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This website (French) explains:

N'étendez jamais votre linge de couleur un soir de pleine lune. En effet, ces nuits sont plus froides que les autres et font poindre une rosée contenant du peroxyde d'hydrogène, composant qui décolore le linge.

My translation:

Never put your clothes to dry on a full moon night. Indeed, these nights are colder than others, and trigger a dew containing hydrogen peroxide, a substance that removes clothes' color.

My grandmother used to tell me the same thing. Should I obey her?

nic
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    So, why should nights be colder at full noon, and why should dew (any) contain hydrogen peroxide? – John Dvorak Jan 10 '16 at 12:01
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    Perhaps if you can see the full moon then (a) it is night time and (b) there is no/less cloud so it tends to be colder than if (c) you see other phases of the moon near dusk or dawn or (d) you cannot see the moon due to cloud. As for actual evidence, in 1995 there seems to have been [a small effect reported](http://www.science-frontiers.com/sf100/sf100g11.htm) which may be harder to explain but might not have much impact on drying. – Henry Jan 11 '16 at 17:15
  • @JanDvorak: Why shouldn't dew or rain scavenge hydrogen peroxide and other soluable molecules from the atmosphere? E.g. http://www.seppyo.org/bgr/pdf/27/BGR27P1.pdf – Henry Jan 11 '16 at 17:20
  • surely the formation of dew at all is reason enough not to put your clothes outside to dry at night? By morning they'll be wetter than they were at the end of the spin cycle, full moon or no full moon! – Joseph Rogers Jan 18 '16 at 08:56
  • @JosephRogers: I have no more authoritative references than you about that, but I often put my clothes to dry at night and find them dry in the morning. Even more true when I wake up late. And even more for people living in areas where the sun rises at 5AM. – nic Jan 18 '16 at 09:18
  • @nic interesting, I've never tried it as I assumed dew would be a problem, as you say I'm sure it varies by region and as always there's the possibility that it's less of a problem than I expected. – Joseph Rogers Jan 18 '16 at 09:25

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There are two parts to this book's statement: 1) That nights with a full moon are colder [than those without] 2) That cold temperature increases hydrogen peroxide formation in dew.

For the first part, this stack exchange page addresses the issue of the moon's affect on the weather (summary: negligible):

https://physics.stackexchange.com/questions/83574/does-the-moon-affect-the-earths-climate

This page shows the high and low temperatures in August 2015 in the city I live in.

http://www.accuweather.com/en/us/salt-lake-city-ut/84111/month/331216?monyr=8/01/2015

Full moon was on August 29 when the low temperature was 73 degrees F. This was the 2nd HIGHEST low temperature for the month.

This page from the U.S.National Weather Service shows high and low temperatures in the city of Binghamton, NY for every day in 2015:

http://www.weather.gov/bgm/climatePlots2015BGM

This NASA.com page gives the dates of full moons in 2015:

http://eclipse.gsfc.nasa.gov/SKYCAL/SKYCAL.html?cal=2015#skycal

Here is a summary of a comparison:

  • Jan: Night of the full moon was the HIGHEST low
  • Feb: 9 nights with LOWER temps
  • Mar: There was only 1 night with a LOWER temp
  • Apr: 3 nights with a lower temps
  • May: 7 nights with lower temps
  • June: 2 nighs with lower temps
  • July: Two full moons in this month (1st and 31st). 17 nights were colder than the coldest full moon night.
  • August: 3 nights were colder
  • Sept: 3 nights were colder
  • Oct: 3 nights were colder
  • Nov:3 nights were colder
  • Dec. 18 nights were colder

There are ways (other than monthly) that the data can be grouped. Here is a summary of the 7 days before and after each full moon:

  • Jan 4: 71% were colder than full moon
  • Feb. 3: 14% were colder than full moon
  • Mar 5: 57% were colder than full moon
  • Apr 4: 21% were colder than full moon
  • May 3: 35% were colder than full moon
  • June 2: 14% were colder than full moon
  • July 1: 78% were colder than full moon
  • July 31: 85% were colder than full moon
  • Aug 29: 14% were colder than full moon
  • Sep 27: 50% were colder than full moon
  • Oct 27: 0% were colder than full moon
  • Nov 25: 21% were colder than full moon
  • Dec 25: 64% were colder than full moon

I didn't run a statistical analysis to look for the amount of correlation between phase of the moon and temperature, but as a absolute rule (full moon is always colder [than nights without full moon] there are numerous counter-examples to show that is false. As a general rule (that may have exceptions) . . .well, there are LOTS of exceptions.

For the 2nd claim, that the amount of hydrogen peroxide produced in dew increases with decreasing temperature: Even if it is true, you would need to evaluate the risk to your laundry using exactly that: Temperature (not phase of the moon).

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    Not that I believe in the opposite, but do you have more solid references? 1) During winter every night is colder -> What if the phenomenon is caused not by absolute temperature but relative to the previous few days? 2) Full moon is not always the coldest -> Devil's advocate would accuse you of having picked the month, so wider statistics would be welcome. 3) hydrogren peroxide is considered a color-safe bleach -> Nice, a solid reference should be easy to find for this one so please edit your answer to add it. Thanks! – nic Jan 16 '16 at 02:44
  • nic, you are right. Here are specific replies: 1) the statement that EVERY night in the late fall is colder than any night in the summer was too general. I will edit to fix. 2)Even if I did pick one month that illustrated my point, isn't one counter-example enough to disprove a blanket statement like the book made? 3) This was an blunder on my part. I removed the comment. – Randall Stewart 2 hours ago – Syntax Junkie Jan 16 '16 at 19:48