How much light illumination would the sky provide during a voyage out towards the stars?[An Astronomical paper by A. Ahad]
Article posted: 10 July 2004, with later revisions
Clearly, stars in themselves are very bright sources of light providing illumination throughout our galaxy. But if we excluded all light emanating from the Sun "How bright would the night sky be overall?", "How much starlight does the universe actually throw at us?", "How bright are the vast regions of empty space _between_ stars in the solar neighbourhood?", "How much light is illuminating objects in the Oort cloud?", "How much overall light illumination would a starship sailing out beyond our solar system, experience?" "How much light is illuminating non-luminous gas and dust in interstellar space?"
This paper provides an analytical estimate of the cosmic night sky's visual integrated brightness, as seen from an interstellar location. The originality of the method behind this work and its robustness was first discussed across several newsgroups in the 'sci' category back in July 2004, and subsequently acknowledged by Dr. Roger Griffin at the UK Institute of Astronomy, Cambridge and the Papers Section of the British Astronomical Association, London.
Provisional results were later published in the Journal of the BAA in October 2005, and archived for historic records purposes in J.Br.Astron.Assoc. Vol. 115, No. 5, page 297. A PDF version of that archive is accessible here. Read a discussion of this topic here.
The Definition Appearing in Wikipedia (July 2007)
Ahad's constant is an analytical quantification of the universe's total background light flux reaching the Earth's surface from all cosmic sources, such as stars, star clusters, galaxies and quasars, excluding all light coming from the nearby Sun. It was first defined by Abdul Ahad in March 2004, as the end result of a logarithmic series whose input parameters are the apparent visual magnitude of every single cosmic source ever catalogued. The series converges toward a final value of some -6.5 magnitudes or approximately 1/300th of a Full Moon's worth of light. The progression of the series is such that as one moves toward integrating light from fainter stars of lower magnitudes, the star count increases exponentially, but the cumulative contribution of light toward the constant itself tails off more rapidly, thereby resulting in convergence. The flux equations that lead to Ahad's constant are defined as follows.
Suppose we have two stars of apparent magnitudes m1 and m2. Then their luminosities L1 and L2 are related by the Pogson Ratio:-
L2/L1 = 10^[0.4*(m1-m2)]
The luminosity of the pair of stars is L1 + L2 = L1(1 + L2/L1), and their combined magnitude is then given by:-
Mc = m1 - 2.5*log10 (1 + L2/L1)
For the general case, where the magnitudes of n stars need to be aggregated, we can generalize this by computing all the ratios:-
Li/L1 = 10^[0.4*(m1-mi)]
for all stars i from 2 through n. Then:-
Ahad's constant = m1 - 2.5*log10 (1 + L2/L1 + L3/L1 + ... + Ln/L1)
Comparing this brightness of the universe's starlight of -6.5 magnitudes with the magnitude of a Full Moon shining down from the sky on Earth (-12.7), we have a magnitude difference of 6.2, which equates to a brightness ratio, R, given by:
R = 10^[0.4*(M1-M2)] = 302
Thus, the cosmic night sky has an integrated brightness of c. 1/300th of a Full Moon's worth of light that some have informally coined "Ahad's Constant".
Ahad Radius and Ahad's Sphere
The apparent visual magnitude, m, of a star whose absolute magnitude is M, as seen from a distance of d light-years is given by:-
m = M - [5 - 5 * log10(d / 3.2616)]
Using the above formula the fall off in apparent magnitude of the Sun with increasing distance can be charted, thus:-
At a distance of circa 11,500 astronomical units going radially outward from the Solar System the Sun's apparent light output matches Ahad's constant.
It is thus possible to draw an imaginary sphere around the Sun of such a radius, within which the Sun would remain the most supreme source of light, relative to the universe's total background illumination:
The outer edge of such a sphere, in principle, defines an edge of the Sun's monopoly of light and heat provision to our Solar System and nearby interstellar space; an effective end of its light dominion.
Ahad Radius definition in Wikipedia (July 2007)
"Ahad radius defines the theoretical edge of the Sun’s sphere of light dominion above the collective light contribution of the surrounding cosmic night sky. The existence of this boundary, at c. 11,500 AUs going radially outward from the Solar System in all directions, was first postulated and quantified by Abdul Ahad in July 2004. A preliminary outline of the concept was later published in October 2005 [1] and featured in his fictional novel series First Ark to Alpha Centauri [2]."
Ahad's Constant Media Article [From Mathaba News Network]
Ahad's Constant at Relativistic Speeds
The magnitude scale for stellar brightness
Descriptions of the various star catalogues
The Seekingcosmos Directory
Copyright © 2004 Abdul Ahad. All rights reserved.