Why distant objects appear smaller than nearer ones

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

23 April 2023

Githuku Mungai was amazed to find out that the diameter of the sun is 1.39 million kilometers, yet, when viewed from Earth, some 150 million km away, it appears like a small ball. As amazing as it may be, that should not be surprising. We see this effect everyday and we should be accustomed to it.

For example: through the window from my sitting room, I can see my neighbour’s house in full. But the window is just 1.5m wide. How does a house that is at least 10m in width fit in a 1.5m hole on my wall? It is a question of perspective: the farther away an object is, the smaller it appears.

For this reason, scientists define the “apparent size” of an object (that is, how big it appears to be) as the ratio of its actual size to its distance from the observer. Thus, a house that is 10m wide and 50m away has an apparent size of 0.2; while a window that is 1.5m wide and 5m away has apparent size of 0.3. Therefore, the window appears larger than the house.

What is truly surprising, however, is that the sun and the moon appear to be the same size when viewed from Earth. This is why, during a total solar eclipse, the moon covers the sun almost exactly.

With a diameter of 1.39 million km and located 150 million km away, the apparent size of the sun is 0.0093. The moon is 3,480km in diameter and it orbits the Earth at a distance of 384,000km making its apparent size 0.0091. This is about 98 per cent that of the sun. Consequently, the two celestial bodies seem the same size to us event though one is larger that the Earth and the other is smaller than our planet.

So, how big does the sun (or the moon) appear to be when viewed from Earth? Here is a good illustration…Take a piece of paper and punch a hole on it using a normal office holepunch. If you hold the paper at arms-length – about 50cm away – the sun (or the moon) will easily fit inside the hole. That’s how small they are to us!

Finally, it is important to point out that while microscopes magnify the real size of small objects (making them bigger that they are), telescopes amplify the apparent size of large objects (making them appear nearer than they actually are).