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The Sky and Horizon-page explains how the Moon moves along the sky and what the phases of the Moon look like then.

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## 1. The Moon

The Moon is the only natural satellite of the Earth and orbits around the Earth. We can only see the Moon because it reflects light from the Sun, just like all other moons and planets are only visible because they reflect light from the Sun. The Moon is below the horizon (invisible) for on average half of the time, is visible during on average about half of the daytime, and is visible during on average about half of the nighttime as well.

Read the Sky and Horizon-page to find out about the phases of the Moon.

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The distance between the centers of the Earth and the Moon is about 384,400 km on average, but varies between about 356,400 and about 406,700 km.

The Moon recedes from the Earth at an average rate of about 3.8 cm per year, but the monthly peak-to-peak variation in the distance of the Moon from the Earth is about 40,000 km, which is far greater. The long-term rate of change is far smaller than the short-term variability.

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The Moon rises at a different hour each day, and also sets at a different hour each day, because the Moon moves quite a distance in the sky relative to the stars each day. See question 63.

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A method for calculating the approximate position of the Moon is described on the Calculation Page on Positions in the Sky.

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## 2. The Moon Has No Natural Moons

If the Moon has any natural moons of its own, then they must be really small. No such moons have ever been discovered. A moon with a diameter of 5 km (3 mi) in orbit around our Moon and made of the same material as the Moon would be as bright in the sky as the brightest stars, so such a moon would have been discovered long ago.

If such a moon had a diameter of 500 m (1500 ft), then it would be as bright as the faintest stars that one can see without binoculars or a telescope from a dark place, so such a moon would probably have been discovered by now as well.

Pluto was discovered in 1930 with a brightness that was 1200 times less than that. If the second moon had a diameter of about 12 m (30 ft) then it would look about as faint as Pluto, but we've had the technology to detect even such a small moon since (before) 1930.

Nowadays there are even better telescopes, and there is a far greater number of telescopes than in 1930, so it seems very likely to me that even a second moon as small as 12 m in diameter would have been seen by now by many (amateur) astronomers.

The Spacewatch Project (//spacewatch.lpl.arizona.edu/scopes.html) searches the sky automatically for celestial objects that might hit the Earth. Their telescopes can detect celestial objects that are 1600 times dimmer than Pluto. A second moon of the Earth would have to have a diameter smaller than about 30 cm (1 ft) to escape detection by Spacewatch.

Any moon orbiting around our Moon could not be further away from the Moon than about 35,000 km (22,000 mi), which is about 10 times the diameter of the Moon, because orbits beyond that distance would be disturbed so much by the gravity of the Earth that moons in such orbits would probably have escaped into space or fallen to the Moon or the Earth. (The "tidal boundary" between the Earth and the Moon lies about 35,000 km from the Moon.)

The Moon has had artificial moons: satellites such as Clementine and the Lunar Prospector that were sent from Earth into an orbit around the Moon to study the Moon. It is possible that some of those artificial satellites are still circling around the Moon, though they are usually deliberately crashed into the Moon once their mission is complete.

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## 3. The Moon Falls Towards But Not Onto The Earth

The Moon falls around the Earth all the time. If the Earth did not pull at the Moon, then the Moon would disappear into space, roughly along a straight line. The attraction between the Earth and the Moon pulls the Moon away from that straight line towards the Earth (and likewise pulls the Earth from a straight line towards the Moon), but not enough to make the Moon fall down unto the Earth.

In other words: The Moon has a large sideways speed (not directed towards the Earth, but rather perpendicular to that direction), so when the Moon has fallen a bit towards the Earth, then in the same time it has also moved sideways a bit, so that it is at about the same distance from the Earth as before.

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## 4. Daytime and Nighttime Moons

The Moon that we sometimes see during the day is the very same Moon that we sometimes see at night. We can only ever see the same side of the Moon, whether we see the Moon during the day or during the night. The dark regions that one can see on the Moon at night can also be seen during the day. The daytime Moon is almost equally bright as the nighttime Moon of the preceding or following night. The Moon does not seem to be very bright during the day because we then compare it with the bright blue sky, but the Moon does appear very bright at night because then the sky is very dark.

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## 5. If the Moon Disappeared

If the Moon disappeared then the tides would reduce in strength by about two thirds. There would still be tides, because the Sun causes tides, too (see the Conjunctions Page).

The Moon keeps the angle between the rotation axis of the Earth and the plane of the orbit of the Earth within a fairly narrow range, so that the strength of the seasons cannot differ too much from its current value. If the Moon disappeared, then the inclination of the rotation axis of the Earth would vary much more over periods of thousands of years and could get much further away from the upright position, with corresponding greater differences between summer and winter, and hence with great influence on the climate, such as Mars has experienced (without any large moon). See //adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1993Natur.361..615L, //adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2002A%26A...384..689E and //arxiv.org/abs/astro-ph/0112399 (for //adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2001EM%26P...85...61B).

I've heard of kinds of animals that synchronize some rhythms of their lives with the phases of the Moon, and the sudden disappearance of the Moon could cause trouble for them. I believe I've heard of some kinds of turtles that come to lay their eggs on the beach at a certain Full Moon, and that the nightlife of deer and similar animals takes the phase of the Moon into account. In any case, fishermen and hunters seem to take the phase of the Moon into account, but perhaps that is because they would like to be able to see something at night. I am not a biologist, fisherman, or hunter, so I do not know the details of this.

It is highly unlikely that the Moon will just disappear. Only the very close passage of a celestial object of the size of a planet could wrench the Moon from the grip of the Earth's gravity, and such an event could also change the orbit of the Earth itself markedly, so then the disappearance of the Moon might not be the most important thing. Calculations of the future of the orbits of the planets show that such an event will not happen during the coming thousands of millions of years (at least not with one of the other planets of our Solar System as the disturbing object). See //adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=2002MNRAS.336..483I and //adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1996CeMDA..64..115L.

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## 6. The Influence of the Moon

There are people who claim that the Moon or the phase of the Moon (full moon, new moon) has influence on all kinds of things where you would not immediately expect such influence, such as the birth dates of children, or how much luck you have, or the weather. Is that true? Sometimes these people suggest that this influence comes from special lunar forces that science doesn't know or does not want to know. Can that be true?

### 6.1. Direct Influence by the Moon

The only direct influence that the Moon has on Earth is through its gravity and its light. The gravity of the Moon causes part of the tides on Earth. The direct influence of the gravity of the Moon on people is much smaller than the influence of the gravity of earthly things that are much closer, such as houses and cars and other people, and that influence is already so small that you don't notice it. (See the Conjunctions Page for more information about this.) Moonlight is reflected sunlight and allows us to see better sometimes at night, though we are much less dependent on moonlight these days, with all of our streetlights and lamps in our homes.

