moon

The Moon is Earth's only natural satellite and the fifth largest satellite in the Solar System. It is the largest natural satellite of a planet in the Solar System relative to the size of its primary (though Charon?, which orbits the dwarf planet Pluto, is proportionally larger), a quarter the diameter of Earth and 1⁄81 its mass. The Moon is the second densest satellite after Io?. It is in synchronous rotation with Earth, always showing the same face; the near side is marked with dark volcanic maria among the bright ancient crustal highlands and prominent impact craters. It is the brightest object in the sky after the Sun, although its surface is actually very dark, with a similar reflectance to coal. Its prominence in the sky and its regular cycle of phases have since ancient times made the Moon an important cultural influence on language, calendars, art and mythology. The Moon's gravitational influence produces the ocean tides and the minute lengthening of the day. The Moon's current orbital distance, about thirty times the diameter of the Earth, causes it to appear almost the same size in the sky as the Sun, allowing it to cover the Sun nearly precisely in total solar eclipses. Wikipedia Moon

Moon vs Sun Luminosity
We will assume you will use the full moon to start a fire. Fortunately, the moon has almost exactly the same apparent diameter as the sun and is a sunlit object so that simplifies matters greatly. We shall also ingnore spectral balance differences and only take into account the difference in apparent magnitude. The sun is assigned a magnitude of -26.7 and the full moon about -12.6. As each magnitude is equal to the fifth root of 100 (a change of about 2.5119 times per magnitude) this means the full moon is about 444,631 times dimmer than the sun. So, if we assume you can start a fire with the sun using a magnifier of 1 inch diameter we need a lens (or mirror) of 444,631 times greater area. This gives
.785398 X 444,631=349212.
349212/3.1415=111157.
Sqrt of 111157=333.4
333.4 X 2 / 12 = 55 foot diameter mirror. (from http://bbs.homeshopmachinist.net/threads/5698-Aluminum-telescope-mirrors/page2)

Blue Moon
This month's full moon, which rises on Tuesday (Aug. 20, 2013), is not just a Blue Moon — it's also the Full Sturgeon Moon, the Full Red Moon, the Green Corn Moon and the Grain Moon.

Today's full moon qualifies as a Blue Moon because it's the third full moon in a season with four (most seasons have only three). Historically, there have been two different definitions of a Blue Moon.

Technically, a Blue Moon is the third full moon in a four-full-moon season. However, a 1946 article in "Sky & Telescope" magazine mistakenly defined it as the second full moon in a single month (since most months have only one full moon), and the definition stuck. Because August will have just this one full moon, it wouldn't meet the mistaken, though commonly used, definition, though it does qualify as a technical Blue Moon. 10 Surprising Moon Facts

The moon's extra names come from traditional monikers for the full moon of a given month. A few hundred years ago, Native American tribes in what's now the northeastern United States kept track of seasons by ascribing particular names to each full moon. Later, European settlers added their own names for the full moons to the lexicon.

The annual August full moon has come to be known as the Full Sturgeon Moon, because the large fish called sturgeon can most easily be caught at this time of year. The name came from tribes who caught this fish in bodies of water such as the Great Lakes and Lake Champlain.

Another name for this month's full moon is the Full Red Moon, because the weather and atmospheric conditions during this season can often make the moon look reddish when it rises through a haze.

And finally, because crops grow tall at this time of year, this month's moon is sometimes called the Green Corn Moon or the Grain Moon.

Full moons occur every 29.5 days on average, when the moon is directly opposite the sun from the perspective of Earth. This causes its whole disk to be fully illuminated as a large, bright circle. Usually, when the moon is full, it passes either above or below Earth's shadow, but sometimes, when it is perfectly aligned, it travels right through the shadow, causing a lunar eclipse, when its disk is dark.

Blue Moons don't happen too often, which is why the phrase "once in a Blue Moon," has sprung up to mean only very rarely. After Tuesday's event, the next Blue Moon isn't set to occur until 2015. [source unknown]