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{ Practical astronomy | Astronomy | The Moon }

The Moon

Phases

the month's lunar phases day to day
Lunar phases.

The triangle formed by Sun, Earth and Moon changes continuously: The Moon revolves around the Earth in 27.3 days, while the Earth drags it along in its own revolution around the Sun once a year. As a result, the overlap between the bright – Sun-facing – half of the Moon and the near – Earth-facing – half of the Moon changes with a period of 29.5 days. At Full Moon, the two coincide: The Earth is between Sun and Moon, the Moon appears fully in sunlight, and it is above the horizon all night and not at all during the day. At New Moon the Moon is between Earth and Sun, we cannot see it in the bright daylight, it is below the horizon all night, and if we could see it, we would see only its dark side.

The image is a montage of images collected over a few years, showing the change of this lunar phase roughly from one day to the next. At some New Moons the alignment is so precise that the Moon actually covers part or all of the Sun. In the montage the New Moon at the start is an annular eclipse, the one at the end a total eclipse.

very thin lunar crescent
New Moon, 2005-03-11.

The Gregorian calendar months have different length that do not match the lunar phases. Months are a secondary feature of that calendar, the main units are the year and the day. The Islamic calendar, on the other hand, is a pure lunar calendar and adjusted according to observations of the lunar crescent after New Moon. The second image here was taken just after the end of the 30th day of Muharram and the start of the first day of Safar of the Islamic year 1426 AH.

Physical parameters:

The phases of the Moon are very easy to observe. Difficulties are presented by the very thin crescents, which are less bright and have to be observed in rather bright twilight skies. The evening (morning) crescent is best observed in spring (autumn), when the altitude difference to the Sun is greatest. Imaging should be relatively easy, the twilight sky and the Moon itself are not much fainter than a daytime landscape, so that exposures will be quite short. A long focal length is required, and hence also a tripod.

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Earth shine

Earth shine
Earth shine, 2013-01-15.

When we have a New Moon, an observer on the near side of the Moon would see a Full Earth in their night sky. The Earth is not only larger than the Moon, it is also more reflective – Full Earth nights on the Moon are much brighter than Full Moon night on Earth. When the lunar crescent is thin, we can actually see the "dark" side of the Moon illuminated by the Earth.

Physical parameters:

Although the Earth shine is readily seen with the naked eye, taking an image will require a long focal length, as always with the Moon. A tripod will not really be sufficient; the required exposure tends to be several seconds so that tracking the Moon with a motorised equatorial mount will be very helpful. Another problem is the immense contrast between the bright crescent and the Earth shine. It requires high quality optics to avoid the glare from the crescent interfering with the feeble light from the dark side. A telescope objective is better suited to this task than most photographic lenses. This object can be a good application of high dynamic range processing, where several frames of decreasing exposure are combined and cleverly filtered (tone-mapped) to retain some contrast both in the faint and the bright parts of the object. The image shown here is just a single exposure, and so the lunar crescent is simply overexposed.

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Albedo

images of and brightness cuts through a lump of coal and the Moon
The Moon and a lump of coal, 2010-10-30.

After the Sun, the Moon is the brightest object in the sky. Astronomical observatories divide their observing programmes into those that can tolerate a moonlit night sky and those that require a moon-less sky. But is the Moon really that bright? Its "albedo" – the fraction of incident light that it reflects – is in fact similar to that of coal, roughly 10%.

The montage of images shows on the left a lump of coal perched on a wall and in silhouette against the blue sky. On the right is the Moon at the same time in the daytime sky. Both images have the same exposure, and are raw data with dark and bias signals subtracted. In the intensity plots below the images, zero then means no light. We can see that the lump of coal reflects at a brightness of 3500 to 3800 intensity units. For the Moon, we have to subtract the daytime sky, as it is located between the camera and the Moon and adds to the lunar light. We measure about 1000 in the dark maria and 3000 in the bright highlands near the limb. If anything, the Moon appears to be even darker than coal. But closer to Full Moon it would probably be similar to coal.