### 6.2. Indirect Influence by the Moon

These direct influences yield indirect influences. Without tides, there would be no tidal areas such as the Waddenzee on the coast of the Netherlands, with the related plants and animals and tidal power stations. Many animals prefer to look for food at night when the Moon is shining. The full moon at harvest time was called the Harvest Moon because people could continue to harvest after sunset by the light of that moon. However, for all of these things it is not important that it is the Moon that provides the tides or the light, but only that there is something that provides tides or light.

If something depends directly or indirectly on the Moon, then all things that depend on that first thing can themselves start depending on the Moon. If the farmer can keep harvesting for longer by the light of the full moon, then he'll probably sleep less than usual afterwards, so he'll be more sleepy the next day than usual. That means there's a connection between the phase of the Moon and the sleepiness of the farmer, even though no special sleepiness rays come from the Moon to affect farmer's brains. That sleepy farmer may not feel like playing his usual card game with the neighbors the next day, so then there is a connection between the lunar phase and the playing of card games. The neighbors may have seen this coming, and may have decided not to bake the cake that they usually eat while playing cards, so now there's a connection between the lunar phase and the sale of cake ingredients. In this way, very indirect connections can arise between things of which you would not expect this at first sight.

The problem with such indirect connections is that it is often almost impossible to determine where they came from. If you notice that there is a connection between the lunar phase and the sale of sugar in a particular village, then you may not immediately realize the importance of the card game buddies of a farmer in harvest time, especially because one can think of many other equally indirect ways in which there may be a connection between the phase of the Moon and the sale of sugar in the village, and perhaps all of them are important.

### 6.3. Correlation with the Lunar Phase

If someone claims that there is a connection between something and the phase of the Moon, then you should ask the following questions:

How certain is it that the claimed correlation really exists?

No source is given for many of these stories, so it is almost impossible to determine if the story is based on solid research, or if someone just made it up.

Besides, if you compare two things that both vary with time but that have absolutely nothing to do with each other, then they'll still occasionally go up or down or appear to be connected in some other way, purely by chance. If you happen to study those things during such a period, then you could conclude that they are connected, even when they aren't.

In addition, people tend to remember or pass stories on to others much more easily if the stories are about strange or unexpected things or if the stories agree with ideas that the people already had. For example, if a hundred researchers study the connection between the color of babies' eyes and the lunar phase at their birth (to name something for which a connection seems unlikely), and if they use a test that is 99% accurate, then probably one out of the one hundred researchers will by accident get data from which he concludes that there is a connection, even if there really is no such connection and even if all researchers work accurately and honestly. If all researchers publish their results independently, then the results of the one researcher that found the strange connection are likely to get much more interest than the results of the 99 researchers that didn't find anything special. It is therefore much more likely that you'll hear about the one study that found something strange than that you'll hear about the 99 other studies that didn't find anything unusual.

How much of the variation is explained by the lunar phase?

Even if a scientifically thorough study shows that there is some correlation between something and the lunar phase, then that doesn't mean that this is at all useful in practice. For example, if 90% of the variation in temperature during a month were explained by the lunar phase, then you could make a pretty reasonable prediction of the temperatures for the coming month from the expected lunar phases during that time, with only 10% of temperature variation due to other things. If instead only 0.1% of the variation in temperature is correlated with the lunar phase, then knowing the lunar phase does not help you at all in predicting temperatures, because then 99.9% of the variation is not connected with the lunar phase.

People should always mention how much of the natural variation in the investigated thing can be explained from the lunar phase. Any found connection is only useful if you can explain a large fraction of the variation from the lunar phase.

Because of the innumerable indirect connections in nature and between human actions and affairs, it is likely that almost anything is somehow connected with the phase of the Moon, so if you can do a sufficiently big statistical investigation, then you can detect lunar influence in almost everything, but in almost all cases the influence of the lunar phase is so incredibly small that it is of no use at all in practice.

### 6.4. The Phase of the Moon Might Have Influence on...

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#### 6.4.1. ... Insomnia

It is possible that people sleep worse at full moon, because of the extra light that is then around at night. It is not important that the extra light comes from the Moon; if instead a bright lamp shone into the bedroom that appeared as bright as the full moon, then you'd have the same trouble to sleep. Thicker curtains and better closing of the gaps through which light can still enter the bedroom might help.

### 6.5. The Phase of the Moon Can Have a Tiny Effect on...

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#### 6.5.1. ... the Weather

Some people think that the weather is related to the phase of the Moon. For example, that there is a greater chance of frost at Full Moon than at other phases of the Moon. Any such relationships are at best very weak, because the weather can be very different from place to place, while everyone has the same phase of the Moon at the same moment, and the weather can be very different from day to day or even from hour to hour while the phase of the Moon changes only slowly. I think it is fair to say that there is no correspondence between the phase of the Moon and the weather that you could use to measurably improve weather predictions.

Perhaps the idea that a Full Moon gives a greater chance for frost is derived from the observation that if there is frost and if you can then see the Moon, then there is a greater than average chance that that Moon will be full. That correlation is easy to understand: Frost occurs most often in winter. In winter, the Full Moon is longer above the horizon than the other phases of the Moon are, because the Full Moon is always exactly opposite the Sun in the sky, and the Sun is less visible in winter. So, in winter there is a greater than average chance to get frost and also a greater than average chance to see a Full Moon. "Seeing more Full Moon" and "experiencing more frost" go together. However, not every correlation is a causation. In other words: that two things go up or down together doesn't mean that one of them must be causing the other. In this case, both things are caused by the season. If you don't care about seeing a Full Moon but only about it being a Full Moon, then the chances for each phase of the Moon are equal also in winter, and then there turns out to be no useful correlation between the phase of the Moon and the weather.

The weather and weather-related events (such as crop losses because of unexpected early frosts) have been recorded for a very long time already, and the phase of the Moon can be calculated for any date, so if any useful correlations exist between the phase of the Moon and some aspect of the weather, then it should not be difficult to find it. Yet, I have not heard of any such useful correlations, so I must assume that none have been found. (See below for my own research into the connection between the Moon and the temperature.)

