Sun, Moon and Machu Picchu

This is something I have been wanting to post for a very long time. While watching Satyajit Ray’s last film Agantuk, featuring Utpal Dutt, I was very impressed with one observation. The reason I hadn’t published this so far was because I wanted people to watch this clip, and the VCD was not available at hand.

For those not familiar with Bengali, here is the translation:

Utpal Dutt: … What did I say the name of the city was?
Kids: Machu Picchu!
Utpal Dutt: Machu Picchu… Here, take a look at this (shows photo)
Kids: Wow! Have you been to this place?
Utpal Dutt: Of course! It was I who took this picture. I had gone there 20 years back, riding a mule. Looking at the city I was awestruck. It was made entirely of stone, but there was no stone to be seen nearby. Where did they get the stone? How did they raise the stone up the mountains (the Andes)? Nobody knows. The Incas were a wonderful civilization.
Kids: Tell us another story.
Utpal Dutt: No, no more stories. Let me show you a magic trick (takes some coins out of a pouch)
Kids: What are these?
Utpal Dutt: I am going to ask you a few questions. Let’s see if you can answer correctly. Ready?
Kids: Ready!
Utpal Dutt: OK, which one is larger, the moon or the sun?
Kids: The sun!
Utpal Dutt: How did you know? Wait … (lays two coins of the same size side by side). This is the moon and this is the sun. They appear to be of the same size in the sky…
Kids: That’s because the sun is a lot further away.
Utpal Dutt: How far? Let me tell you. The sun is 95 million miles from the earth and the moon is just 500,000 miles away.
Kids: That is why they appear to be of the same size.
Utpal Dutt: Now let’s say that the moon wasn’t 500,000 miles away, but 200,000 miles away.
Kids: Then the moon would appear much larger.
Utpal Dutt: (Replaces the “moon” coin with a larger coin) Like this, right?
Kids: Yes
Utpal Dutt: And what if the moon was 800,000 miles away?
Kids: It would appear a lot smaller.
Utpal Dutt: (Replaces the “moon” coin with a smaller coin) Like this, right?
Kids: Yes
Utpal Dutt: But that did not happen. The moon was just far enough to appear to be of the same size as the sun (puts back the original “moon” coin). That is why when the moon comes in front of the sun and slowly covers it, the edges match up perfectly…
Kids: Solar eclipse!
Utpal Dutt: Total solar eclipse. And when the earth’s shadow covers the moon, again the edges match up perfectly.
Kids: Lunar eclipse.
Utpal Dutt: Total lunar eclipse. How does this happen? (The kids look at one another) Don’t know, right? Ask the greatest scholar on earth – even he wouldn’t be able to tell you. Nobody can tell you. This is a puzzle. In my opinion this is the biggest puzzle in the universe. The sun and the moon, the king of the day and the queen of the night, and the shadow of the earth on the moon – all circles of the same size. Magic!

I found this quite profound, and indeed a very big puzzle. Of course, some of you might argue that for the moon to cover the sun during a solar eclipse, the moon has to appear smaller than the sun, not the same size (think cones), but the fact remains that the moon covers the sun perfectly during the total solar eclipse. Intriguing, right?

One Response to “Sun, Moon and Machu Picchu”

  1. […] Now there is one important fact that was not at all overlooked by the Greek scholars: the apparent sizes of the moon and the sun are quite close to each other. This means that if we send the moon to the distance of the keeping the same solid angle created by the moon, the moon will become as big as the sun, i.e. the angles subtended by the moon and the sun on a point on the earth are the same. For this reason during the total solar eclipse the moon can perfectly fit to block almost all the rays coming from the sun and the umbra tapers to the earth’s surface. The coincindence of same apparent sizes has been beautifully mentioned, in a way of story-telling to the kids, in the film Agantuk by the famous Indian filmmaker Satyajit Ray. The story-teller (acted by Utpal Dutta) says that it is an unresolved magic (see the youtube link below or […]

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