The size distribution of solar energetic particle (SEP) events, which represent a more energetic subset than flare events, is mostly found to follow power law distribution functions, rather than Poissonian random distribution functions. However, the numerical value of the power law slope is generally flatter than the slopes of the flare size distributions in hard X-rays, soft X-rays, and EUV (Hudson 1978), which can be explained in at least four different ways: (i) normal flares and proton flares are produced by two fundamentally different acceleration mechanisms; (ii) proton flares behave differently than normal flares; (iii) the fractal dimensionality of SEP events is different from normal flares; (iv) proton flares are subject to a selection bias toward the most energetic events and thus are not a representative sample of large flares. Nevertheless, the standard fractal-diffusive SOC model can explain the observed slopes of SEP size distributions, but observations reveal deviations from straight power law functions, or broken power law slopes, and thus are not unique and need to be modeled in more detail.

We focus on the statistics of SOC-related solar flare parameters in soft X-ray wavelengths, including their size and waiting time distributions. An early SOC model assumed a linear increase of the energy storage, but this pioneering model is not consistent with the expected correlation between the waiting time interval and the subsequently dissipated energy. The Neupert effect in solar flares implies a correlation between the hard X-ray fluence and the soft X-ray flux, which predicts identical size distributions for these two parameters. Quantifying of thermal flare energies in soft X-ray emitting plasma needs also to include radiative and conductive losses. The intermittency and bursty variability of the solar dynamo implies a nonstationary SOC driver, which yields a universal value for the power law slope of fluxes, but the power law slopes of waiting times vary with the flare rate. While our focus encompasses primarily SOC models, alternative models in terms of MHD turbulence can explain some characteristics of SOC features also, such as size distribution functions, Fourier spectra, and structure functions.

The total 2pN net shifts per orbit and the orbital precessions are calculated as the sum of two contributions: the direct ones due to the 2pN acceleration and the mixed, or indirect, ones caused by the 1pN instantaneous shifts during the orbital revolution. A comparison with other approaches existing in the literature is made.

This chapter explores a core question in astrobiology: what is the future of life on Earth and beyond? The first part describes the cessation of habitable conditions in Earth’s distant future (about a billion years hereafter), and the myriad risks that apparently confront humanity on shorter timescales, ranging from wars and artificial intelligence to asteroid impacts and massive volcanoes. The second segment outlines the possibility of humans migrating to other worlds in the solar system, and the numerous technological and logistical challenges expected to arise during this endeavour. The even more daunting notion of interstellar travel is also touched upon, and the propulsion systems and spacecraft advanced in this regard are sketched. The textbook comes to a close by taking stock of the fates that might await humankind.

Mars has always been one of the most promising targets in the search for current or extinct extraterrestrial life. The chapter commences with a brief summary of Mars’ basic characteristics, before describing its potential for instantaneous habitability (e.g., energy sources, bioessential elements), with an emphasis on the availability of water. This is followed by an exposition of how several aspects of Martian habitability have diminished over time, ranging from extensive atmospheric loss to the shutdown of its dynamo, both of which might have contributed to the emergence of its cold and arid climate today. Nevertheless, some specialised abodes where life may have persisted are touched upon (e.g., deep subsurface). In the last part of the chapter, the contentious history of life detection on Mars – the Viking mission experiments in the 1970s and the meteorite ALH84001 – is reviewed, and forthcoming missions to Mars are surveyed.

Icy worlds with subsurface oceans are potentially among the most common repositories of liquid water in the Universe. Moreover, the solar system is confirmed to host a number of such worlds, notably: Europa, Enceladus, and Titan. Motivated by these considerations, this chapter examines the habitability of icy worlds from a general standpoint. The oceanic properties of Europa, Enceladus, and Titan are reviewed, followed by a simple analysis of the physical conditions in which subsurface oceans may be supported. The pathways for the formation of the building blocks of life, their assembly into polymers, and subsequent delivery to the subsurface ocean are elucidated. The possible constraints on the availability of energy sources and bioessential elements are delineated, as well as the types of organisms and ecosystems that could exist. The chapter concludes by briefly speculating about the trajectories of biological evolution conceivable on icy worlds.

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.