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The monochromatic AB magnitude is defined as the logarithm of a spectral flux density with the usual scaling of astronomical magnitudes and a zero-point of about 3 631 janskys (symbol Jy), [1] where 1 Jy = 10 −26 W Hz −1 m −2 = 10 −23 erg s −1 Hz −1 cm −2 ("about" because the true definition of the zero point is based on magnitudes as shown below).
The zero point is used to calibrate a system to the standard magnitude system, as the flux detected from stars will vary from detector to detector. [2] Traditionally, Vega is used as the calibration star for the zero point magnitude in specific pass bands (U, B, and V), although often, an average of multiple stars is used for higher accuracy. [3]
Therefore, the magnitude m, in the spectral band x, would be given by = (,), which is more commonly expressed in terms of common (base-10) logarithms as = (,), where F x is the observed irradiance using spectral filter x, and F x,0 is the reference flux (zero-point) for that photometric filter.
A particle, carrying a charge of one coulomb (C), and moving perpendicularly through a magnetic field of one tesla, at a speed of one metre per second (m/s), experiences a force with magnitude one newton (N), according to the Lorentz force law. That is, =.
The zero-point energy makes no contribution to Planck's original law, as its existence was unknown to Planck in 1900. [25] The concept of zero-point energy was developed by Max Planck in Germany in 1911 as a corrective term added to a zero-grounded formula developed in his original quantum theory in 1900. [26]
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal n̂, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
Mathematically, mass flux is defined as the limit =, where = = is the mass current (flow of mass m per unit time t) and A is the area through which the mass flows.. For mass flux as a vector j m, the surface integral of it over a surface S, followed by an integral over the time duration t 1 to t 2, gives the total amount of mass flowing through the surface in that time (t 2 − t 1): = ^.
For objects within the immediate neighborhood of the Sun, the absolute magnitude M and apparent magnitude m from any distance d (in parsecs, with 1 pc = 3.2616 light-years) are related by = = (), where F is the radiant flux measured at distance d (in parsecs), F 10 the radiant flux measured at distance 10 pc.