I was sitting by the pool today (as I often do), thinking about stuff (as I often do)…
I was thinking about a movie called Sunshine released in 2007. An excellent Si-Fi movie set 50 years into the future when the sun is dying. (Worth a watch by the way. It’s a straight forward and complex concept.)
I was thinking about the “sun room” on the space ship. The crew often go there, and after requesting the computer to open the screen only 2% or 3% they watch the sun from close up. They learn a lot about themselves by doing this – watch it, you’ll understand what I mean.
That got me thinking, how close would the earth be to get a suntan in 5 minutes that now takes 1 hour? Crazy thought, but I was lying in the sun pondering it?
So I decided to do a mind exercise to work it out:
Let’s assume that the atmosphere remains as it is. It just makes it easier.
Now for some straight physics and geometry: The surface of a sphere is calculated by 4 time Pi times Radius squared – 4 x pi x r^2.
I.e. Surface Area of a sphere is proportional to the square of its radius.
When the sun emits energy in any given second (all across the frequency range: gamma rays, ultraviolet, light, infrared, and a heap of photons all charged up and going somewhere fast), that particular unit of energy spreads out around an ever-growing sphere as it moves away from the sun, i.e. it decreases directly in proportion to the square of the distance away from the sun. I.e. Energy is proportional to Radius^0.5
To get a 1 hour sun tan in 5 minutes we need to cram in 12 times as much energy in 5 minutes as we would have done in 60 minutes.
What is the square root of 12? It’s only 3.46, about 4.
That means we need to move the Earth only a 107 million miles closer to the sun and you’ll only need 5 minutes to get a tan! And 10 minutes to burn, and 1 hour, hmmm… probably a cinder?? !!
There you go. Stuff you really need to know.
Some interesting facts on the sun and the Earth’s relationship to it.
- It’s ‘only’ 150 million kilometers from the Earth to the sun (That’s the distance it takes to go around the earth 3,750 times) (So to tan in 5 minutes we need to move the earth to an orbit of 43 million kilometers, inside the orbit of Mercury).
- It takes the light from the sun about 8 minutes to reach us.
- The estimated temperature in the center of the sun is 15,000,000 °C.
- Diameter of the sun is 1.39 million kilometers (That’s 34 times the earth’s circumference)
- Surface temperature of the sun is 6,000 degrees celsius.
Puts our home into perspective a little doesn’t it.