Frequently, in my descriptions of the pictures of the Moon, I refer to the "lunar day" or sometimes just the "day". This can be confusing and I apologise for that confusion, but I hope that, in most cases, my meaning will be clear. The purpose of this page is to explain what I mean, and how the various values are calculated.
The Moon revolves on its axis once every 27.3 days (or about 656 hours), so on the Moon the siderial day would be about 655¾ hours. However, if you were on the Moon, you would see sunrise at somewhat longer intervals because of the Moon's orbital motion and that of the Earth around the Sun. On the Moon this would be on average 708¾ hours (or 29.53 Earth days). Because the Moon's rotation is locked to its orbital period, the interval between one New Moon and the next is also about 29.5 days, varying a little bit because the Moon's motion is not constant.
The age of the Moon is conventionally measured in Earth days starting at the moment of New Moon and the age it this time tomorrow will be exactly one more that it is now. This age does not correspond well to the phase of the Moon as seen from Earth. This arrises because the moon's orbit is not circular and its speed therefore varies as it moves around its orbit, being a little faster when it is near its closest to the Earth (called perigee) and slower when at it furthest (called apogee).
Strictly speaking, the phase of the Moon is measured as the angle Sun-Moon-Earth and is zero at Full Moon and 180° at New Moon. (This convention arrises from the optical definition of Phase Angle as the angle between the source of light and the observer as seen from the reflecting object.) Professional astronomers may use this as the phase of the Moon, but I don't think most amateurs would do so. Most of us, I believe, think of the phases starting at New Moon and increasing to Full Moon, and believe that the phase relates directly to the percent illumination. This is given by the closely related angle Sun-Earth-Moon. On this web site I use this angle divided by 360° and multiplied by 29.5 and call it the age in days. This is highly unconventional, but I think it gives a measure of the age of the Moon which corresponds more closely to the fractional illumination as seen from the Earth.
I should point out at this stage that all the numbers given above should be taken as approximate. Small corrections are necessary because the Sun is not an infinite distance from the Earth and the angle Earth-Sun-Moon is not zero, but is always small. However, to be strictly accurate, it needs to be taken into consideration. Also the Moon's orbit is not in the same plane as the Earth's orbit around the Sun (the ecliptic) so that, for example, the illumination at Full Moon may not be exactly 100%.
So, we have three meanings to the word "day":
1. The day on the Earth of 24 hours.
2. The day if you were on the Moon of 708¾ hours.
3. The day as a unit of angle in the representation of the phase of the Moon. This unit is not quite constant but averages 24 hours in length.
I use these three meanings as required, and I hope that which meaning I am using will be apparent from the context. As Humpty Dumpty said in Through the Looking Glass "When I use a word, it means just what I choose it to mean—neither more nor less". However, I hope it will always be clear. In particular, I may use the term "Lunar Day" in two ways. I may refer to a picture being taken "early in the lunar day" meaning that the Sun was low in the eastern sky of the Moon. Similarly I might say "this picture was taken in the early morning" meaning "early morning on this part of the Moon". Although I always give the date and time at which a picture was taken, I am not really concerned about the time on Earth. I know of one exception where I say "this picture was taken shortly after sunrise" and I mean sunrise here on Earth, not on the Moon. Hopefully the context makes it clear.
Finally I need to make one more point. In considering how sunlight is falling on any given part of the Moon, the libration also needs to be taken into account. The phase determines how much of the visible face of the Moon is illuminated by the Sun. But libration causes the Moon to wobble as seen from the Earth, so any given feature moves east or west, north or south relative to the central part of the visible hemisphere. So, for example at first quarter, a feature on the prime meridian (which passes straight down the centre of the Moon when in its average position) may be in sunlight or may be in darkness, depending on the libration. There are a number of examples of this on my site here, for example my two pictures of the area west of Mare Humorum (look at Gassendi), and my two pictures of the 6.3-day Moon.
There are two methods. Both methods start at the moment of New Moon and reach 29.5 days at the next New Moon, but the intermediate values are different.
1. In the conventional method of calculation, the age is set to zero at New Moon and increases with time measured in days. Thus the age of the Moon at this time tomorrow will be exactly 1 day more than it is now. This sounds simple and logical, but the days so calculated do not correspond well to the phase of the Moon as seen from the Earth. The reason for this is that the Moon's orbit is not circular and the speed with which it moves is not constant, When it is nearer to the Earth it moves more quickly than it does when it is further away. So the interval between, for example, New Moon and First Quarter (when the Moon is exactly half illuminated as seen from the Earth) varies slightly through the year depending on which part of its orbit is involved. For example, if New Moon occurs a week before perigee (the point where the Moon is closest to the Earth), then the Moon is moving at its fastest and the time it takes to get to First Quarter is shorter than it is if New Moon occurs a week before apogee (when it is furthest from the Earth and moving more slowly).
2. In my view, a better (but, I have to admit, unconventional) way to calculate the age of the Moon is to calculate the angle Sun-Earth-Moon (in degrees) and divide that by 360 and multiply by 29.5. This gives "days" which are not of equal length, but during that time the terminator (the dividing line between the dark part and the sun-lit part of the Moon), as seen from Earth, moves the same amount. In my view this is a much better way to present the phase of the Moon as an age in days than the simpler method outlined above because it relates better to the phase as we see it. All the ages I quote on this web site are calculated this way, and are taken from MyStars!, a useful planetarium program. In this method of calculation, First Quarter is always at day 7.375, Full Moon is always at day 14.75, and third quarter is always at day 22.125.
I show pictures of the Moon at each day of a lunar cycle here and the thumbnail pictures are labelled with the age in days calculated by this second method. Unfortunately it is not practicable (where I live anyway) to take pictures at exactly one-day intervals, so the sequence is a little less even than I would have liked.
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