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| Home and Church |
Note: Please click on the images to see them.
Today is the feast of St. Sebastian's Church. It is one of the most celebrated feasts in our neighbourhood. Apart from colourful fireworks, sky lanterns were also sent. I was at home then. After the lanterns got to some level, almost all of them turned off. I wanted to calculate that height.
As the above figure shows church and our house are 746.02m apart (Google Earth helped me there). I found the angle of inclination of that height. That was about \(45^o\). Assuming the lanterns travel straight up and the church and our house are at the same level, the height the lantern goes up would be about 750 meters.
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| That height! |
Our village is close to sea. So maybe a ship far away might see those lanterns. What would be the maximum distance of a ship which might have seen those? Google tells me that the diameter of earth is 12742 km. We have to remember that this value is an average and Earth is not a perfect sphere. The tangent to the Earth from that maximum height point will help us now.
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| This image is a bit exaggeration on h.. |
That will be about \(r\cos^{-1}(\frac{r}{h+r})\) where \(r\) is the radius of the Earth and \(h\) is the maximum height of the lantern. Wolfram tells
97.8 km is that distance. What if we want to find the area covered by that Lantern? i. e. the area of the Earth for which the lantern is visible. Wolfram tells it's
30020 \(km^2\)! Here we assumed that area is planar. We can safely assume that because it's an itzy-bitzy portion of the giant Earth.
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| Area "covered" by our lantern |
Can you see people near Pattipola and even Negambo can see that lantern? Actually that candle light is scattered in the atmosphere. So they missed that ;) ... Hm... What a journey!
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