SI units in the context of Geopotential number

The mile, sometimes the international mile or statute mile to distinguish it from other miles, is a British imperial unit and United States customary unit of length; both are based on the older English unit of length equal to 5,280 English feet, or 1,760 yards. The statute mile was standardised as a unit of length between the Commonwealth of Nations and the United States by an international agreement in 1959, when the yard was formally redefined with respect to SI units as 0.9144 metres, making the mile exactly 1609.344 metres (1.609344 kilometres). For everyday use, five miles equates roughly to eight kilometres.

With qualifiers, mile is also used to describe or translate a wide range of units derived from or roughly equivalent to the Roman mile (roughly 1.48 km), such as the nautical mile (now 1.852 km exactly), the Italian mile (roughly 1.852 km), and the Chinese mile (now 500 m exactly). The Romans divided their mile into 5,000 pedes (lit. 'feet'), but the greater importance of furlongs in the Elizabethan-era England meant that the statute mile was made equivalent to 8 furlongs or 5,280 feet in 1593. This form of the mile then spread across the British Empire, some successor states of which continue to employ the mile. The US Geological Survey now employs the metre for official purposes, but legacy data from its 1927 geodetic datum has meant that a separate US survey mile (⁠6336/3937⁠ km) continues to see some use, although it was officially phased out in 2022. While most countries replaced the mile with the kilometre when switching to the International System of Units (SI), the international mile continues to be used in some countries, such as the United Kingdom, the United States, and a number of countries with fewer than one million inhabitants, most of which are UK or US territories or have close historical ties with the UK or US.
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In statistical thermodynamics, thermodynamic beta, also known as coldness, is the reciprocal of the thermodynamic temperature of a system:$${\displaystyle \beta \equiv {\frac {1}{k_{\rm {B}}T}}}$$ (where T is the temperature and k_B is Boltzmann constant).

Thermodynamic beta has units reciprocal to that of energy (in SI units, reciprocal joules, ${\displaystyle [\beta ]={\textrm {J}}^{-1}}$). In non-thermal units, it can also be measured in byte per joule, or more conveniently, gigabyte per nanojoule; 1 K is equivalent to about 13,062 gigabytes per nanojoule; at room temperature: T = 300K, β ≈ 44 GB/nJ ≈ 39 eV ≈ 2.4×10 J. The conversion factor is 1 GB/nJ = ${\displaystyle 8\ln 2\times 10^{18}}$ J.

Geopotential height, also known as geopotential altitude or geopotential elevation, is a vertical coordinate (with dimension of length) representing the work involved in lifting one unit of mass over one unit of length through a hypothetical space in which the acceleration of gravity is assumed constant. Geopotential heights are referenced to Earth's mean sea level, taking its best-fitting equigeopotential as a reference surface or vertical datum.In SI units, a geopotential height difference of one meter implies the vertical transport of a parcel of one kilogram; adopting the standard gravity value (9.80665 m/s), it corresponds to a constant work or potential energy difference of 9.80665 joules.

Geopotential height differs from geometric height (as given by a tape measure) because Earth's gravity is not constant, varying markedly with altitude and latitude; thus, a 1-m geopotential height difference implies a different vertical distance in physical space: "the unit-mass must be lifted higher at the equator than at the pole, if the same amount of work is to be performed".It is a useful concept in meteorology, climatology, and oceanography; it also remains a historical convention in aeronautics as the altitude used for calibration of aircraft barometric altimeters.

The surface gravity, g, of an astronomical object is the gravitational acceleration experienced at its surface at the equator, including the effects of rotation. The surface gravity may be thought of as the acceleration due to gravity experienced by a hypothetical test particle which is very close to the object's surface and which, in order not to disturb the system, has negligible mass. For objects where the surface is deep in the atmosphere and the radius not known, the surface gravity is given at the 1 bar pressure level in the atmosphere.

Surface gravity is measured in units of acceleration, which, in the SI system, are meters per second squared. It may also be expressed as a multiple of the Earth's standard surface gravity, which is equal to

The SI base units are the standard units of measurement defined by the International System of Units (SI) for the seven base quantities of what is now known as the International System of Quantities: they are notably a basic set from which all other SI units can be derived. The units and their physical quantities are the second for time, the metre (sometimes spelled meter) for length or distance, the kilogram for mass, the ampere for electric current, the kelvin for thermodynamic temperature, the mole for amount of substance, and the candela for luminous intensity. The SI base units are a fundamental part of modern metrology, and thus part of the foundation of modern science and technology.

The SI base units form a set of mutually independent dimensions as required by dimensional analysis commonly employed in science and technology.

The pound per square inch (abbreviation: psi) or, more accurately, pound-force per square inch (symbol: lbf/in), is a unit of measurement of pressure or of stress based on avoirdupois units and used primarily in the United States. It is the pressure resulting from a force with magnitude of one pound-force applied to an area of one square inch. In SI units, 1 psi is approximately 6.895 kilopascals.

The pound per square inch absolute (psia) is used to make it clear that the pressure is relative to a vacuum rather than the ambient atmospheric pressure. Since atmospheric pressure at sea level is around 14.7 psi (101 kilopascals), this will be added to any pressure reading made in air at sea level. The converse is pound per square inch gauge (psig), indicating that the pressure is relative to atmospheric pressure. For example, a bicycle tire pumped up to 65 psig in a local atmospheric pressure at sea level (14.7 psi) will have a pressure of 79.7 psia (14.7 psi + 65 psi). When gauge pressure is referenced to something other than ambient atmospheric pressure, then the unit is pound per square inch differential (psid).

Dynamic height (symbol ${\displaystyle H^{\text{d}}}$ or ${\displaystyle H^{\text{dyn}}}$) is a way of specifying the vertical position of a point above a vertical datum; it is an alternative for orthometric height or normal height. It can be computed (in SI units of metre) by dividing the location's geopotential number (symbol C, in square metre per square second) by the normal gravity (symbol g_c, in metres per square second) at 45 degree latitude and zero height, a constant value (9.806199203 m/s):

Dynamic heights are usually chosen so that zero corresponds to the geoid.

Specific force (SF) is a mass-specific quantity defined as the quotient of force per unit mass.

It is a physical quantity of kind acceleration, with dimension of length per time squared (TL) and SI units of metre per second squared (m·s).

In physics and engineering, heat flux or thermal flux, sometimes also referred to as heat flux density, heat-flow density or heat-flow rate intensity, is a flow of energy per unit area per unit time. Its SI units are watts per square metre (W/m). It has both a direction and a magnitude, and so it is a vector quantity. To define the heat flux at a certain point in space, one takes the limiting case where the size of the surface becomes infinitesimally small.

Heat flux is often denoted ${\displaystyle {\vec {\phi }}_{\mathrm {q} }}$, the subscript q specifying heat flux, as opposed to mass or momentum flux. Fourier's law is an important application of these concepts.