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-------------------------- 2764 - NIGHT SKY - why is the night sky dark?
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- If we were in the middle of an infinite forest on flat land, the forest would have an infinite number of trees and whatever direction you look your line of sight would eventually run into a tree. The same thing should happen in the night sky. No matter which direction you look in an infinite Universe you would eventually see star light. The night sky should be glowing in starlight, not darkness.
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- Since there is darkness there must be an explanation. Either the Universe is not infinite and there are not an infinite number of stars, or the Universe is not static, it is expanding and the star light has not reached us yet, or, the stars are so distant they are too dim for us to see with our most powerful telescopes.
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- Let’s examine the causes for the darkness at night?
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- Astronomers have found that galaxies on the largest scale fill all of space more or less uniformly and have measured the density of the galaxies in the Observable Universe to be 0.0029 galaxies per cubic million lightyears. Astronomers estimate that there are 10^10 stars in the average galaxy. So, on average there must be 2.9*10^7 stars per cubic million lightyears.
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- So the next question is that if we know that density of stars and we know the average cross-section of the average star we can calculate the distance that your line of sight can travel before running into a star.
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---------- The average star is 7*10^8 meters in diameter, that is 3.5 *10^8 meters radius.
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---------- The cross-section area is pi*r^2 = 38*10^16 meters^2.
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---------- The density is 2.9*10^7 stars/MLY^3
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---------- The density ( lightyear = 9.5*10^21 meters) is = 0.34*10^-58 stars / meter^3
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- The concept here is that a line of sight traverses a distance (dx) until it hit’s a star. If we know the density of stars per unit volume, (n), then the number of hits per unit area lying in the line of sight is (n) * (dx) = (number of stars per cubic meter) * (distance to hit a star). If each star has a cross-section area of (A), then the number of collisions with stars = “N” = (A)*(n)*(dx).
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- If we set the number “N” equal to “1” then calculate the distance we travel before we hit the first star, 1 = (A)*(n)*(dx).
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------------------------ 1 = (38*10^16 meters^2) * 0.34*10^-58 stars / meter^3 * (dx)
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------------------------ dx = 7.6*10^40 meters
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------------------------ dx = 8*10^24 lightyears
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------------------------ dx = 8*10^18 million lightyears.
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- So the average distance your line of sight would travel before landing on a star is 8*10^15 billion lightyears. However, the Universe is only 13.7 billion years old. So, the sky is dark because our line of sight has not landed on a star yet in most every direction we look.
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- This also means that Cosmic Inflation is one explanation for the Universe expanding faster than the speed of light in its early formation. That is the only way that stars could get that far away. The edge of the Observable Universe is 10^10 lightyears away and the distance to that first star in any line of sight is 10^24 lightyears.
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- Therefore, the Observable Universe is mostly Dark because the starlight has not reached us yet.
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- The other explanation is that the Universe is not old enough yet. That light has not have “time” to reach us. Therefore, we have concluded that the night sky is dark because the Universe is finite, not infinite, and it has a finite age, not infinite.
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- Now, that we have the radius of the Observable Universe at 10^10 lightyears we can calculate the number of stars, since the density is 2.9*10^7 stars / million lightyears^3.
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- The volume of the Universe with a radius of 13.7*10^3 million lightyears. Multiply these two terms gives us 4.7*10^19 stars. Another estimate Astronomers come up with is that there are 10^11 galaxies and 10^11 stars per galaxy giving us 10^22 stars in the Observable Universe. This is within 2 orders of magnitude to our other calculation. So roughly, there are 1,000,000,000,000,000,000,000 stars out there.
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- How many stars would it take to have the same luminosity at night that we have in the day from our Sun? The luminosity of the Sun has been calculated to be 3.8^10^26 watts. Dividing by the surface area of a sphere that is 93 million miles in radius will tell us how much of this luminosity reaches Earth / meter^2.
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--------- F = Luminosity / 4*pi*d^2
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--------- F = 3.8*10^26 / 6.28 * (1.5*10^11 meters)^2
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---------- F = 1,300 watts / meter^2, very bright
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- How many stars like our Sun would we need out to 10 billion lightyears away in order to have the same brightness as daylight?
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--------- F = Luminosity / 4*pi*d^2
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--------- F = 3.8*10^26 / 6.28 * (10^11*9.5*10^15 meters)^2
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---------- F = .68*10^-26 watts / meter^2, very dim
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- How many stars would have to be out there to have the same brightness as daylight?
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--------- N = 1.3*10^3 watts / m^2 / .68*10^-26 watts / m^2
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--------- N = 2*10^29 stars
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- We would need 10^31 stars to have daylight and we only have 10^22 stars. That is a 10 million times more stars are needed to light up the night sky to daylight. But, how about lighting up the night sky just to starlight, instead of sunlight. How many stars would that take?
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- A typical star might be Proxima Centauri that is our second closest star at 4.2 lightyears away. The luminosity is 0.0006 Solar Luminosity. Using the same formula as above the flux we see is 22.8*10^-22 watts / m^2.
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- How many stars would have to be out there to have the same brightness as starlight?
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--------- N = 22.*10^-12 watts / m^2 / .68*10^-26 watts / m^2
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--------- N = 3.2*10^14 stars
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- We would need 10^17 stars to have solid starlight in the night sky, and we have 10^22 stars out there. There are enough stars out there, there must be more to explaining why the night sky is dark.
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- The rest of the answer lies with the fact that the Universe is not static. Unlike the trees in the infinite forest the Universe is expanding. At the edge of the Observable Universe the Universe is expanding faster than the speed of light and that light will never, never reach us.
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- The Cosmic Microwave Background radiation solves this in an amazing way. Each line of sight does indeed reach a star. There are enough stars out there to light the entire night sky with the brightness of a starlight.
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- We are inside this oven, but the temperature is so small because the expansion of the Universe dilutes the radiation emitted down to harmless microwave energies, at temperatures of only 2.725 degrees above Absolute Zero. The wavelengths of starlight have been redshifted to longer microwave wavelengths.
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- The are other explanations for darkness that do not hold water. One is that the dust in intergalactic space blocks the starlight. Well, this only works for a little while because the radiation would eventually heat up the dust to the same temperatures and it would begin radiating on its own. We would still see light in every direction even if much of it would be infrared light coming from the dust.
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- Another explanation is that the stars are dying. They do not have an infinite lifetime and many of these 10^22 stars would have evolved into Neutron Stars or White Dwarf stars that no longer radiate much light. These stars would be dark in the night sky.
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- This does not work either because past every dark star must lie another lighted star. And, new stars are being born out of the dead stars that go dark. New light is constantly being produced. Dead stars are not the reason for the dark sky.
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- The Universe is believed to be 10^58 meters in radius, or 10^42 lightyears. The Observable Universe is 1.37*10^10 years old and 10^26 meters in radius. The night sky is dark because we can not see most of the Universe, what we see is finite and much of the light has not reached us yet because the Universe is a finite age and there has not been enough time.
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- Lastly, the night sky is dark because the Universe is expanding and the light radiation has shifted into darkness to our eyes, into the microwave region.
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- In the Dark of Night, astronomers are making these calculations. The math was there astronomers just had to discover it. But, it seems like such a simple question. Why is the night sky dark? Why is the day sky blue? Little kid questions.
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- Better do well in school if you are going to discover the answers.
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- The Universe is more complicated than you can imagine.
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- June 21, 2020 865 2764
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--------------------- Sunday, June 21, 2020 -------------------------
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