Was out running this morning and noticed the both the sun and the moon in the sky. The part that has me stumped is that both the sun and the moon were up at around 60 degrees relative to the horizon on opposite ends of the sky but the moon was not full. The moon was just over 1/2 lit even though it was obvious that the earth was not casting any kind of shadow on the moon and the position of the sun on the opposite end of the sky should have lit the moon at around 90%. So why was the moon only just over 1/2 full ? I googled for an answer and really could not find anything satisfactory to explain this.
The moon was just over 1/2 lit even though it was obvious that the earth was not casting any kind of shadow on the moon and the position of the sun on the opposite end of the sky should have lit the moon at around 90%.
That the Earth's shadow is responsible for the phases of the Moon apparently is a widely held misconception, enough so that multiple sites spend some time addressing this concept. The Earth's shadow is responsible for lunar eclipses, but not the phases of the Moon. The Moon's orbit about the Earth is what is responsible for the phases of the Moon. This is depicted below.
Except for lunar eclipses, the Sun always illuminates about half of the Moon, but that illuminated half typically is not the same half we see from the Earth. Today is one day before the Moon will be half full (waning), which is position 7 in the above diagram. We only see half of the Moon being lit in that position because the other half of the Moon we see is shadowed by the Moon itself.
Lunar eclipses occur when the Moon's orbit takes the Moon into the Earth's shadow. From the diagram, it should be obvious that this can only happen when the Moon would otherwise be full. We do not see an eclipse every month as the above diagram would suggest. This is because the Moon's orbit about the Earth is tilted with respect to the Earth's orbit about the Sun. Instead, total lunar eclipses occur only about once per year.
The last full moon was on August 18. At full moon, the moon rises at pretty much the same time as the sun sets, so you won't see both in the sky at the same time. As you say the moon was about half lit, which tells you that, relative to the Earth, the sun and moon are at right angles to each other (actually that won't be until tomorrow, Aug 24).