If studies have found no correlation between the phase of the Moon and the occurrence of frost, then any direct or indirect effects of the Moon on frost must be so small as to be of only academic interest (if even that). This won't change, no matter how much we discuss potential sources of such effects. If we discovered a potential source that ought to have sufficient effect to be clearly noticeable, then we would have to conclude that there must be some other effect to counteract the first one, if the observations tell us that the net effect of all known and unknown contributions is too small to measure.

Notwithstanding the merely academic interest, we can still discuss the heat reaching the Earth from the Moon. Heat loss through thermal radiation is proportional to the fourth power of the temperature (relative to the absolute zero point of temperature; e.g., measured in kelvin) at the locations from where the radiation escapes. (This is expressed by the Stefan-Boltzmann Law, see, e.g., //en.wikipedia.org/wiki/Stefan-Boltzmann_law.)

So, if an object attains room temperature (290 K) in sunlight, then its heat loss is proportional to 290⁴ = 290×290×290×290 = 7073 million units, so its heat gain through sunlight must be similar to that number. The brightness of the Full Moon is about one part in half a million of the brightness of the Sun, so the heat gain through moonlight would be about 7073 million units divided by half a million, or about 14,000 units. Adding these 14,000 units to the 7073 million units leads to a rise in the temperature of at most about 0.00015 kelvin (because the fourth power of 290.00015 is about 14,000 units more than the fourth power of 290), which corresponds to about 0.00027 degrees Fahrenheit. I expect such an increase to be completely negligible.

//adsabs.harvard.edu/cgi-bin/nph-bib_query?2001EM%26P...85...99C says that any temperature effects with a roughly monthly cycle are more likely associated with solar activity (the Sun rotates in about a month) than with heating by the Moon. In other words, effects from solar activity are greater than effects from the Moon, and solar activity is not tied to the phase of the Moon.

//adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1999GeoRL..26.1605C says that there is on average a 0.1 degree Celsius greater daily surface temperature range (difference between maximum and minimum temperature) near full moon than near new moon, which is mostly caused by higher maximum surface temperatures near full moon, which are themselves attributed to the Earth being slightly closer to the Sun at Full Moon than at New Moon (because of the gravity of the Moon).

But once more, all of this talk is academic if no useful correlation is actually found to exist between the phase of the Moon and the occurrence of frost (or any other characteristic of the weather).

### 6.6. The Phase of the Moon has no Influence on...

If below I write that the phase of the Moon has no influence on something, then I mean that there is at most a (highly) indirect connection between the phase of the Moon and that thing, and that in practice knowledge of the lunar phase provides no useful advantage in predicting that thing.

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#### 6.6.1. ... the Gender of Children

The gender of a child is determined by coincidence, with an almost equal chance for a girl as for a boy. There is no connection between the gender of a child and the phase of the Moon during conception or birth of that child, or between the equality or inequality of the genders of two successive children in the same family and the phase of the Moon during the birth of the first or the second child, or any other combination of phases of the Moon and children. At least, such connections have never been proven scientifically, and according to modern science such connections are not expected.

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#### 6.6.2. ... the Birth Date of Children

It is claimed that more babies are born near full moon, but that claim is scientifically controversial. According to an article in the Brazilian Journal of Medical and Biological Research from 2002 there are about as many investigations that have found evidence for such a link as investigations that have not found evidence for such a link. That means that the effect, if it exists at all, is so small that it is hard to measure, and therefore not important in practice.

The lunar phase is not mentioned in the methods that I've seen for calculating the expected date of birth. At //www.9maanden.com/zwanger/zwanger/zpm.php (in Dutch), for example, it is explained that you should add 40 weeks to the first day of the last period of the woman before the pregnancy. The full moon is not taken into account.

If there were any correspondence between daily birth counts and the lunar phases, then I would not ascribe that to any force of nature associated with the Moon, but rather to a psychological effect.

In some societies the lunar phase at birth is seen as an important clue to the future of the child. For example, the full moon may be thought to have good influence, and the new moon to have bad influence, or perhaps the other way around. In such a culture, a birth may be delayed or sped up, or the birth may be reported to have occurred earlier or later, either on purpose or subconciously, in hopes of improving the future of the child. The influence of such effects is difficult to determine.

The precise date of birth of a child can be guided somewhat with some medical assistance, and nowadays the gender of a child can be detected with reasonably accuracy before birth, so one could guide the date of birth so as to force a connection between the phase of the Moon and the birth date or the gender, but I very much doubt that prospective parents or medical personnel have any interest in this -- and rightly so.

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#### 6.6.3. ... the running over of a glass of water

There are no scientific reasons at all to assume that a glass of water will run over at the instant of new and full moon, and even if it did it would not yield a good or very useful way of measuring longitude.

The only force from the Moon that can affect a glass of water is the force of gravity, and the strength of that force is not tied to the phase of the Moon (full or new). Moreover, gravity doesn't care whether the attracted material is glass or water, so it pulls equally hard at the glass and the water.

The glass could run over if the water expanded more than the glass did, or if the glass shrunk more than the water did, so that the water would not all fit in the glass anymore. However, there is no scientific reason why water or glass would expand or contract exactly at full or new moon.

Also, there are other influences that affect a glass of water. For example, the water evaporates, which lowers the level of the water in the glass, making it more difficult for it to run over. Also, how well water creeps up along the edge of the glass depends on how clean the glass is, so a small jolt that might cause some water to spill out of a dirty glass might not be enough to cause water to spill out of a clean glass. The kind of glass or the method of its production might also have an effect here. One would have to eliminate all of these effects in order to get consistent results.

A correspondent writes that someone suggested in 1687 to determine one's geographical longitude from the measurement of when the full or new moon makes a full glass of water run over, but even if a glass of water did run over exactly at full and new moon, this would not be very useful for determining the longitude. The determination of longitude was only a big problem at sea, and the heaving of the ship on the rough sea makes water spill out of full glasses all the time.

Moreover, the determination of longitude is really a determination of the difference between the local time (according to the Sun) at your present location and the local time at some standard location. You could only use the "glass of water" trick (assuming it worked at all) if you could predict the times of new and full moon at the standard location accurately enough: then you could say something like "according to the predictions, new moon was at 10 a.m. local time at home, but here on this ship the glass of water shows that new moon was at 11 a.m. local time, so there must be one hour difference between the local times of here and home, so we must be 360×1/24 = 15 degrees west of home". The models for the motion of the Moon were not yet very accurate in 1687, and any inaccuracy in the prediction of the exact time of full or new moon would immediately translate into inaccuracy in the longitude. A mistake of 1 minute of time at 40 degrees latitude would correspond to a mistake of 21 km or 13 mi in the determined position of the ship, which can make the difference between smooth sailing and getting stuck on a reef or rock.

