Hydrostatic equilibrium in the context of Astrophysics

A planet is a large, rounded astronomical body that is generally required to be in orbit around a star, stellar remnant, or brown dwarf, and is not one itself. The Solar System has eight planets by the most restrictive definition of the term: the terrestrial planets Mercury, Venus, Earth, and Mars, and the giant planets Jupiter, Saturn, Uranus, and Neptune. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a young protostar orbited by a protoplanetary disk. Planets grow in this disk by the gradual accumulation of material driven by gravity, a process called accretion.

The word planet comes from the Greek πλανήται (planḗtai) 'wanderers'. In antiquity, this word referred to the Sun, Moon, and five points of light visible to the naked eye that moved across the background of the stars—namely, Mercury, Venus, Mars, Jupiter, and Saturn. Planets have historically had religious associations: multiple cultures identified celestial bodies with gods, and these connections with mythology and folklore persist in the schemes for naming newly discovered Solar System bodies. Earth itself was recognized as a planet when heliocentrism supplanted geocentrism during the 16th and 17th centuries.

Hydrostatics is the branch of fluid mechanics that studies fluids at hydrostatic equilibrium and "the pressure in a fluid or exerted by a fluid on an immersed body". The word "hydrostatics" is sometimes used to refer specifically to water and other liquids, but more often it includes both gases and liquids, whether compressible or incompressible. It encompasses the study of the conditions under which fluids are at rest in stable equilibrium. It is opposed to fluid dynamics, the study of fluids in motion.

Hydrostatics is fundamental to hydraulics, the engineering of equipment for storing, transporting and using fluids. It is also relevant to geophysics and astrophysics (for example, in understanding plate tectonics and the anomalies of the Earth's gravitational field), to meteorology, to medicine (in the context of blood pressure), and many other fields.

The International Astronomical Union (IAU) adopted in August 2006 the definition made by Uruguayan astronomers Julio Ángel Fernández and Gonzalo Tancredi that stated, that in the Solar System, a planet is a celestial body that:

1. is in orbit around the Sun,
2. has sufficient mass to assume hydrostatic equilibrium (a nearly round shape), and
3. has "cleared the neighbourhood" around its orbit.

A non-satellite body fulfilling only the first two of these criteria (such as Pluto, which had hitherto been considered a planet) is classified as a dwarf planet. According to the IAU, "planets and dwarf planets are two distinct classes of objects" – in other words, "dwarf planets" are not planets. A non-satellite body fulfilling only the first criterion is termed a small Solar System body (SSSB). An alternate proposal included dwarf planets as a subcategory of planets, but IAU members voted against this proposal. The decision was a controversial one, and has drawn both support and criticism from astronomers.

A dwarf planet is a small planetary-mass object that is in direct orbit around the Sun, massive enough to be gravitationally rounded, but insufficient to achieve orbital dominance like the eight classical planets of the Solar System. The prototypical dwarf planet is Pluto, which for decades was regarded as a planet before the "dwarf" concept was adopted in 2006.Many planetary geologists consider dwarf planets and planetary-mass moons to be planets, but since 2006 the IAU and many astronomers have excluded them from the roster of planets.

Dwarf planets are capable of being geologically active, an expectation that was borne out in 2015 by the Dawn mission to Ceres and the New Horizons mission to Pluto. Planetary geologists are therefore particularly interested in them.

Gonggong (minor-planet designation: 225088 Gonggong) is a dwarf planet and a member of the scattered disc beyond Neptune. It has a highly eccentric and inclined orbit during which it ranges from 33–101 astronomical units (4.9–15.1 billion kilometers; 3.1–9.4 billion miles) from the Sun. As of 2019, its distance from the Sun is 88 AU (13.2×10^ km; 8.2×10^ mi), and it is the sixth-farthest known Solar System object. According to the Deep Ecliptic Survey, Gonggong is in a 3:10 orbital resonance with Neptune, in which it completes three orbits around the Sun for every ten orbits completed by Neptune. Gonggong was discovered in July 2007 by American astronomers Megan Schwamb, Michael Brown, and David Rabinowitz at the Palomar Observatory, and the discovery was announced in January 2009.

At approximately 1,230 km (760 mi) in diameter, Gonggong is similar in size to Pluto's moon Charon, making it the fifth-largest known trans-Neptunian object (apart possibly from Charon). It may be sufficiently massive to be in hydrostatic equilibrium and therefore a dwarf planet. Gonggong's large mass makes retention of a tenuous atmosphere of methane just possible, though such an atmosphere would slowly escape into space. The object is named after Gònggōng, a Chinese water god responsible for chaos, floods and the tilt of the Earth. The name was chosen by its discoverers in 2019, when they hosted an online poll for the general public to help choose a name for the object, and the name Gonggong won.

In astrophysics, the main sequence is a classification of stars which appear on plots of stellar color versus brightness as a continuous and distinctive band. Stars spend the majority of their lives on the main sequence, during which core hydrogen burning is dominant. These main-sequence stars, or sometimes interchangeably dwarf stars, are the most numerous true stars in the universe and include the Sun. Color-magnitude plots are known as Hertzsprung–Russell diagrams after Ejnar Hertzsprung and Henry Norris Russell.

When a gaseous nebula undergoes sufficient gravitational collapse, the high pressure and temperature concentrated at the core will trigger the nuclear fusion of hydrogen into helium (see stars). The thermal energy from this process radiates out from the hot, dense core, generating a strong pressure gradient. It is this pressure gradient that counters the star's collapse under gravity, maintaining the star in a state of hydrostatic equilibrium. The star's position on the main sequence is determined primarily by the mass, but also by age and chemical composition. As a result, radiation is not the only method of energy transfer in stars. Convection plays a role in the movement of energy, particularly in the cores of stars greater than 1.3 to 1.5 times the Sun's mass, again depending on age and chemical composition.

