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I know the apparent magnitude of sun is -26.74, but I wonder how to get this value if we don't know the absolute magnitude?

Thanks!

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    $\begingroup$ You would measure the apparent magnitude, the absolute magnitude is what would be calculated. $\endgroup$ Commented May 25, 2023 at 20:13

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The apparent magnitude is found by direct observation. You can find the apparent magnitude using a light-sensitive device.

This is true for all observed bodies. The apparent magnitude is how bright it "appears" to be from Earth. The only difficulty with finding the apparent magnitude of the sun is that it is so bright that the highly sensitive light detectors that would be used to measure the apparent magnitude of a star would be damaged by the brightness of the sun. But that is a practical difficulty.

Having found the apparent magnitude, one can calculate the absolute magnitude if (and only if) you know the distance to the star. The absolute magnitude can be calculated from the apparent magnitude and the distance of the sun. It is known to be 4.83.

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If you know neither the absolute nor apparent magnitude, you can find absolute magnitude with the following formula:

  • M = absolute magnitude
  • L = luminosity (in watts) of the object
  • L0 = zero-point luminosity, AKA 3.0128E+28 watts

M = (log10(L/L0)) * -2.5

Once you have the absolute magnitude, apparent magnitude is calculated with this formula:

  • m = apparent magnitude
  • d = distance in parsecs

m = (M-5) + (log10(d*5))

Credit goes to https://www.omnicalculator.com/physics/luminosity#absolute-and-apparent-magnitude. I just altered the formula to make sense for those with less experience in mathematics, such as myself.

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  • $\begingroup$ Both formulae are incorrect. Or at least the second formula is incorrect and the first is incorrect if $L_0$ is defined as the luminosity of the Sun (it isn't). $\endgroup$
    – ProfRob
    Commented May 26, 2023 at 6:35
  • $\begingroup$ Thank-you. That's actually meant to be "zero-point luminosity" and I've edited accordingly. Are there still issues? $\endgroup$
    – Kazon
    Commented May 26, 2023 at 17:46
  • $\begingroup$ my "issue" would be that luminosity cannot be observed. One can only observe luminous flux, from which one can calculate apparent magnitude, and from that you can calculate absolute magnitude and luminosity from the distance of the object. You can't calculate apparent magnitude from luminosity, because the only way to know the luminosity is to use the magnitude (or the luminous flux) $\endgroup$
    – James K
    Commented May 26, 2023 at 20:15
  • $\begingroup$ I also have a formula for calculating luminosity with a star's radius and temperature, but again, I suppose a star would already have a measured magnitude if it has those? I'm accustomed to using Simbad and NASA's exoplanet catalogue, wherein a single, simple apmag/abmag is rarely given. $\endgroup$
    – Kazon
    Commented May 26, 2023 at 22:37

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