Physical parameters:

With these images, we carry out a crude form of photometry, measuring the brightness of things. It is important to use an image format that stores numbers for each pixel that are proportional to the amount of light received by the pixel. The raw format of dSLR cameras usually does this. The JPG format from any camera most definitely does not do this. In the case here, it is also important to have the correct zero level. While the shutter is open and the detector collects light, it also collects "dark current" – electrons that are collected whether there is light or not. Even before the exposure begins, it already has a "bias" charge of electrons. In addition to the image of the object itself, we must take a dark/bias image and subtract it from the image proper. A dark/bias image can be taken simply by repeating the exposure with the lid on the lens so that the detector is in darkness. When working with raw images, it is best to convert these to floating-point FITS format (separately for the RGB colour channels or only for the G channel when not interested in colour).

Image parameters:

Perigee and apogee

Moon near perigee and near apogee
Moon near perigee and near apogee.

The revolution of the Moon around the Earth is not in a circular orbit. Half the orbit, the Moon is closer than average, half the orbit further away. The montage of two images of the Moon illustrates how its apparent size changes. On the left, it is near its closest to the Earth. Half a month later (right), it shows not only the opposite phase, but is also near its furthest distance from Earth. The distance – and hence apparent diameter – varies about 7.5% either way from the average. These two images were in fact not taken during the same month. The image on the right is from 2005-02-18 and the one on the left from 2007-04-13.

When perigee falls close to Full Moon, this is called by some a "supermoon". Due to its larger size, it is 0.15 mag brighter than the average Full Moon. Casual observers will notice neither the increased size nor the increased brightness.

This phenomenon must not be confused with the optical illusion that a Moon on the horizon appears to the human brain larger than a Moon high in the sky. The opposite is true: When the Moon is in the zenith, the observer is 1.7% closer to the Moon than when it rises on the horizon.

Physical parameters:

The phases of the Moon are easy enough to observe. For this project, the images have to be taken with the same camera, same lens and same focal length. The image scales are then the same and the size comparison becomes possible. A variation of the project is to catch both perigee and apogee at Full Moon and show them side by side or as a positive/negative overlay.

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Libration

libration in longitude - Mare Crisium - and latitude - Aristoteles and Eudoxus
Libration of the Moon.

libration in longitude - naked-eye resolution
Libration of the Moon, to the naked eye.

On average, the Moon always shows the same side to Earth. Over millennia, the Earth's tidal forces have adjusted the lunar rotation period to equal its revolution period. There are two imperfections in this synchronisation of spin and orbit. First, the rotation is at constant speed while the orbital motion speeds up near perigee and slows down near apogee. Second, the spin axis is not exactly perpendicular to the orbital plane.

The first imperfection leads to libration in longitude, allowing us to see a bit more on the left or on the right in different parts of the month. This can be seen best in the shape of Mare Crisium. In the right image it is closer to the limb and looks less circular.

The second imperfection leads to libration in latitude, allowing us to see a bit more at the top or at the bottom. In the image pair this is quite apparent from the two craters toward the North. The larger one is called Aristoteles, the smaller Eudoxus.

Galileo – one of the first astronomers to point a telescope at the Moon – denied the existence of libration in longitude, perhaps because he considered the lunar orbit circular. On the other hand, observers before Galilei might have noticed the libration even without a telescope. The second pair of images has been smoothed and re-sampled to a resolution similar to that of the naked eye.

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Moonscapes

the Moon
Moon on 2001-10-27.

The Moon is extremely rich in surface detail. The large, dark, often circular, and almost crater-less areas are maria (singular mare, Latin for "sea"). Although they seem almost as flat as the Earth's oceans, the surface is solid. The maria are huge impact basins that filled up with lava from the lunar interior. In contrast, the bright areas riddled with craters are called highlands. These areas are indeed higher than the maria; the surface is older and has suffered more meteorite impacts after their formation.

Lunar craters are very varied. They are not volcanoes, but result from the impact of meteorites. The largest are 250 km in diameter, while the smallest you can image are as small as your equipment allows. Old craters have craters within them, large craters have central mountains and terraced rims; some of them have huge "rays" of ejecta.

The rims of maria create mountain ranges. There are steps of perhaps 100 m height in maria, which can be seen when close to the terminator (the boundary between light and shadow). In fact, all features are better observed not far from the terminator, as it is mostly the play of light and shadow that allows us to see these features.

