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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.
Because Solar System bodies are illuminated by the Sun, their brightness varies as a function of illumination conditions, described by the phase angle. This relationship is referred to as the phase curve. The absolute magnitude is the brightness at phase angle zero, an arrangement known as opposition, from a distance of one AU.
The apparent magnitude (m) is the brightness of an object and depends on an object's intrinsic luminosity, its distance, and the extinction reducing its brightness. The absolute magnitude ( M ) describes the intrinsic luminosity emitted by an object and is defined to be equal to the apparent magnitude that the object would have if it were ...
Brightness is an attribute of visual perception in which a source appears to be radiating or reflecting light. [1] In other words, brightness is the perception elicited by the luminance of a visual target.
Apparent magnitude (m) is a measure of the brightness of a star, astronomical object or other celestial objects like artificial satellites. Its value depends on its intrinsic luminosity, its distance, and any extinction of the object's light caused by interstellar dust along the line of sight to the observer.
The object's actual luminosity is determined using the inverse-square law and the proportions of the object's apparent distance and luminosity distance. Another way to express the luminosity distance is through the flux-luminosity relationship, = where F is flux (W·m −2), and L is luminosity (W). From this the luminosity distance (in meters ...
Isolating from the equation =, finds that the distance (or, the luminosity distance) in parsecs is given by = + The uncertainty in the distance in parsecs ( δd ) can be computed from the uncertainty in the distance modulus ( δμ ) using δ d = 0.2 ln ( 10 ) 10 0.2 μ + 1 δ μ ≈ 0.461 d δ μ {\displaystyle \delta d=0.2\ln(10)10^{0. ...
The relationship is represented by the equation: = where L ⊙ and M ⊙ are the luminosity and mass of the Sun and 1 < a < 6. [2] The value a = 3.5 is commonly used for main-sequence stars. [ 3 ] This equation and the usual value of a = 3.5 only applies to main-sequence stars with masses 2 M ⊙ < M < 55 M ⊙ and does not apply to red giants ...