The possibility cannot be excluded that there might be forces that science doesn't yet know of which might cause a glass of water to run over at new or full moon, but then they would have to be subtle enough as to escape scientific detection until now. I consider that possibility about as likely as the possibility of it starting to rain chicken soup across the whole country.

You do not have to take my word for it: just try the experiment yourself. However, do not limit yourself to just one glass. If the Moon affects one glass, then it should also affect ten glasses. If you set up the experiment with ten glasses on ten different tables and all of them run over at exactly the time of full and new moon, then perhaps there is something there after all. I don't expect that to happen, though.

### 6.7. The Moon and the Temperature

The next two figures show the frequency spectrum of the mean ("gem"), lowest ("min"), and highest ("max") daily temperatures in Rotterdam between October 1956 and the eind of 2000, calculated from data supplied by the KNMI (Royal Netherlands Meteorological Institute). The first figure shows the whole spectrum, and the second figure only a small part of it. The frequency (in units of 1 per day) is shown along the horizontal axis, and the square of the amplitude (the "power") along the vertical axis.

Fig. 1: Temperature Frequency Spectrum (1)

Fig. 2: Temperature Frequency Spectrum (2)

Figure 1 shows a large peak at a period of 1 year (ν = 0,00274 d−1). That peak by itself contains 71 % of all energy from the spectrum, which means that 71 % of the variation in the daily temperatures are explained by the year (the seasons). The peak contains at least a hundred times more energy than any other peak, so any other influence is at least a hundred times less important than the year.

Figure 2 shows the part of the spectrum that includes the various definitions of a month. The locations of the various definitions of the month are indicated by vertical lines between the values 3 and 5. The line just to the left of ν = 0,034 indicates the synodical month, of which one might expect the greatest influence on the temperature. There are no clearly higher peaks associated with any month. The small peak just left of ν = 0,034 contains about 0.0010 times as much energy as the peak at 1 year, so if you ascribe that small peak to the influence of the synodical month then that influence is a thousand times smaller than that of the year. The small peak has an amplitude of 0.28 degrees Centigrade, so the influence of the Moon on the temperature is certainly not more than that.

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## 7. People on the Moon

So far, twelve people have been on the Moon, all between 1969 and 1972. Each time, three people flew to the Moon, of which two landed on the Moon in a lunar module and the third one stayed in the space ship in an orbit around the Moon until the other two returned, and then they all went back to the Earth. Their missions were called Apollo 11, 12, 14, 15, 16, and 17. The Apollo missions with numbers less than 11 were test missions that did not land on the Moon. Apollo 13 was intended to land on the Moon but they had an accident along the way and did not get to land. They passed behind the Moon and then immediately returned to Earth. A nice movie was made of their story a few years ago, and it was also called "Apollo 13".

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## 8. The Mean Moon

The motion of the Moon in the sky is subject to many perturbations that cause the dates and times of the true or apparent conjunction of the Sun and the Moon to deviate from a simple arithmetical progression where you can just add a fixed number of days to the previous date to find the next one. This means that if you want to calculate the time of the apparent conjunction to great accuracy, then you have to calculate and add up hundreds of different periodic terms, some of which depend on your location. Such a calculation is usually performed in two steps: First, the conjunction is calculated for the "mean Moon", which is a fictitious Moon that has the same average motion as the true Moon but that is not subject to any perturbations. This calculation is relatively simple and fast, and yields the time of what is called the "mean conjunction". Then, the effect of all of the perturbations is calculated and applied as a correction to the mean conjunction. This second step is relatively time-consuming.

If no great accuracy is required, i.e., if you don't mind an error of up to about half a day, then you can omit the second step and use the times of the mean conjunction as estimates for the times of the apparent conjunction.

The recognition of a mean conjunction can be understood from the history of the calculation of the position of the Moon. To be able to provide better predictions for the conjunctions of the Moon, you must compare accurate observations of such conjunctions with the predictions that your current method yields for those conjunctions. If you notice recurring patterns or periods in the deviations, then you can capture those in mathematical terms and add them to your method of prediction. The very first step in this process is to find the best-fitting simple arithmetical progression in the dates of conjunctions, which is essentially equivalent to defining a mean conjunction. You can start investigation the (much smaller) perturbations only after you've found how to determine the times of the mean conjunctions with sufficient accuracy. So, also historically, prediction of times of conjunctions started with mean conjunctions, although they were probably not called that at first. The Babylonians had a predictable lunar calendar already 2500 years ago, so predictions of mean conjunctions are at least that old.

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## 9. The Surface Markings of the Moon

Many different kinds of things are visible on the Moon, such as craters, bright rays that point at craters, large smooth dark areas, valleys, ridges, and cliffs. Almost all craters and bright rays on the Moon were formed by meteorite impacts. The youngest craters have rays. The large smooth dark areas are called mare (the Latin word for sea). They aren't seas of water but of cooled lava that flowed from surface cracks in giant impact basins thousands of millions of years ago. Some ridges and valleys were formed by tectonic activity involving fault lines.

The current features of the Moon were determined by meteor impacts and (very old) lava.

For tectonic activity you need to have a layer of molten material below the surface for the tectonic plates to float upon. The Moon is relatively small, so it had less heat to begin with and has lost a lot of heat through its surface, so that its outer layers have quickly solidified ("frozen") to great depth and do not allow tectonic activity.

Very early in the history of the Solar System there were still many big chunks of rock floating around, and a few of them have hit the Moon and formed the very big circular basins that we can still see today. The mountain ranges on the Moon are the rims of those really big craters from long ago.

Radioactive materials below the Moon's surface helped heat up and melt some layers not far below the surface a very long time ago, and the melted stone rose to the surface in the really big and deep craters (where the molten lava did not have to rise that far and had many cracks to rise through) and filled them up, and those are what we call the "seas" of the Moon today (like Mare Imbrium).

Smaller meteors formed the very many smaller craters that we can see on the Moon. Most of them fell a very long time ago (thousands of millions of years). New craters are still formed today, but they are mostly really small (maybe a few meters in size).

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## 10. Moon Rocks

The rocks that were brought back from the Moon to the Earth by the astronauts of the Apollo program could be investigated in detail in laboratories. We could determine from their composition how they were formed, and hence what the history of the Moon was. From the ratios of various products of radioactivity that were in the rocks (in minute quantities) we could determine the age of the rocks and of the Moon. The Moon turned out to be 4.55 thousand million years old. We assume that the Moon formed inside the Solar System, so this means that the Solar System is also at least 4.55 thousand million years old.