Physical parameters:

The Moon deserves the use of high resolution, i.e. a camera behind a telescope, in prime focus or using eyepiece projection for extra magnification. I find it difficult to focus a dSLR in this situation; it would need a zoomed live-view feature to help focussing. A webcam has live-view "built in", actually on the laptop screen. While this helps getting a good image, the field of view is very small. Atmospheric seeing should limit resolution to one to three arc seconds, corresponding to between 1.5 and 5 km on the Moon. By selecting better than average frames and stacking a number of these, images can usually be unsharp-masked and may then show detail at the 1 or 2 km level.

Ideally, the telescope should be tracking while you take images. This makes it easier to compose the images, and it may also help a little if the exposures are a bit long. When taking stacks of images, tracking should be at lunar speed to avoid a significant drift of the field of view across the Moon during the sequence of frames.

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Lunar eclipses

lunar eclipse during penumbral phase
Lunar eclipse 2007-03-03, penumbra.
  		lunar eclipse during partial phase
Lunar eclipse 2007-03-03, partial phase.
 
lunar eclipse during partial phase, deep image
Lunar eclipse 2007-03-03, partial phase.
 
lunar eclipse during total phase
Lunar eclipse 2007-03-03, total phase.

A lunar eclipse occurs when the Full Moon moves through the shadow of the Earth. In the first image, two thirds of the Moon have moved into the penumbra - a zone of semi-shadow where the amount of sunlight is reduced only slightly. In the second image, the Moon has moved deeper into the shadow and 30% of it is now in the umbra - the dark core where in theory no sunlight reaches. Indeed, the umbra appears to be completely dark at this short exposure.

In the third image, the Moon is 70% inside the umbra. This longer exposure reveals that some - mostly red - light does enter the umbra. This is because the Earth's atmosphere acts as a lens and refracts some sunlight into its shadow. Also note the two stars: On the left is 59 Leonis (5.0 mag), on the right 56 Leonis (5.8 mag). Use the stars as reference points, and the final image shows how the Moon has moved by more than its radius and is now entirely deep into the umbra. The image is overall fainter, because no direct sunlight hits the Moon, which would in turn spoil our sky background as it does in the third image. Still, the umbra is not evenly dark, the top of the Moon is brighter, because it is less deep into the umbra than the rest of it.

Unlike moonscapes, photographing a lunar eclipse really requires to have the whole moon in the field of view. Deep into the eclipse, other objects nearby may be interesting to capture as well. A field of view of 2° or more seems advisable. At the same time, the Moon itself should be recorded with at least, say, 500 pixel diameter.

Observe that the umbral exposures here are 1000 times longer than exposures of the penumbral Moon, which is almost at Full Moon brightness. If you go for longer focal length, even longer exposures are needed. Tracking (at lunar rate) is necessary.

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Conjunctions and occultations

Moon and Jupiter some distance to the left
Jupiter close to the Moon 2004-12-07.

Moon and Saturn close to its limb
Occultation of Saturn 2002-04-16.

The Moon on its monthly round of the sky passes all the planets. Most of these encounters are no closer than a few degrees, but sometimes the encounter is more dramatic. In the first image, while for Europe the Moon passes below the planet (some hours after this image during the day), the United States observe an occultation, with the Moon passing in front of the planet. In the second image, Europe was lucky and the Moon occulted the ring planet Saturn. The image shows the planet just after it emerges from behind the Moon.

Physical parameters (Moon and Jupiter):

Physical parameters (Moon and Saturn):

The imaging strategy is dictated by how close the planet and Moon get. The field of view has to match this. The first image is essentially similar to the atlas of lunar phases. The second image is equivalent to imaging the planet or lunar detail, and so a webcam was used. Luckily, the Moon was only a crescent and not too bright compared to Saturn. An occultation of a planet is a very photogenic and dynamic event. You should consider taking a time-lapse or real-time movie.

Image parameters (Moon and Jupiter):

Image parameters (Moon and Saturn):

Attribution-Noncommercial-No Derivative Works 3.0 Unported
Content available under Creative Commons licence
Attribution-Noncommercial-No Derivative Works 3.0 Unported

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