Why do celestial bodies appear the same distance from us?

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

03 May 2020

There are some uncanny numbers in the universe. The speed of light is about 300,000,000 metres per second while the speed of sound is about 300 metres per second. It makes me wonder whether the fact that light is one million times as fast as sound was just accident of nature.

Here are some others: the sun is about 150 million kilometres from Earth and it measures about 1.5 million km across. The moon is about 384,000km away and its diameter is about 3,500km. Those numbers look unrelated, but when we divide the distance by the size, we find that the ratios are approximately equal: 100 for the sun and 109 for the moon.

For this reason, both celestial bodies appear equal in size when viewed from earth. The sun appears to be only slightly bigger that the moon yet the reality is that it is over 400 times larger.

Two months ago, I wrote here what our science teacher used to tell us: “the earth is so large that we can’t even form its image in our mind”. But the sun is even larger: the earth is only 12,800km across while the sun is 1.5 million km. The ratio of the two sizes is 109…that number again!

Remember that 109 is also the ratio of the distance to the moon to its diameter. I am not sure if that similarity has any physical meaning…

So, now we understand why the sun and the mood appear to be the same size, but why do the two seem to be the same distance from us? The answer to that has to do with the limitation of our vision.

The reason we have two eyes is to help us judge how far an object is from us. Each eye sees a slightly different image and, from these, the brain works out the distance to the object.

When you look at an object, the brain notes the angle between two lines: from left eyes to object and from right eye to object. The farther away the object is, the smaller this angle becomes.

Of course, there is a limit of how small an angle the human brain can detect. About 80 per cent of all people can discern down to about 0.01 degrees and over 97.5 per cent of us can distinguish more than 0.04 degrees.

Considering that the distance between our eyes is about 6.5cm, it turns out that the limit of our perception of depth is about 93m to 180m. Objects that are farther than that will appear as if they are the same distance from us.

This explains why mountains seem to be deceivingly near. Indeed, there were pictures posted on the internet showing the city of Nairobi with Mount Kenya in the background. Many people dismissed the images as fake since the mountain appear too close to the city. Well; they are real and now you know what’s going on…