Home > Inverse-square law

• the gravitational attraction between two massive objects, in addition to being directly proportional to the product of their masses, is inversely proportional to the square of the distance between them; this law was first suggested by Ismael Bullialdus but put on a firm basis by Isaac Newton;

• the force of attraction or repulsion between two electrically charged particles, in addition to being directly proportional to the product of the electric charges, is inversely proportional to the square of the distance between them; this is Coulomb's law;

• the intensity of light radiating from a point-source is inversely proportional to the square of the distance from the source. An object twice as far away (of the same size), receives only 1/4 the energy (in the same time period). More generally, the irradiance, i.e., the intensityIn physics, intensity is a measure of the time-averaged energy flux. To find the intensity, take the energy density (that is, the energy per unit volume) and multiply it by the velocity at which the energy is moving. The resulting vector has the units of (or powerMechanical power In physics, power (symbol: P is the amount of work W done per unit of time t''. This can be modeled as an energy flow, equivalent to the rate of change of the energy in a system, or the time rate of doing work, as defined by : where P is per unit area in the direction of propagationThe word propagation can mean: Multiplication or increase, as by natural reproduction. In genetics, propagation is another term for the elongation part of transcription. In agriculture and horticulture, propagation is the production of increased numbers o), of a spherical wavefront varies inversely with the square of the distance from the source (assuming there are no losses caused by absorptionAbsorption is the process by which the energy of a photon is taken up by another entity, for example, by an atom which makes a transition between two electronic energy levels. The photon is destroyed in the process. Molecules can lose absorbed energy by h or scatteringIn physics, scattering is a class of phenomena by which particles are deflected by collisions with other particles. In astronomy and optics scattering is deflection of photons by either macroscopic surfaces such as an asteroid or by small particles as in). For example, the intensity of radiation from the SunThe Sun (also called Sol is the star in our solar system. Planet Earth orbits the Sun. Other bodies that orbit the Sun include other planets, asteroids, meteoroids, comets and dust. Not all objects passing through the solar system have been orbitally capt is 9140 wattThe watt (symbol: W is the SI derived unit for power. It is equivalent to 1 joule per second (1 J/s), or in electrical units, 1 volt- ampere (1 V · A). It is the rate in joules per second at which energy is being converted, used or dissipated. Equations :s per square meter at the distance of MercuryMercury is the closest planet to the Sun, and the second-smallest planet in the solar system. Mercury ranges from 0. 5 in apparent magnitude; Mercury is sufficiently "close" to the Sun that telescopes rarely examine it (the greatest elongation is 28. (0.387AU); but only 1370 watts per square meter at the distance of Earth (1AU)—a three-fold increase in distance results in a nine-fold decrease in intensity of radiation.

For another example, let the total power radiated from a point source, e.g., an omnidirectional isotropic antenna, be P. At large distances from the source (compared to the size of the source), this power is distributed over larger and larger spherical surfaces as the distance from the source increases. Since the surface area of a sphere of radius r is , then intensity of radiation at distance r is

.

(The intensity, measured in dB, would decrease by about 6.02 dB every time that the distance r is doubled.) This is the fundamental reason why intensity of radiation, whether it is electromagnetic or acoustic radiation, follows the inverse-square behavior, at least in the ideal 3 dimensional context (propagation in 2 dimensions would follow a just an inverse distance behavior).

Source (partial): from Federal Standard 1037C