A protoplanet or planetary embryo is an astronomical body originated within a protoplanetary disk that has undergone internal melting to produce a differentiated interior.

Protoplanets are thought to form out of kilometer-sized planetesimals that gravitationally perturb each other's orbits and collide, gradually coalescing into larger bodies through a process known as "runaway growth". Once accumulated enough mass, protoplanets will begin to assume a spherical shape due to hydrostatic equilibrium and become dwarf planets, those of which that subsequently succeed in dominating their own orbit will become planets proper.

A planetary-mass object (PMO), planemo, or planetary body (sometimes referred to as a world) is, by geophysical definition of celestial objects, any celestial object massive enough to achieve hydrostatic equilibrium and assume an ellipsoid shape, but not enough to sustain core fusion like a star.

The purpose of this term is to classify together a broader range of celestial objects than just "planet", since many objects similar in geophysical terms do not conform to conventional astrodynamic expectations for a planet. Planetary-mass objects can be quite diverse in origin and location, and include planets, dwarf planets, planetary-mass moons and free-floating planets, which may have been ejected from a system (rogue planets) or formed through cloud-collapse rather than accretion (sub-brown dwarfs).

A planetary-mass moon is a planetary-mass object that is a natural satellite of another non-stellar celestial object. Because of their mass, these moons are large and ellipsoidal (sometimes spherical) in shape due to hydrostatic equilibrium caused by internal partial melting and differentiation and/or from tidal or radiogenic heating, in some cases forming a subsurface ocean.

Planetary-mass moons are sometimes called satellite planets by some planetary scientists such as Alan Stern, who are more concerned with whether a celestial body has planetary geology (that is, whether it is a planetary body) than its solar or non-solar orbit (planetary dynamics). Thus they consider planetary-mass moons to be a subset of the planets. This conceptualization of planets as three classes of objects (classical planets, dwarf planets and satellite planets) has not been accepted by the International Astronomical Union (the IAU).

In meteorology, the synoptic scale (also called the large scale or cyclonic scale) is a horizontal length scale of the order of 1,000 km (620 mi) or more. This corresponds to a horizontal scale typical of mid-latitude depressions (e.g. extratropical cyclones). Most high- and low-pressure areas seen on weather maps (such as surface weather analyses) are synoptic-scale systems, driven by the location of Rossby waves in their respective hemisphere. Low-pressure areas and their related frontal zones occur on the leading edge of a trough within the Rossby wave pattern, while high-pressure areas form on the back edge of the trough. Most precipitation areas occur near frontal zones. The word synoptic is derived from the Ancient Greek word συνοπτικός (sunoptikós), meaning "seen together".

The Navier–Stokes equations applied to atmospheric motion can be simplified by scale analysis in the synoptic scale. It can be shown that the main terms in horizontal equations are Coriolis force and pressure gradient terms; therefore, one can use geostrophic approximation. In vertical coordinates, the momentum equation simplifies to the hydrostatic equilibrium equation.

The Chandrasekhar limit (/ˌtʃəndrəˈʃeɪkər/) is the maximum mass of a stable white dwarf star. These stars resist gravitational collapse primarily through electron degeneracy pressure, compared to main sequence stars, which resist collapse through thermal pressure. The Chandrasekhar limit is the mass above which electron degeneracy pressure in the star's core is insufficient to balance the star's own gravitational self-attraction. The value of the Chandrasekhar limit depends upon the ratio of the number of electrons to nucleons (neutrons plus protons) in the star. For small stars this ratio is around 1/2 and the limit is about 1.44 M_☉ (2.765×10 kg). The limit was named after Subrahmanyan Chandrasekhar.

The carbon-burning process or carbon fusion is a set of nuclear fusion reactions that take place in the cores of massive stars (at least 4 M_☉ at birth) that combines carbon into other elements. It requires high temperatures (>5×10 K or 50 keV) and densities (>3×10 kg/m).

These figures for temperature and density are only a guide. More massive stars burn their nuclear fuel more quickly, since they have to offset greater gravitational forces to stay in (approximate) hydrostatic equilibrium. That generally means higher temperatures, although lower densities, than for less massive stars. To get the right figures for a particular mass, and a particular stage of evolution, it is necessary to use a numerical stellar model computed with computer algorithms. Such models are continually being refined based on nuclear physics experiments (which measure nuclear reaction rates) and astronomical observations (which include direct observation of mass loss, detection of nuclear products from spectrum observations after convection zones develop from the surface to fusion-burning regions – known as dredge-up events – and so bring nuclear products to the surface, and many other observations relevant to models).

The Jeans instability is a concept in astrophysics that describes an instability that leads to the gravitational collapse of a cloud of gas or dust. It causes the collapse of interstellar gas clouds and subsequent star formation. It occurs when the internal gas pressure is not strong enough to prevent the gravitational collapse of a region filled with matter. It is named after James Jeans.

For stability, the cloud must be in hydrostatic equilibrium, which in case of a spherical cloud translates to

A stellar core is the extremely hot, dense region at the center of a star. For an ordinary main sequence star, the core region is the volume where the temperature and pressure conditions allow for energy production through thermonuclear fusion of hydrogen into helium. This energy in turn counterbalances the mass of the star pressing inward; a process that self-maintains the conditions in thermal and hydrostatic equilibrium. The minimum temperature required for stellar hydrogen fusion exceeds 10 K (10 MK), while the density at the core of the Sun is over 100 g/cm. The core is surrounded by the stellar envelope, which transports energy from the core to the stellar atmosphere where it is radiated away into space.