistent framework. Both instantaneous and averaged orbital shifts are worked out to the first and second order in the perturbing acceleration. Also, mixed effects, due to the simultaneous action of at least two perturbing accelerations, are treated.

The precessions of the Keplerian orbital elements induced by several modified models of gravity are calculated. The latter ones are Yukawa, power-law, logarithmic, dark matter density profiles (exponential and power-law), once per revolution accelerations, constant accelerations, and Lorentz-violating symmetry.

The orbital precessions of the Keplerian orbital elements induced by the 1pN gravitomagnetic spin octupole moment of a rigidly rotating oblate spheroid are calculated in their full generality for an arbitrary orientation of the primary’s spin axis and a general orbital configuration of the test particle.

The search for extraterrestrial intelligence (SETI) represents a well-known area of astrobiology. This chapter is dedicated to technosignatures, that is, markers produced by extraterrestrial intelligences (ETIs). The famous Drake equation for roughly estimating the number of communicative ETIs is introduced, its various factors are defined, and some of its shortcomings and implications for detecting technosignatures are discussed. Next, the Fermi paradox is delineated: if ETIs are widespread, where are they? Three major classes of solutions to this classic paradox (e.g., we are effectively alone) are considered, along with their accompanying ramifications. After a brief segue into the Kardashev scale for grouping ETIs, the final segment of the chapter categorises the diverse landscape of technosignatures – ranging from artificial radio and optical signals to atmospheric pollutants and waste heat arising from energy harvesting and dissipation – and outlines the current limits derived for the frequency of technosignatures, as well as the anticipated future constraints in this context.

The impact of the 1pN gravitoelectric mass monopole acceleration, both in the test particle and in the two-body system of finite, comparable masses cases, 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). 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 manifold requirements for a world to sustain habitability on long timescales (continuous habitability) are delineated in this chapter. The first part offers a brief introduction to climate physics (e.g., greenhouse effect), and thereupon formulates the notion of the habitable zone, that is, the region where liquid water could exist on rocky planets orbiting stars; the boundaries of the habitable zone as a function of the stellar temperature are also presented. In the second part, the various stellar factors potentially involved in regulating planetary habitability are sketched: winds, flares and space weather, and electromagnetic radiation. The third part chronicles some planetary variables that may affect habitability: mass, plate tectonics, magnetic field, tidal locking, and atmospheric composition. The last part is devoted to examining the high-energy astrophysical processes that might impact habitability on galactic scales: candidates in this regard include supernovae, gamma-ray bursts, and active supermassive black holes.