## 11. The Formation of the Moon

In the past, there have been many different theories about how the Moon formed. Some thought that the Moon formed someone else in the Solar System and was then captured by the Earth, and some thought that the Moon formed when the Earth split in two because it was rotating too fast.

The first theory (capture) is unlikely to be correct because it is very difficult for a planet to capture something that comes from a very different region of the Solar System than where the planet itself is, because it is very difficult to get rid of the great speed that such objects have when they pass by the Earth, because there is no friction worth mentioning in space. Also, the materials detected at the surface of the Moon are similar to the materials present in the Earth but not similar to materials present much closer to or further away from the Sun than the Earth is.

The second theory (fission) is also very unlikely because the Moon would then have been hurled away from the Earth perpendicular to the rotation axis of the Earth, so it would have ended up in an orbit above the equator of the Earth, in the plane of the equator, but today the orbit of the Moon makes an angle of about 5° with the equator of the Earth. If you calculate the evolution of the orbit of the Earth back into the past, then that angle only increases as the Moon gets closer to the Earth.

The currently most popular theory is one that says that the very young Earth was hit by a Mars-sized object, which caused some material from the Earth and the object to be broken apart and launched into space, where part of that material clumped together and formed the Moon.

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## 12. Heat from the Moon

The Moon does not by itself generate any heat that is worth mentioning (unlike stars). The decay of radioactive material that occurs naturally in the Moon is the only way by which the Moon can generate heat of its own, but the amount of heat that this can produce is completely negligible.

Even though the Moon does not produce any heat, it can yet get up to 120 degrees Centigrade (250 degrees Fahrenheit) there, because the the Moon is heated by sunlight. If the Sun sets somewhere on the Moon, then it gets bitter cold there. The lowest temperature that has been measured on the Moon is about −180 degrees Centigrade (−290 degrees Fahrenheit), and the only reason why it doesn't get any lower is because the Sun rises again after at most two weeks. (Only near the poles of the Moon are there places in craters where direct sunlight never comes, and it could be a lot colder there than −180 , but those places are not well visible from Earth so we haven't yet been able to measure the temperature there.)

The Moon produces no heat, but does still contain a lot of heat below the surface. That heat is left from when the Moon formed, about five thousand million years ago. The Moon (and also the Earth and other moons and planets) formed in a hail of collisions of many small pieces and in every collision the energy of speed (kinetic energy) was transformed into heat. Since then, that heat has been slowly leaking into space, but even after five thousand million years some of it is left. That's why it gets hotter the deeper you go into the Moon. In the center it is probably still about 1500 degrees Centigrade.

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The Earth does receive some heat from the Moon. Some of it comes from the inside of the Moon, and some comes from reflected heat from the Sun. The fuller the Moon appears, the brighter it appears, so there is a correlation between the amount of reflected light and heat and the phase of the Moon. However, the amount of sunlight and heat that is reflected by the Moon to the Earth is about half a million times less than the amount of sunlight and heat that we receive directly from the Sun, so the heating by moonlight is not important in the least.

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## 13. The Moon has no Atmosphere

The Moon has no atmosphere worth mentioning because it did not have enough mass to keep an atmosphere from quickly escaping into space, and because it is geologically dead so the lost gases are not replenished.

The Earth is much more massive than the Moon, so the Earth's atmosphere leaks into space much more slowly. Also, the Earth is geologically and biologically active, which produces gases to make up for the gases lost to space.

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## 14. The Center of the Moon

All detailed knowledge we have of the Moon's interior comes from seismographic observations made with instruments installed on the Moon by the Apollo astronauts. These seismographs worked for a couple of years and recorded moonquakes. A moonquake is like an earthquake, but on the Moon. By trying different compositions of the Moon's interior and seeing which one gave the closest match to the seismic observations, scientists deduced the internal structure of the Moon.

It turns out that the Moon is molten (or at least viscous) from about 1000 kilometers (600 mi) below the surface on down, but no separate metallic core has been detected. If the Moon does have a metallic core (like the Earth does), then its radius is at most 300 km (200 mi).

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## 15. Travel to the Moon

The astronauts who went to the Moon took about three days to fly from the Earth to the Moon. They followed a route that took as little fuel as possible, namely "only" about 30 kilograms of fuel for each kilogram of spaceship that went to the Moon. If you can afford more fuel (which is very expensive) then you can fly faster, and then it takes less time.

Until now, most rockets have been chemical rockets which provide a lot of thrust (push) but burn up all of their fuel in just a few seconds. During the last few years an ion engine has been developed for spaceships which gives much less thrust than a chemical rocket but that can continue to work for many months. For example, the Smart-1 satellite that was launched at the end of September 2003 takes 18 months to get to the Moon, using an ion engine. This would be far too long for a journey with people on board.

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## 16. The Size of the Moon

The Moon has a diameter of 3476 km. The Earth's is 3.7 times as great. The Moon has a surface area of 152 million square kilometers. That of the Earth is 13.5 times larger. The Moon has a volume of 176 thousand million cubic kilometers. The Earth's is 49.4 times as large. The Moon has a mass of 7.36 × 1022 kg. The Earth's is 81.2 times as great.

De Moon is bigger in the sky than the stars are, but that is only because the Moon is so very much closer to us than the stars are. If you could measure their size with a yardstick, then all stars that you can see at night would be very much larger than the Moon is. In fact, if you put an average star in place of the Moon, then that star would reach all the way to us. We would then be inside that star. That's how much bigger stars are than the Moon.

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## 17. The Distance of the Moon

The least and greatest distance between the Earth and the Moon are not the same each month. The orbit of the Moon is not a fixed ellipse, because other forces than just the gravity of the Earth act on the Moon. An important other force that acts on the Moon is the gravity of the Sun. That force causes the Moon to sometimes get a bit closer to or further from Earth than usual. This depends on how close the date of perigee of the Moon is to the date of Full Moon. In March of 2011 those dates are close together. Then the long axis of the orbit of the Moon points at the Sun, and the eccentricity of the orbit of the Moon is greatest. This happens again after roughly every 206 days, but the Moon is not always in a perigee as well at that time.

In March of 2011 the Moon got closer to Earth than usual, but the difference wasn't all that great. Usually the Moon in perigee is at about 94.5% of its average distances (averaged over many years). In March of 2011, the Moon got as close as 92.8% of its average distance.

In November of 2034 the Moon will get even closer, to 356,445 km. That is the least distance for all years between 1960 - 2040.

