What is the resolution of the sky? Well, it is a perfect 25K screen.

Summary :: Have you ever wondered what is the resolution of the screen over our head up all time throughout the year ? One day, this idea hit my mind and I tried to actually calculate the resolution of the sky that we see. The result is very interesting. Find out more about this in this writing.

Reading Time :: 10 minutes.

There is a giant screen above our head, the biggest & the brightest amphitheater around us, built by the nature. It is the brightest in the day, and it is also the darkest in the night, unless the street lights mess up with the natural panorama of the beautiful stars all over the sky. There is hardly anyone there who did not ever look up into the sky in a solo night, did not get mesmerized in its beauty and did not ponder upon the questions like who are we… where did we come from… what is the meaning of this universe…

Well, I am just like that common man who has always been a fan of the night sky. How the stars, uncountable in number, twinkle restlessly, how they tell us the story about the immortality of time, how the deepest silence rein all over the sky in a moonless night – have always attracted me like anything. I have been looking up into the sky every evening. On one such day, the idea came to my mind about the resolution of this scene.

Let us consider some facts and do little bit of calculation. Our eyes are made of very precious nerves and very delicate mechanisms that enable us to see the beauty of this world around us. Still, there are some limitations or boundaries in our eyes. No, it is not the dark spot I am talking about, which you must have read in the school books. I am talking about the maximum and minimum limits to which our eyes can stretch themselves for vision. One such limitation is the smallest size our eyes can see. We know that we cannot see tiny elements… for example, we cannot see electrons, protons or viruses. But what is the smallest size that we can actually see ?

Honestly, there is no ‘smallest size’ in absolute terms. What matters is the angle made by the object in our eyes. If we just imagine two rays coming from two extreme points of an object (let us consider the Sun in this case), the rays make an angle when they meet our eyes. Check the diagram below. For the Sun, this angle is approximately half a degree. A smaller object in the sky, will make a smaller angle when we see them. But there is a limitation there. An object must make an angle of half minute or more in order to be distinctively visible by our eyes. Here minute is not a measurement of time, one minute is 1/60-th part of one degree. It is a measurement of angle, very tiny angle.

If the two points are such that they make an angle less than half minute, our eyes cannot distinguish them as separate points. They will appear as one single point in our eyes (if at all visible). This is the case with the most perfect eye in the world, although on an average, we all have lesser resolving power in our eyes. But let us assume here that we all have perfect eyes and hence all of us can distinguish a half minute angle. This is the boundary value we will use in order to calculate the resolution of the sky.

Before that, let us understand this part of the math little better.

We said, the angle made by an object must be at least half minute. But we did not specify the actual size of the object. Why ? Because the actual size does not matter. If we draw a half minute angle from our eyes, taking any one eye as the vertex of a triangle, and extend the angle further, the two lines will move apart from each other as we extend them. The distance between the two lines will increase if we go far & far. This means, the actual object may be of any size, but it can make a small angle in our eyes if the object is far away from us. This is why we do not take the actual distance between two points on an object, instead, we take their angular distance i.e. the angle they make in our eyes. If their angular distance is half minute or more, they appear as two distinct points to us. We see in the above figure that the Sun makes an angle of half degree in our eyes. A half minute angle will be 1 of 60 parts of it.

Now… what is a resolution ? You probably already know that, but here is a quick recap.

A resolution means, how many ‘dots’ are present on a screen. A dot is the tiny unit on the screen that emits a single light beam & represents one pixel of the image on the screen. Our smart phones typically has 720p or 1080p resolution. That means, the mobile screen has got 720 or 1080 dots (or pixels) along its width (the shorter dimension). Here ‘p’ stands for pixels and we assume the mobile is held in portrait mode. Based on the aspect ratio of the screen, there will be a fixed number of dots (or pixels) along its height too. The most common aspect ratio is 1.778. Using that, the number of dots (or pixels) along the height will be 1280 for a 720p display and 1920 for a 1080p display. Thus, we can imagine the mobile screen as a matrix of 1280 by 720 pixels. This is called HD (High Definition) screen. The larger screen of 1920 by 1080 pixels is known as Full HD (FHD).

With that much knowledge in our kitty, let’s now try to figure out the resolution of the biggest & the brightest screen of all times.

We can imagine the sky as a hemisphere. Two distinct dots on this hemisphere can be imagined as two distinct stars. If these two stars make an angle less than half minute, they will appear as one single star. Hence let us assume the sky is full of such stars which is barely just distinct in our eyes. How many such stars do we need in order to fill the entire sky ?

If the radius of our imaginary hemisphere is R, then the two distinct stars making a half minute angle in our eyes, will be separated by an aerial distance of Rθ where θ = 0.5 minute angle expressed in the radian system (1 radian = 57.3 degrees approximately). Each star will have to maintain this distance in all directions, hence each star can be imagined to occupy a circle of diameter Rθ (or radius Rθ/2).

Let us calculate the value of θ in radian first.

θ = 0.5 minute = 0.5 × π / (180 × 60) = 0.000145 radian.

The sky is imagined as a hemisphere here. Total surface area of one hemisphere is 2πR². So the number of dots (stars in this case) required to fill the entire sky is given by:

2πR² / π(Rθ/2)² = 8/θ² = 378,179,292. If we put any more stars there, they will get superimposed on some existing stars and won’t be visible distinctively in our eyes.

From this result, we can conclude that the sky has got a total of 378,179,292 pixels as visible in our eyes. Wow, that’s whooopping 378 megapixel screen over there! To express this pixel set in our common resolution format of width by height, we must first transform this hemisphere-shaped sky into a rectangular plane, much like how the map of our round-shaped Earth is usually drawn on a rectangular paper.

Maintaining the commonly used aspect-ratio of 1.778, we can see that,

378,179,292 = approximately 25930 (width) × 14584 (height) in landscape mode.

Taking the wider dimension, we see that the screen has a resolution of 25930 pixels. In binary mathematics, 1024 is taken as 1K. For example, a 4K television has nearly 4 × 1024 or 4096 pixels along its width (somewhat less than that due to commercial reasons). So dividing 25930 by 1024 we get approximately 25K. Yes, that’s the number we were looking for. We can say that the celestial hemisphere above our head, known as sky, is a perfect screen of 25K resolution. None of the planetariums in the world has gone up to that level yet. Maximum resolution we can see in a planetarium projector, is 8K. And that looks quite good. But with advent of new technology, we will one day see 25K screen as well. I have no doubt about it.

One point needs to be noted here. When I say the resolution of the sky, I mean the sky as we observe. The sky itself is not 25K, in fact no matter has any finite limit up to which you can divide it or partition it to count its units. We are talking about the resolution at which our eyes see the sky. If we replace the sky with an artificial screen, and it has better resolution than 25K, our eyes wont be able to catch the difference. So the maximum resolution at which we see the sky, stands at 25K.

But is the sky real ? Whatever we see in the night sky, does that really exist or is it just our perception and imagination ? Have you ever heard about immaterialism that questions the validity of the reality itself ? Stay tuned for my next article on this blog.

Thanks for reading!

I cordially welcome your comments if you have to say anything on this write up.

~ Jeet Guha Thakurta