When Neil Armstrong and the astronauts that followed after him were on their way to the moon back in the late 1960s and early 1970s, they were surrounded by a dark void, virtually of infinite size and scale in all directions. Apart from those rare moments when their gaze happened to be directed towards the nearby sun, the earth or the moon in the sky, they will have seen nothing but tiny pinpricks of stars set against this engulfing blackness of infinity all around. Thinking on another level, if we were to travel out of our Solar System on an imaginary voyage toward the nearby stars, all light coming from the sun would gradually fall out of the equation. But just how bright would space be when we’re sailing between the stars? We know it’s extremely dark out there, but just how dark is very dark?

Now a UK based scientist claims to have found the answer. Abdul Ahad, a freelance astronomer and sci-fi author has produced an article that tells us just how much star light the universe is sending our way, if we exclude all light coming from the nearby sun. According to his calculations, it comes to roughly 1/300th of a full moon’s worth. Some of his colleagues and fan club have even coined it “Ahad’s constant”.

Below is a brief rundown of the complex mathematical computations involved.

Astronomers measure the brightness of stars across the night sky using something called the magnitude scale, first introduced by the Greek astronomer Hipparchus in the second century B.C. The scale in itself can be somewhat confusing, since a first magnitude star is actually brighter than a second magnitude star, opposite to what you’d expect going purely by every day common sense. You can learn more by searching Google for ‘magnitude scale for star brightnesses’.

Suppose we have two stars of magnitudes M1 and M2. Then their luminosities L1 and L2 are related by the formula:-

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 generalise this by computing all the ratios:-

Li/L1 = 10^[0.4*(M1-Mi)] for all stars i from 2 through n. The combined magnitude is then:-

Mc = M1 - 2.5*log10 (1 + L2/L1 + L3/L1 + ... + Ln/L1)

"Ahad's constant" is simply defined to be the sum of all the individual magnitudes of every single star across the entire night sky, right down to the faintest star that could ever be seen with the most powerful telescope ever invented or is likely to be invented in the future. In other words, the value of "n" in the above formulae (i.e. the star count) will tend to infinity. Based on Ahad’s numerical integrations, he has found that as n tends to infinity, the variable Mc in the above equation tends toward a bottom line figure of some -6.5 magnitudes (1/300th of a full moon equivalent worth of light - the so-called “Ahad’s constant”).

The constant cannot be appreciated by someone sailing more than a couple of light years beyond the neighbourhood of the Sun in any direction. When you're that far out, you’d want certain physical barometers to pinpoint your overall ‘existence.’ One of them might be knowing whether the environment your ship is sailing through is a complete vacuum. Another might be knowing your distance from the next nearest planet or star. Yet another might be to know how much net starlight the sky is providing. It will remain an invariant celestial constant to a traveller located in deep interstellar space within several hundreds - if not thousands - of light years from here. All that humanity can ever hope to physically experience or meaningfully contemplate over within the foreseeable future of our species...”

Stars in the neighborhood of the sun are extremely feeble in their intrinsic brilliance - most of them being tiny red dwarves of < 0.1 x sun power - and the average spacing between them is approximately 5 light years. Hence, 99.9% of the time during an interstellar voyage between any two stars in this part of the galaxy, you will be travelling under the feeble illumination quantified by "Ahad's constant":

As we venture outward from our Solar System, the sun would diminish in its apparent brightness, much like how the green light from a traffic signal gradually fades to a star-like point in the rear view mirror inside a car, as it pulls away.

By working out a point in space where the sun’s light intensity becomes exactly equal to that of the surrounding cosmic illumination of -6.5 magnitudes, Abdul Ahad has defined an imaginary sphere. That has now become generally known in Physics and Astronomy circles as the “Ahad Sphere of Solar Illuminance”, and its radius extends approximately one trillion miles or about eleven thousand five hundred astronomical units outward from the sun.