Apparent Magnitude, Absolute Magnitude, and Distance

A simple equation relates apparent magnitude, absolute magnitude, and distance.  Know any two, and you can calculate the third.


Known: Apparent Magnitude (m), Absolute Magnitude (M)
Unknown: Distance (d), in parsecs


Known: Apparent Magnitude (m), Distance (d)
Unknown: Absolute Magnitude (M)


Known: Distance (d), Absolute Magnitude (M)
Unknown: Apparent Magnitude (m)


If this were a perfect universe, the known quantities could always be measured as precisely as one desires.  But, of course, that isn’t the case.

Apparent Magnitude – if the observations are made from the surface of the Earth, atmospheric reddening and extinction (atmospheric r/e) must be taken into account to determine the apparent magnitude above the Earth’s atmosphere.  Even above the Earth’s atmosphere, cosmic reddening and extinction (cosmic r/e) must also be quantified.  Both atmospheric r/e and cosmic r/e1 cause the observed apparent magnitude to appear fainter than it otherwise would be, and bluer wavelengths are more severely affected than redder wavelengths.  The net result is to make objects appear fainter and redder than they would be if there were a perfect vacuum between source and observer.

Absolute Magnitude – is a measure of the intrinsic brightness of a celestial object, and this can only be measured indirectly for objects outside of our solar system.

Distance – is difficult to measure for objects outside of our solar system.  Trigonometric parallax gives the most accurate results for nearby stars, but uncertainty increases rapidly with increasing distance.

Apparent magnitude is the only one of these quantities that is a direct instrumental measurement: absolute magnitude and distance are determined indirectly and thus are subject to greater uncertainty.

1Atmospheric reddening and extinction (atmospheric r/e) is traditionally called atmospheric extinction, and cosmic reddening and extinction (cosmic r/e) is traditionally called interstellar reddening.  Since in both cases light is both reddened and diminished in intensity, and because "cosmic" encompasses both interstellar and intergalactic matter between source and observer, I suggest here that atmospheric r/e and cosmic r/e might be an improvement in terminology.

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