cubic metre per kilogram per second squa — from formula anatomyThe cubic metre per kilogram per second squared (m³/(kg·s²)) is a derived SI unit that appears in physics as the reciprocal of density times acceleration, or equivalently as the unit of specific volume times acceleration. It is not a common standalone unit but emerges in formulas involving gravitational potential, pressure gradients, or fluid dynamics. In particular, it appears in the gravitational constant's units when expressed as N·m²/kg², which simplifies to m³/(kg·s²).
This unit is not named after a person or given a special name; it is simply a derived unit from the SI base units. It has been used implicitly since Newton's time, but the formal SI system codified it in 1960.
The unit combines volume (m³), mass (kg), and time (s²) in a way that reflects how a force per unit mass scales with distance. For example, in Newton's law of gravitation, the gravitational constant G has this unit, meaning that the force between two masses depends on their separation squared and their masses inversely. The unit ensures dimensional consistency in equations, allowing calculations to balance correctly.
It appears in calculations of gravitational forces, orbital mechanics, and in the equations of general relativity, where the stress-energy tensor has units of energy density, but the constant G carries this unit.
The gravitational constant G, with units m³/(kg·s²), is one of the least precisely measured fundamental constants, known to only about four significant digits.
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