Apparent Stellar Magnitude

9006-007

The relationship between Apparent Stellar Magnitude (m) and the brightness of a star like the Sun, may be expressed in the form:

m = -[19 + (2.5).log(I)]

where I = received intensity (W/m²).

For instance, in the vicinity of the Earth, the solar power density I = 1.39 kW/m². Plugging this value into the above equation, we find that the Apparent Solar Magnitude is -26.8. The 5 meter diameter Hale telescope on Mt. Palomar has a photographic sensitivity to "see" to +23 Magnitude, so that if we used a sufficiently narrow incoherent optical filter centered on 656 nm to cut out the planckian starlight, this telescope could just detect the mean power in the 1 kW ETI signal (9006-019) at a range of 10 light years (I = I_r = 2.04 x 10^-17 W/m²), corresponding to the 23rd magnitude (uncorrected for wavelength).

The Planck radiation from the aliens' star has a received intensity I_r reduced by a factor of (1 A.U./10 L.Y.)² compared to our Sun, and this makes the star appear as a +2 Magnitude object. Note that the 10 meter diameter Keck telescope and the 2.4 meter diameter Hubble Space Telescope (HST) can just "see" +28 Magnitude, while the naked eye can see to the 6th magnitude (9006-023).

The Columbus Optical SETI Observatory
Copyright (c), 1990