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It allows the overall brightnesses of objects to be compared without regards to distance.
Absolute Magnitude for stars and galaxies (M)
In defining absolute magnitude it is necessary to specify the type of electromagnetic radiation being measured. When referring to total energy output, the proper term is bolometric magnitude. The dimmer an object (at a distance of 10 parsecs) would appear, the higher its absolute magnitude. The lower an object's absolute magnitude, the higher its luminosity. A mathematical equation relates apparent magnitude with absolute magnitude, via parallax.
Absolute magnitudes for stars generally range from -10 to +17. The absolute magnitude for galaxies can be much lower (brighter). For example, the giant elliptical galaxy M87 has an absolute magnitude of -22.
where is 10 parsecs (≈ 32.616 light-years) and is the star's distance; or:
where is the star's parallax and is 1 arcsec.
- Rigel has a visual magnitude of mV=0.18 and distance about 773 light-years.
- MVRigel = 0.18 + 5*log10(32.616/773) = -6.7
- Vega has a parallax of 0.133", and an apparent magnitude of +0.03
- MVVega = 0.03 + 5*(1 + log10(0.133)) = +0.65
- Alpha Centauri has a parallax of 0.750" and an apparent magnitude of -0.01
- MVα Cen = -0.01 + 5*(1 + log10(0.750)) = +4.37
Given the absolute magnitude , you can also calculate the apparent magnitude from any distance :
Absolute Magnitude for planets (H)
In this case, the absolute magnitude is defined as the apparent magnitude that the object would have if it were one astronomical unit (au) from both the Sun and the Earth and at a phase angle of zero degrees. This is a physical impossibility, but it is convenient for purposes of calculation.
Formula for H: (Absolute Magnitude)
Moon: = 0.12, = 3476/2 km = 1738 km
The absolute magnitude can be used to help calculate the apparent magnitude of a body under different conditions.
is the phase integral (integration of reflected light; a number in the 0 to 1 range)
- Example: (An ideal diffuse reflecting sphere) - A reasonable first approximation for planetary bodies
- A full-phase diffuse sphere reflects 2/3 as much light as a diffuse disc of the same diameter
- is the distance between the observer and the body
- is the distance between the Sun and the body
- is the distance between the obverser and the Sun
- = +0.25
- = = 1 au
- = 384.5 Mm = 2.57 mau
- How bright is the Moon from Earth?
- Full Moon: = 0, ( ≈ 2/3)
- (Actual -12.7) A full Moon reflects 30% more light at full phase than a perfect diffuse reflector predicts.
- Quarter Moon: = 90°, (if diffuse reflector)
- (Actual approximately -11.0) The diffuse reflector formula does better for smaller phases.
- Full Moon: = 0, ( ≈ 2/3)
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