The Moon on average spans about 1860 arcseconds in the sky (about 31 arcminutes, roughly half a degree). In March 2011, the apparent diameter of the Moon was about 1860/0.0928 = 2000 arcseconds (about 33 arcminutes).

You can expect a more extreme spring tide when the eccentricity of the lunar orbit is at its maximum, but that difference, too, will be only a few percent, just like for the distance and angular size of the Moon.

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## 18. How Full is the Full Moon?

The Moon is full if she is in the exact opposite direction in the sky from where the Sun is, i.e., when we are exactly between the Sun and the Moon. However, if the Earth is exactly between the Sun and the Moon, then the shadow of the Earth falls across the Moon, so then the Moon is not nearly as bright as one would expect from a Full Moon.

Lunar eclipses don't occur every month, so in most cases when we call it "Full Moon" the Moon is actually not exactly opposite the Sun in the sky. At Full Moon, the Moon can be up to 5 degrees away from the direction opposite the Sun. If the Moon is 5 degrees away from that "opposite point", then she is still 99.8 percent full. Without special equipment, you can't tell the difference between 99.8 percent full and 100 percent full.

The Moon will be fullest if she touches the umbral shadow of the Earth. If the Moon gets any closer to the direction opposite the Sun, then she'll be partly in the umbral shadow of the Earth and won't look full anymore. If the Moon gets any further from the direction opposite the Sun, then the defect compared to perfect fullness increases.

I think that the most favorable case is when the Moon touches the umbral shadow of the Earth at the moment that the Earth is closest to the Sun (in the perihelion, around 4 January) and the Moon is furthest from the Earth (in the apogee). According to my calculations, the center of the Moon would then be 0.875 degrees from the point opposite the Sun, and the Moon would then be 99.9942 percent full.

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## 19. Dates of Full and New Moon

The dates of New Moon and Full Moon for the years 2000 through 2019 are listed on a page of tables. For years before 2000 or after 2018 you should add or subtract 19 until you end up between 2000 and 2018. For example, the dates for 1965 are the same as those for 1965 + 2×19 = 2003.

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The following formula for the Julian Day Number of the mean phases of the Moon (ignoring perturbations by the Sun or other planets) is based on the book [Meeus], after omission of higher-order terms that contribute less than a minute:

$$J = 2451550.09765 + 29.530588853 k$$

where a whole number for $$k$$ yields a date for a New Moon, a whole number + 1/4 a First Quarter, + 1/2 a Full Moon, and + 3/4 a Last Quarter. An estimate for $$k$$ follows from

$$k = (a - 2000.1 + m/12) × 12.3685 \label{eq:k}$$

where $$a$$ is the year number and $$m$$ the month number. If the New Moon falls at the beginning of the month, then set $$m$$ equal to the month number (1 for January, 2 for February, and so on). If New Moon falls after the beginning of the month, then add an appropriate fraction, so you get (for example) 2.5 for the middle of February or 6.9 for about the 27th of June.

If you don't want a New Moon but a First Quarter, then add 0.25 to $$k$$. Add 0.5 for a Full Moon, or 0.75 for a Last Quarter.

If you specify the year and month correctly (i.e., they really do correspond to the desired lunar phase), then $$k$$ from Eq. \eqref{eq:k} will be close to a whole number and that whole number then indicates which instance it is in a sequence where each next instance of that lunar phase has a number that is one greater than the previous one, with instance number 0 falling near the start of the year 2000. (The formula becomes increasingly less accurate the further away you go from the year 2000, but ought to be OK for at least a couple of centuries.)

For example, there was a New Moon near 6 January 2000, so $$a = 2000$$ and $$m = 1.2$$ (6 days = about 6/30 = 0.2 through month number 1), so then $$k = (2000 - 2000.1 + 1.2/12)×12.3685 = 0$$.

Likewise, there is a New Moon near 27 November 2008, so $$a = 2008$$ and $$m = 11.9$$ (near the end of month 11), so $$k = (2008 - 2000.1 + 11.9/12)×12.3685 = 8.892×12.3685 = 109.98$$ which is near 110, so that is New Moon number 110. The New Moon of 27 November 2008 is 110 − 0 = 110 lunar cycles after the New Moon of 6 January 2000.

How about the beginning of 1900? Then $$a = 1900$$ and $$m = 1$$, so $$k = (1900 - 2000.1 + 1/12)×12.3685 = −100.17×12.3685 = −1237.056$$ which is a tad before −1237, so New Moon number −1237 fell a few days after the beginning of the year 1900. The number of lunar cycles between that New Moon and the one of 27 November 2008 is 110 − (−1237) = 110 + 1237 = 1347.

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## 20. Lunar Phases and Constellations

A particular lunar phase (such as the first quarter moon) is not found in the same constellation each month. A particular lunar phase is a fixed number of degrees to the east of the sun along the ecliptic, and the sun moves about one constellation per month, so the next time the Moon reaches that same phase it is usually in the next constellation over from the previous time.

The first quarter moon is in the constellation where the sun will be 3 months later. The full moon is in the constellation where the sun will be 6 months later and where the sun was 6 months ago. The last quarter moon is in the constellation where the sun was 3 months ago.

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## 21. The Direction of Moonrise and Moonset

The motion of the Moon is much more difficult to calculate than the motion of the Sun.

If you want very precise directions, then you're best off using a planetarium program, which can calculate the direction of the Moon for whatever time and location you want, and (usually) can calculate the direction at moonrise and moonset as well. Some examples are Redshift 5 (for Microsoft Windows; //www.maris.com) and xplns (for Linux; //www.astroarts.com/products/xplns/), but there are many more.

If you don't mind doing some calculations yourself, then you can try the instructions from the "Positions in the Sky"-page.

If you just want the general direction, and already know where the Sun rises and sets in each season for the location that you are interested in, then you can figure it out as follows: If the Moon is $$x$$ days beyond the phase of New Moon, then it rises and sets roughly where the Sun does $$x$$ times 2/5 months later and $$x$$ times 4/5 hours earlier, as seen from the same location on Earth. Likewise, if the Moon is $$x$$ days before New Moon, then it rises and sets roughly where the Sun does $$x$$ times 2/5 months earlier and $$x$$ times 4/5 hours later.

For example, in the evening of 9 November 2005, the Moon was about 7.5 days beyond New Moon (i.e., the Moon's age was 7.5 days), so then it rose about where the Sun rises 7.5 times 2/5 = 3 months later and 7.5 times 4/5 = 6 hours earlier, which is about 6 hours earlier on February 9th. The precise year does not matter to the Sun, it rises in about the same direction every year on the same date. So, on 9 November 2005, the Moon rose and set about where the Sun rises and sets about 6 hours earlier around February 9th of every year.

