How Many Lumens Is The Sun?
When checking the features and specifications of various flashlights, one always checks the amount of lumens that the flashlight can produce.
Since our Sun converts ~4.000.000 tons of mass into energy every second(!), many people wonder how many lumens the sun is, despite it radiating the energy in a very broad spectrum.
Anyway, the sun is a very powerful "flashlight" ...
Published: December 12, 2022.
Solar Constant is the value of the average spectral irradiation of Earth above the atmosphere by the Sun, and it has a value of 1361 W/m2 during the solar minimum and 1362 W/m2 during the solar maximum.
Note: Solar minimum and Solar maximum cycle lasts 11 years.
But Solar Constant tells us the irradiation of Earth above the atmosphere, and it includes the full electromagnetic spectrum.
When calculating the Sun lumens, we must use visible light.
Luminous Efficiency of the Suns: Watts to Lumens
The sun is a star with a black body temperature of ~5800 K and it features luminous efficiency of 93 lumens (of visible light) for every Watt.
That means that each square meter of Earth (above the atmosphere) gets 1362 x 93 = 126666 lumens (lm) of visible light. And that is a lot...
Calculating Sun's Lumens
Since the Sun is 149600000 km away from the Eart (one Astronomical unit), that means that the sphere around the Sun at the Earth's distance has a surface of:
Sphere's Surface = 4 * 149.6 * 106 * 149.6 * 106 * π = 281237.385 * 1012 km2 = 281237.385 * 1018 m2 = 281.237385 1021 m2
So, the sphere surface at the Earth's distance from the Sun is 281.237385 Zm (zetta-meters, or sextillion meters (short scale, US), or trilliard meters (long scale, Europe, for example).
Now that we know the surface of the sphere, we can calculate the lumens of the sun:
ΦSun = 281.237385 * 1021 m2 * 126666 lm/m2 = 35623214.6 * 1021 lm = 35.6232146 * 1027 lm = 35.6232146 Rlm (ronna-lumens)
So, next time if somebody asks how many lumens is the Sun, feel free to say that it is ~35.6 ronna-lumens :)
Again, that is a lot ... The Sun will continue to glow for 4-5 billion (short scale, US) or 4-5 milliard (long scale, Europe) years, converting its mass into energy. That would be a lot of batteries ...