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The solar "constant" is not a physical constant in the modern CODATA scientific sense; that is, it is not like the Planck constant or the speed of light which are absolutely constant in physics. The solar constant is an average of a varying value. In the past 400 years it has varied less than 0.2 percent. [2]
The solar constant is the amount of power that the Sun deposits per unit area that is directly exposed to sunlight. The solar constant is equal to approximately 1,368 W/m 2 (watts per square meter) at a distance of one astronomical unit (AU) from the Sun (that is, at or near Earth's orbit). [99]
The factor 4 π is ubiquitous in theoretical physics because in three-dimensional space, the surface area of a sphere of radius r is 4 π r 2. This, along with the concept of flux , are the basis for the inverse-square law , Gauss's law , and the divergence operator applied to flux density .
Thus, from the Stefan–Boltzmann law, the luminosity is related to the surface temperature T S, and through it to the color of the star, by = where σ B is Stefan–Boltzmann constant, 5.67 × 10 −8 W m −2 K −4. The luminosity is equal to the total energy produced by the star per unit time.
So = where is the gravitational constant. The acceleration of Solar System body number i is, according to Newton's laws: ¨ = ^ where is the mass of body j, is the distance between body i and body j, ^ is the unit vector from body i towards body j, and the vector summation is over all bodies in the Solar System, besides i itself.
Solar radiation pressure on objects near the Earth may be calculated using the Sun's irradiance at 1 AU, known as the solar constant, or G SC, whose value is set at 1361 W/m 2 as of 2011. [17] All stars have a spectral energy distribution that depends on their surface temperature. The distribution is approximately that of black-body radiation.
The Stefan–Boltzmann equation applied to a black body gives the value for luminosity for a black body, an idealized object which is perfectly opaque and non-reflecting: [11] =, where A is the surface area, T is the temperature (in kelvins) and σ is the Stefan–Boltzmann constant, with a value of 5.670 374 419... × 10 −8 W⋅m −2 ⋅K −4.
The Planck constant, or Planck's constant, denoted by , [1] is a fundamental physical constant [1] of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a matter wave equals the Planck constant divided by the associated particle momentum.