Conceptualising the distances to the moon and to the sun

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

03 November 2024

I was seated at my desk doing some idle Internet browsing when a neighbour’s 12-year-old son came and asked me this question: “If the earth was here [touching one corner of the desk] and the moon was here [touching another corner], where would the sun be?” I looked up to him thinking, “Whatever are they teaching children in this Competency Based Curriculum [CBC] is good!”.

Any way, I asked him if he knew how far the sun and the moon were in reality and he said he couldn’t remember. That’s where we started the lesson: the moon is 384,000km from Earth and the sun is 1.5 million km away. So, going to the sun is equivalent to going to the moon 390 times [195 round trips!].

Next, we measured the length between the two corners of my desk that he had touched and it came to 120cm [1.2m]. So, I went to explain that, if the distance to the moon was reduced to 1.2m, then that to the sun would be 390 multiplied by 1.2m. The answer is 468m.

“Wow! That’s very far away….is it as far as our house?” He enquired. Well, I went to Google Maps and selected the “measure distance” function which gives straight-line distances between places. By sheer coincidence, it turned out that the distance to their house is about 460m from ours.

“Wow, baba Kihanya, that is very far; how come we can see the sun when it is so far away?” Children are amazingly curious! I explained that it is because the sun is very big and very bright. To which quickly asked: “How big is it?”

The sun is 1.4 million km across, so, if we keep this scale, it would be about 1.4 million divided by 390, which comes to about 3.6m in diameter. Another “Wow!” and then: “That must be bigger than my bedroom”. He picked the piece of paper on which we were doing all this, shot out of my house and ran to his friends playing on the road outside…

I did not get the chance to point out to him the other interesting coincidence that if we divide the distance to the moon [384,000km] by its diameter [3,400km] we get 113. If we do the same to the sun, 150 million km divided by 1.4 million km, we get 107. These two numbers, 113 and 107 are not very different. It is no wonder that the two heavenly appear to be the same size when viewed from earth.