= Solution
Interpret <habitability> as the ability to sustain <life> with broadly terrestrial <biochemistry>. \b[Accessible <liquid water>, usable <free energy>, suitable chemical ingredients and sufficiently persistent conditions are the central requirements.] Earth-like geography, a breathable <atmosphere> and actual habitation are not part of that definition.
\b[A viable local physical environment.] The relevant <temperature> and <pressure> must permit <liquid water> where the <organisms> live. For a surface habitat this normally requires an appropriate <atmosphere> and <surface temperature>; the roughly 6.1 millibar triple-point <pressure> of pure <water> is a minimum phase constraint, not a guarantee of a temperate surface. High <salinity>, extreme acidity and low <water activity> can make apparently wet environments unsuitable for known <life>. A subsurface <ocean> beneath ice can provide liquid conditions even when the surface is frozen, so the entire body need not lie in the conventional surface-water <habitable zone>.
\b[A suitable orbit and rotation.] For a surface-water <planet>, orbital distance must give an absorbed <radiation budget> compatible with liquid conditions after the body's <Bond albedo>, <atmosphere> and <greenhouse effect> are included. The simple <planetary equilibrium temperature> estimate
$$
T_{\rm eq}=\left[\frac{(1-A)S}{4\sigma}\right]^{1/4}
$$
uses orbital irradiance $S$, <Bond albedo> $A$ and the <Stefan-Boltzmann constant> $\sigma$, assumes unit thermal emissivity and averages over the whole sphere. It is not a prediction of <surface temperature> beneath a <atmosphere> with a <greenhouse effect>. Excessive absorbed energy risks a <runaway greenhouse>; inadequate surface heating can freeze surface <water>, although <heat> from the interior or <tidal heating> can maintain a subsurface habitat.
The orbit must persist without collision or ejection for a biologically useful interval. Large <orbital eccentricity> can produce extreme variations in heating, but neither exactly circular motion nor Earth's particular <obliquity> is essential. <Rotation period> and <obliquity> govern illumination and seasons; atmospheric and <ocean heat flux> determine how severe those variations become. <Tidal locking> does not automatically make a body uninhabitable, because sufficient heat transport can moderate the day–night contrast. A <natural satellite> also needs a stable orbit around its primary and a tolerable combination of irradiation and <tidal heating>: enough heating may maintain an <ocean>, whereas excessive heating can make the environment hostile. These are constraints on the body's location and path, without requiring a particular kind of surrounding planetary system.
\b[An adequate chemical inventory and access to it.] Known <life> uses <carbon>, <hydrogen>, <nitrogen>, <oxygen>, <phosphorus> and <sulfur>, together with catalytic trace elements. A <rocky planet> supplies mineral surfaces and reservoirs, but total inventory is not enough: <chemical weathering>, <water-rock interaction> or other transport must make <nutrients> accessible. A water-rich body with an <ocean> isolated from its rocky interior by a thick high-pressure ice layer could have difficulty recycling some <nutrients>; this is a possible limitation, not proof of sterility.
\b[A usable energy supply.] <Photosynthesis> can exploit light in an illuminated habitat. A dark subsurface habitat instead needs sustained <chemical disequilibrium>, for example oxidized and reduced species brought together by <water-rock interaction>, <hydrothermal circulation> or <radiolysis>. Warm <water> at complete <chemical equilibrium> is not, by itself, an energy supply for sustained <metabolism>.
\b[Retention, protection and longevity.] The body's <mass>, radius, <surface gravity> and thermal history affect retention of <water> and an <atmosphere>. <Escape velocity> must be considered together with gas <temperature>, molecular mass, <atmospheric escape> and replenishment: there is no universal Earth-mass threshold. An <atmosphere>, ice or <rock> overburden can protect <life> from damaging <ionizing radiation> and short-wavelength light. An intrinsic <planetary magnetic field> can modify charged-particle exposure and escape, but it is neither a universal requirement nor a guarantee of retention.
Finally, conditions must last long enough. Stored formation <heat>, <radiogenic heating> and possibly <tidal heating> can maintain circulation and chemical exchange. <Plate tectonics> can recycle materials and support a <carbonate-silicate cycle>, but it is not established as a necessary condition for every habitable body: conditional long-term <carbon cycling> is possible on a <stagnant-lid planet> as well.<Carbon Cycling and Habitability of Earth-Sized Stagnant Lid Planets by Bradford J. Foley and Andrew J. Smye>[Abstract and coupled thermal/carbon-cycle model; habitability is conditional on degassing, weathering and interior evolution.]{ref} The necessary end result is persistence of a suitable environment, rather than a checklist requiring every feature of the modern <Earth>.
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