APOD: Quarter Moons (2023 Oct 21)

[APOD Robot]

Quarter Moons

Explanation: Half way between New Moon and Full Moon is the Moon's first quarter phase. That's a quarter of the way around its moonthly orbit. At the first quarter phase, half the Moon's visible side is illuminated by sunlight. For the Moon's third quarter phase, half way between Full Moon and New Moon, sunlight illuminates the other half of the visible lunar disk. At both first and third quarter phases, the terminator, or shadow line separating the lunar night and day, runs down the middle. Near the terminator, long shadows bring lunar craters and mountains in to sharp relief, making the quarter phases a good time to observe the Moon. But in case you missed some, all the quarter phases of the Moon and their calendar dates during 2022 can be found in this well-planned array of telephoto images. Of course, you can observe a first quarter Moon tonight.

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[Sa Ji Tario]

I remember having read that the Greeks could know when the Moon was in this phase and through it they could do a triangulation so that with the lunar distance they could know the solar distance which at that time was 86 times the lunar distance, a tremendous error that was corrected many years later, it is assumed that the time was after the existence of Pythagoras because the famous theorem was used, then the Moon made a right angle with the Sun. With the elements of the time the measurements were far from being exact ( The information did not say how they knew the lunar distance)
The images of the day place the Moon at the intersection of the legs for the figure of the theorem.

[orin stepanek]

The moon is almost hypnotic as it goes through it's orbit;
and very romantic!

[johnnydeep]

I remember having read that the Greeks could know when the Moon was in this phase and through it they could do a triangulation so that with the lunar distance they could know the solar distance which at that time was 86 times the lunar distance, a tremendous error that was corrected many years later, it is assumed that the time was after the existence of Pythagoras because the famous theorem was used, then the Moon made a right angle with the Sun. With the elements of the time the measurements were far from being exact ( The information did not say how they knew the lunar distance)
The images of the day place the Moon at the intersection of the legs for the figure of the theorem.

Nice. There's a good discussion here, but two things (in blue) are still left as exercises for the reader - https://astronomy.stackexchange.com/que ... calculated

Using the distance between the cities, Earth's circumference could be calculated.

Once the earth's radius is known, the earth itself can be used as a baseline for determining still greater distances -- the distance to the moon.

[ I ]t becomes possible to work out the earth-moon distance indirectly from the geometry of [lunar] eclipses. Using this method, Hipparchus of Rhodes (fl. 140 BCE) worked out that the distance of the moon was 59 earth radii. It's a good approximation - with 1 1/2 or 2 earth radii of the modern value.

Using the Earth-Moon distance and the separation of the Moon from the Sun in the sky when the Moon was at exactly half-phase, Aristarchus calculated the Earth-Sun distance.

Aristarchus put forward a geometrical argument, based on determining the sun-earth-moon angle at the time the moon's phase is exactly half. For this angle, which is actually 89.86 degrees, Aristarchus used 87 degrees; the disagreement is more significant that it might appear because the critical quantity is the difference between the angle and 90 degrees.

Because of this Aristarchus only got a value of the equivalent of "5 million miles", much too small.

But of course, there's a much fuller explanation at Wikipedia - https://en.wikipedia.org/wiki/On_the_Si ... istarchus)

[Avalon]

The rim of an ancient HUGE crater is lit up in the 3rd quarter images at about between the 11 and 12 o'clock position on the lunar face. What a tremendous event that must have been! How were the major craters on the "visible" side of the moon even created as the earth would probably have been a shield against many of them. Did our planet sustain such catastrophic impacts, as well? Has weathering erased the remnants of such Earth/asteroid encounters?

[johnnydeep]

The rim of an ancient HUGE crater is lit up in the 3rd quarter images at about between the 11 and 12 o'clock position on the lunar face. What a tremendous event that must have been! How were the major craters on the "visible" side of the moon even created as the earth would probably have been a shield against many of them. Did our planet sustain such catastrophic impacts, as well? Has weathering erased the remnants of such Earth/asteroid encounters?

The Earth is not much of a shield to the moon, at least not now (this image is to scale):

Click to view full size image

When the moon first formed 4 billion years ago it was much closer, but even 2.5 billion years ago, it was only 60,000 km closer.

An explanation for why the near side of the moon looks so much less cratered is due to increased heat caused by a concentration of radioactive elements:

The study is centered on a strange geochemical anomaly on the Moon. The near side contains a region called the Procellarum KREEP Terrane. That region contains a large amount of specific elements. KREEP stands for K (the atomic symbol for potassium), REE (rare-earth elements) and P (the atomic symbol for phosphorus). The KREEP terrane also contains the elements thorium and uranium, which decay radioactively and produce heat.
...
The authors of this study wanted to find out if the presence of KREEP could create the conditions for more sustained volcanic activity. KREEP could lower the melting point of the mantle, and the presence of the radioactive elements could’ve compounded the effect, by generating enough heat to fuel volcanic activity in the region long after the rest of the Moon had cooled.
...
The study showed that compositional assymetries between the near side and the far side of the Moon had an effect early in the life of the Moon. The authors wrote, “Our results show that the hemispheric compositional asymmetries on the Moon began to have a dramatic effect on magma production immediately after lunar differentiation.”
...
This is no minor anomaly, and as they wrote, its effect was dramatic. “The large concentration of heat-producing elements on the Moon’s nearside not only had the potential to act as a heat source for melting but also lowered melting temperatures at the crust–mantle interface in a way that could have produced ~4–13 times more crust-building magmas than would have occurred on the farside.”

Distribution of thorium on the lunar surface from the Lunar Prospector mission. Thorium is highly correlated with other radioactive elements (heat producing), with most of it being present on the Earth-facing side (near side). The relationship between this region and many observed features of lunar history is a key question in lunar sciences. Credits: Laneuville, M. et al (2013) Journal of Geophysical Research: Planets.

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[Chris Peterson]

The rim of an ancient HUGE crater is lit up in the 3rd quarter images at about between the 11 and 12 o'clock position on the lunar face. What a tremendous event that must have been! How were the major craters on the "visible" side of the moon even created as the earth would probably have been a shield against many of them. Did our planet sustain such catastrophic impacts, as well? Has weathering erased the remnants of such Earth/asteroid encounters?

The Earth isn't a shield. Indeed, it can even focus bodies onto the Moon that would otherwise have missed. The vast majority of the impacts occurred very early in the evolution of the Solar System, and the Earth was being bombarded as well. Almost all evidence of this has been lost to weathering. There remain a few hundred craters that we can still detect on our planet, however, from more recent impacts.