Around Halloween time, you may see someone dressed up like Satan or maybe watch scary movies that involve Satan or demons. But the day after Halloween is All Saints Day, which celebrates people of a more holy disposition, particularly the Christian Saints. And then there is Christmas in December, celebrating the birth of Jesus with images of singing angels. That’s quite a reversal over night or even in two months, as if Heaven and Hell aren’t so far apart. Granted, they may be metaphysical places that we can’t travel to physically, what if we could? How far apart might they be?
In terms of answers, I’m looking for a distance that physically fits on Earth. Imagery for Heaven often involves clouds, as if in the sky. The atmosphere is said to extend about 6,000 miles above Earth’s surface.[1] Hell is often depicted as being underground with fire. That fits in with lava being (usually) deep within the Earth. The radius of the Earth is about 4000 miles. So I’m basically looking for a distance of 10,000 miles or less. Granted I’m not sure there’s a right or wrong answer.
Turns out, in the late 1600s, the English poet John Milton described a fictitious war between Heaven and Hell in his epic poem, “Paradise Lost.”[2] During that fictitious war, Satan is cast out of Heaven and falls towards Hell for nine days. Yes, the plan here is to use a poem written hundreds of years ago, to calculate a physical distance between two metaphysical places. You can calculate just about anything, if you really want to. You might have to make some assumptions and give up some accuracy, however.
How far did Satan fall in 9 days? We can try using the standard acceleration due to gravity of 32 feet per second per second, for starters. There are 86,400 seconds in one day, so nine days would be 777,600 seconds. For acceleration a and time t, the distance is (1/2)×a×t×t. The final distance comes out to 9,674,588,160,000 feet or about 1.8 billion miles. Considering our upper limit of 10,000 miles for an acceptable answer, this initial estimate of 1.8 billion miles is obviously more than a bit too far. To put things into perspective, the Earth is just over 92 million miles from the sun. Someone else has calculated the distance between Milton’s Heaven and Hell as roughly the distance between Earth and the moon.[3] That’s still a bit far.
Maybe we should take wind resistance into account. Presumably, Satan and other leaser divine beings are shaped like humans, so the physical fall of Satan could very well resemble the fall of a human. If something falls for long enough in a fluid like air or water, it eventually reaches a terminal velocity and does not fall more quickly after that.[4] Some people estimate the terminal velocity of a human skydiver as around 120 mph. A span of 9 days has 24×9=216 hours. Assuming Satan reached the terminal velocity, the distance would be 25,920 miles, roughly the circumference of the Earth (or about 3 times its diameter). While this estimate is much better than the first, it still isn’t quite the answer we’re looking for.
Wind resistance may be a step in the right direction. Satan presumably had wings as an angel, which could help slow his physical descent even further. Not being thoroughly familiar with the details of the poem, I don’t know whether Satan’s wings (assuming he had them) were damaged during his fall. Maybe he could at least glide some. How much can such wings slow his descent? It’s not hard to find information about a bird staying aloft while flapping its wings very little or a glider plane staying traveling many horizontal miles while getting lift from thermals. Neither of these has led to a good answer, so I’m going to guess. Each wing of an angel might have roughly the surface area of a similar-sized wingless human. The terminal velocity happens to be inversely proportional to the square root of the horizontal area. So if we assume our falling angel Satan had about 3 times the horizontal area as a skydiver, then the 120 MPH above can be multiplied by about 1/sqrt(3) = sqrt(3)/3 = ~1.73/3 = ~0.58 or about 60% of what it was. (I’m using sqrt(x) to represent the square root of x.) So now the terminal velocity is about 72 MPH. Again with 216 hours, that comes to roughly 15,500 miles, which is still too far to fit on Earth.
This doesn’t have to be a total failure. There could be other sources of information related to the distance between Heaven and Hell. Or to be more thorough with “Paradise Lost” first, we might assume Satan flapped his wings or found thermals or other sources of rising air to slow his descent. But after all the physics, we still have to admit that there’s no guarantee for finding a definitive physical distance between two metaphysical places. Nor does getting numerical data from a poem help. At least it was interesting to look at some physics implications of the poem. Physics aside, why did Milton have Satan fall specifically for 9 days? Why not 10 days? Both imply Heaven is a great distance above Hell. 9 days is 216 hours, and 216 = 6*6*6. This may refer to 666, the “number of the beast.”[5] Many scary thoughts can be found on that subject (and Satan in general), including plenty from fiction. Let’s just hope Hell and its occupants are far away from Earth as well.
References
[1] https://www.nationalgeographic.org/encyclopedia/atmosphere/
[2] https://www.gutenberg.org/cache/epub/26/pg26-images.html
[3] https://scienceblogs.com/builtonfacts/2008/08/28/falling-from-heaven
[4] https://en.m.wikipedia.org/wiki/Terminal_velocity
[5] https://en.m.wikipedia.org/wiki/Number_of_the_beast
(c) Copyright 2021 by Mike Ferrell
Odd STEM 