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The bolometric correction scale is set by the absolute magnitude of the Sun and an adopted (arbitrary) absolute bolometric magnitude for the Sun.Hence, while the absolute magnitude of the Sun in different filters is a physical and not arbitrary quantity, the absolute bolometric magnitude of the Sun is arbitrary, and so the zero-point of the bolometric correction scale that follows from it.
Vega, the star typically used as the zero point in photometric systems. The equation for the magnitude of an object in a given band is = (()) +, where M is the magnitude of an object, F is the flux at a specific wavelength, and S is the sensitivity function of a given instrument.
Flux decreases with distance according to an inverse-square law, so the apparent magnitude of a star depends on both its absolute brightness and its distance (and any extinction). For example, a star at one distance will have the same apparent magnitude as a star four times as bright at twice that distance.
Consequently, a magnitude 1 star is about 2.5 times brighter than a magnitude 2 star, about 2.5 2 times brighter than a magnitude 3 star, about 2.5 3 times brighter than a magnitude 4 star, and so on. This is the modern magnitude system, which measures the brightness, not the apparent size, of stars.
This shift is the apex angle in an isosceles triangle, with 2 AU (the distance between the extreme positions of Earth's orbit around the Sun) making the base leg of the triangle and the distance to the star being the long equal-length legs (because of a very long distance from the Earth orbit to the observed star).
A star at 10 parsecs has a parallax of 0.1″ (100 milliarcseconds). Galaxies (and other extended objects ) are much larger than 10 parsecs; their light is radiated over an extended patch of sky, and their overall brightness cannot be directly observed from relatively short distances, but the same convention is used.
From this measurement and the apparent magnitudes of both stars, the luminosities can be found, and by using the mass–luminosity relationship, the masses of each star. These masses are used to re-calculate the separation distance, and the process is repeated. The process is iterated many times, and accuracies as high as 5% can be achieved. [8]
Stellar parallax is the apparent shift of position of any nearby star (or other object) against the background of distant stars. By extension, it is a method for determining the distance to the star through trigonometry, the stellar parallax method.