You can find approximate directions to the Sun at sunrise and sunset for the whole world at Solar Position Table, but you'll need to know the latitude of your location in order to use that table.

If you just want a very general direction, then I can tell you that the Moon and the Sun have about the same range of directions in which they can rise, and about the same range of directions in which they can set (for a given location on Earth). So, if the Sun rises roughly between north east and south east every day, then the Moon rises roughly between north east and south east every day as well.

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## 22. The Direction of the Full Moon

The Full Moon is at about the same location in the sky where the Sun is half a year and half a day earlier or later.

The Sun follows about the same path (the ecliptic) between the stars every year, and the Moon is never more than about 6 degrees above or below that path. The Full Moon is always (almost) directly opposite the Sun in the sky, otherwise it would not appear full. For example, if the Moon is full on 21 December then that Full Moon stands between the stars at about the same location where the Sun was half a year earlier (on 21 June), and the Full Moon is then highest in the sky about 12 hours after the Sun is.

A Full Moon is (usually) not exactly as high in the sky at midnight of 21 December as the Sun was at noon on 21 June because (1) the Moon can be up to 6 degrees above or below the path of the Sun, so the Full Moon can be up to 6 degrees higher or lower in the sky than the Sun was six months earlier; (2) if the Moon is not full exactly at midnight then it will be highest in the sky a bit earlier or later, so its height at midnight will be a bit higher or lower; (3) many countries use a different time zone (e.g., Standard versus Daylight Savings Time, or Winter versus Summer Time) on 21 June than on 21 December, and that difference must also be taken into account.

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## 23. The Month

It takes the Moon one month to orbit around the Earth. There are no mile markers in space, so you can only tell if the Moon has completed another orbit if you compare its position with something else. You can pick different things to compare its position with, so you can define different kinds of months.

• the calendar month: a period of between 28 and 31 days that divides calendars. In some calendars, such as the Gregorian calendar that is used in the West, the months are no longer directly tied to the phases of the Moon. In other calendars, such as the Jewish and Islamic calendars, each month starts with a specific phase of the Moon. In some calendars (such as the Gregorian calendar and the Islamic calendar) each year has 12 calendar months, in other calendars (such as the Jewish calendar) some years have 12 months and some have 13 months, and in yet other calendars there are still other numbers of months in a year.
• the sidereal month: the period after which the Moon has returned to the same position (longitude) between the stars. On average, the sidereal month is now 27 days, 7 hours, and 43 minutes long. There are on average about 13.37 sidereal months in a tropical year.
• the synodical month: the period after which the Moon attains the same phase again. The synodical month is now 29 days, 12 hours, 44 minutes, and 3 seconds on average. The are on average about 12.37 synodical months in a tropical year.
• the tropical month: the period after which the Moon returns to the same position relative to the vernal equinox. On average, the tropical month is now 27 days, 7 hours, 43 minutes, and 12 seconds long. There are about 12.37 tropical months in a tropical year.
• the anomalistic month: the period after which the Moon returns to the same position relative to its perigee. This month is currently 27 days, 13 hours, and 19 minutes long on average. There are about 13.26 anomalistic months in a tropical year.
• the draconitic month: the period after which the Moon returns to the same node of its orbit. On average, this month is now 27 days, 5 hours, 5 minutes, and 6 seconds long. There are about 13.42 draconitic months in a tropical year.

Except for the calendar month, none of these months fits into a calendar year a whole number of times, so there is always a bit left over.

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## 24. Day and Night on the Moon

The day and night on the Moon each last about two (earth) weeks. A lunar day and a lunar night together are equal to a synodical month.

To determine if it is nighttime around your house, you check if the Sun is below the horizon as seen from your house. You determine the length of the night by measuring how much time there is between sunset and sunrise as seen from your house. The length of the night at some particular location on the Moon must be determined in the same way: by measuring how much time there is between sunset and sunrise as seen from that location on the Moon.

Consider the location at the center of the disk of the Moon, as seen from Earth. This is some crater. At New Moon the whole near side of the Moon is dark, so our crater is in darkness then, too, so it must be nighttime there. At First Quarter, about a week after New Moon, the boundary between light and dark runs exactly across the middle of the near side of the Moon, so it runs across our crater as well, so it must be sunrise there at that time. At Full Moon, another week later, the whole near side of the Moon is bright, so the Sun shines on our crater then, so it must be daytime there. At Last Quarter, again about a week later, the boundary between light and dark once more runs across our crater, but now with light and dark on the opposite sides from where they were at First Quarter. Our crater experiences sunset then. And at New Moon, again about one week later, the whole near side including our crater is once more in darkness. So, for our crater at the center of the near side of the Moon, the daytime lasts from First Quarter until Last Quarter, and the nighttime lasts from Last Quarter until First Quarter. That daytime and nighttime therefore each last about two weeks.

For another crater at another location on the Moon a similar story holds, but sunrise and sunset may then be at different lunar phases than for the crater at the center of the near side.

You can check this for yourself. Observe the Moon a few times every day and/or night for a month. Pick a particular feature on the Moon and note every time whether that feature is in the bright part of the Moon. As long as the feature is in the bright part, it must be daytime there, and if the feature is not in the bright part, then it must be experiencing nighttime. You'll find that the feature is in the bright part of the Moon for about two weeks, and is in the dark part (and hence invisible) for about two weeks as well.

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## 25. The Orientation of the Crescent Moon

The line that connects the two points of the crescent Moon is always almost at right angles to the path of the Moon along the sky. If the Moon goes up almost straight from the horizon (as it does when seen from the equator), then the crescent appears horizontal. If the Moon rises at a shallow angle (as seen far from the equator), then it moves as well along the horizon towards the west, and then the crescent is mostly vertical. The Moon rises almost vertically as seen from the equator because the orbit of the Moon stands approximately above the equator.

The shape and orientation of the Moon as seen from a spot south of the equator is similar to the shape and orientation of the Moon as seen from a place equally far north of the equator, and vice versa. For example, the Moon has the same orientation as seen from 52 degrees south latitude as from 52 degrees north latitude.

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## 26. The Illuminated Part of the Edge of the Moon

The Moon is illuminated on the side that is closest to the Sun in the sky. On a sphere, the shortest path between two points is a great circle: a circle that is as large as the equator of the sphere, that goes all the way around the sphere, and that has the center of the sphere for its center.

