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Buzz Bloom
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- Quotes from a recent Scientific American will be in the main text. The primary quote is about New Zealand having a 40% stronger UV radiation exposure than places in the northern hemisphere. My effort at understanding the math produces a limit of only a 6.9% stronger UV exposure.
Scientific American
June 2, 2022
Vol 32 Number 6
Page 62
Title: Skin Cancer around the World
Two Quotes:
“The main cause of skin cancer is the exposure to the sun’s ultraviolet rays…”
“UV radiation is about 40% stronger in New Zealand than it is at corresponding latitudes in the Northern Hemisphere. Because of Earth’s tilt, the Southern Hemisphere is closer to the sun than the north is during its own summer. “
I am unable to find any basis for this difference other than that the distance of the sun to the Earth is greater when the Earth is at aphelion (152.1 x 10^6 km) than it is at perihelion (147.1 x 10^6 km).
The amount of sun UV radiation hitting the Earth is related to the Earth’s distance from the sun. If there are two distances being compared, say D1 > D2, then the ratio R of these two radiation densities is (roughly) approximately (D1/D2)^2, which is greater than 1. The larger these distances, then the more precise will be this approximate ratio.
Letting D1 be the aphelion distance and D2 the perihelion distance gives the result:
R = (152.1 / 147.1)^2 = 1.069.
This means that the Earth at perihelion has a radiation density 6.9% greater than the radiation density at aphelion. Seeing this 6.9% result I have not been able to understand how it is possible that the quote “UV radiation is about 40% stronger…” can possibly be correct.
I am hopeful that someone here at the Physics Forums will be able to educate me regarding my apparently incorrect understanding.
June 2, 2022
Vol 32 Number 6
Page 62
Title: Skin Cancer around the World
Two Quotes:
“The main cause of skin cancer is the exposure to the sun’s ultraviolet rays…”
“UV radiation is about 40% stronger in New Zealand than it is at corresponding latitudes in the Northern Hemisphere. Because of Earth’s tilt, the Southern Hemisphere is closer to the sun than the north is during its own summer. “
I am unable to find any basis for this difference other than that the distance of the sun to the Earth is greater when the Earth is at aphelion (152.1 x 10^6 km) than it is at perihelion (147.1 x 10^6 km).
The amount of sun UV radiation hitting the Earth is related to the Earth’s distance from the sun. If there are two distances being compared, say D1 > D2, then the ratio R of these two radiation densities is (roughly) approximately (D1/D2)^2, which is greater than 1. The larger these distances, then the more precise will be this approximate ratio.
Letting D1 be the aphelion distance and D2 the perihelion distance gives the result:
R = (152.1 / 147.1)^2 = 1.069.
This means that the Earth at perihelion has a radiation density 6.9% greater than the radiation density at aphelion. Seeing this 6.9% result I have not been able to understand how it is possible that the quote “UV radiation is about 40% stronger…” can possibly be correct.
I am hopeful that someone here at the Physics Forums will be able to educate me regarding my apparently incorrect understanding.