If the Moon is high in the western sky and the Sun low in the eastern sky, then the shortest path between them in the sky is not a line that goes down and sideways from the Moon to the lower Sun, but a line that goes up and sideways from the Moon until it reaches its highest point near the celestial meridian (roughly due south, as seen from Europe), and then sideways and down towards the Sun. Because the line starts going up and sideways from the Moon, it is that side of the Moon's limb that is illuminated.

You can see this for yourself with a globe and a piece of string, or with a hula hoop. Regard the globe as the celestial sphere and mark the locations of the Sun and the Moon, for example with the Sun in Indonesia (in the east, low above the horizon, which is represented by the equator) and the Moon somewhere in the eastern part of Canada (in the south west, high above the horizon). Now try to make the piece of string run between both points and pull it taut. You'll see that it does not run from Canada down to Indonesia, but starts going up closer to the north pole for a while first. For the same reason, airplanes on their way from Amsterdam to the United States do not fly to the southwest the whole way, but start going to the northwest before finally angling towards the southwest.

With a hula hoop, the instruction is to keep your head exactly in the center of the hula hoop while orienting the hoop in such a way that it covers both the Sun and the Moon. You'll notice that the side of the Moon that is illuminated is alwasy the one that is closest to the Sun along the hoop, and in the direction that the hoop has near the Moon.

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The direction (left or right) of the bright outer edge of the waxing Moon and the direction of the bright outer edge of the waning Moon depend on which of the two ecliptical poles is above the horizon. The ecliptical poles are the two points that are furthest away from the ecliptic (the path that the Sun and Moon and planets roughly follow between the stars in the sky), just like the geographical poles are the two points on Earth furthest from the equator. When the ecliptical north pole is above the horizon, then those directions are like they are in the Netherlands (and all other places to the north of the tropics), and when the ecliptical south pole is above the horizon, then those directions are like they are in South Africa (and all other places to the south of the tropics). When the ecliptical poles at precisely on the horizon, then the ecliptic passes through the zenith and then the Moon's bright outer edge points straight downward (when the Moon is up).

As seen from a location north of the tropics, the bright outer edge of the waxing Moon (between New Moon and Full Moon) points to the right (like the letter "D" ― at least more to the right than to the left), and the bright outer edge of the waning Moon (between Full Moon and New Moon) points to the left (like the letter "C"). As seen from a location south of the tropics this is just the other way around (so from there the waxing Moon looks like the letter "C" and the waning Moon like the letter "D").

North of the tropics, the ecliptical north pole is always above the horizon. South of the tropics, the ecliptical south pole is always above the horizon. Between the tropics, sometimes the one and sometimes the other ecliptical pole is above the horizon, so the appearance of the Moon varies there between "northerly" (as in the Netherlands) and "southerly" (as in South Africa). How long the ecliptical north pole is above the horizon each day, and how long the ecliptical south pole, depends on the geographical latitude, and the time at which they rise and set depends on the seaons, getting earlier by about 4 minutes every day.

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## 27. The Near Side of the Moon

The Moon always shows the same side to us on Earth. You can check this for yourself. If you look at the Moon (with or without binoculars) then you can see darker areas (the so-called lunar seas, which are made of solidified lava). All darker areas that you can ever see on the Moon are also visible during every Full Moon, which is only possible if the Moon always shows the same side to us. The Full Moon every time shows the same dark areas the whole night long, and that, too, is possible only if the Moon always shows the same side to us.

Below is a sequence of pictures of the Moon, taken by the author on, respectively, 2006-01-08, 2006-06-09, 2005-11-14, 2003-04-15, 2001-12-30, 2002-12-19, 2002-01-05 and 2003-01-24. All of these pictures show the same spots and blotches and features (in their illuminated parts), even though they were taken at different phases of the Moon and at different times of night.

The Moon always shows the same side to us, yet people say that the Moon rotates around its axis. How can this be?

Compared to what do you measure speed of rotation? There is no measurable zero point of speed of motion, but there is a measurable zero point of speed of rotation. You can feel how fast you rotate, even with your eyes closed, but you cannot feel how fast you move. Someone who floats through space in a closed spaceship without windows or an engine cannot feel (or measure) how fast the spaceship is moving through space, but he can feel how fast he (or the spaceship) rotates around its axis. You can read the newspaper just as easily in your home as in a train going at 100 km/h or 60 mph compared to your home, or as in an airplane going at 1000 km/h or 600 mph at a fixed altitude, but if you rotate around your own axis twice a second then you cannot read the paper anymore and then it feels as if your arms are pulled from your body. So, there is no fundamental difference between moving at 1000 km/h or moving at 0 km/h, but there is a fundamental difference between rotating around your own axis twice a second or zero times a second.

It turns out that the zero point of the speed of rotation is determined by the average of the far-away stars (and other far-away material), apart from local relativistic effects which become important only at very extreme strengths of gravity.

If someone who feels that he's rotating has a clear view of the night sky, then he'll notice that he rotates compared to the stars. And if someone sees that he's always in the same orientation compared to the stars, then he won't feel any of the effects that are associated with rotating around his own axis. The position relative to the Sun (or any other particular celestial body) is not relevant here.

Rotation is always measured compared to the Universe as a whole, i.e., compared to far-away stars or galaxies. What does the Moon look like as seen from a far-away star? The Moon always shows the same face to the Earth, so when the Moon is at the opposite side of the Earth from the star, then the front side of the Moon is turned to both the star and the Earth. If the Moon is at the same side of the Earth as the star is, then the front side of the Moon faces the Earth, but the back side of the Moon faces the star, because then the Moon is between the star and the Earth. When the Moon is back at the opposite side of the Earth again as seen from the star, then it has completed one orbit around the Earth, and then its front is facing the star again. Any observer near the star will say that the Moon rotates, because in the course of a sidereal month the observer has seen all sides of the Moon. The observer sees the same side of the Moon again just when the Moon has completed one orbit around the Earth, so the observer notices that the spin period of the Moon (period of rotation around its own axis) is equal to the orbital period (period of rotation around the Earth).

Conversely, if the Moon did not rotate around its axis, then the observer near the far star would always see the same side of the Moon, but then we on Earth would see the "front" side of the Moon when the Moon was on the other side of the Earth from the star, but the "back" side of the Moon when the Moon was on the same side of the Earth as the star is, because then the Moon would be between us and the star, so then we would see all sides of the Moon in the course of a sidereal month, so it would seem to us as if the Moon rotated around its own axis in a sidereal month. It may help if you draw a picture of it.

In the above diagrams, the large circles indicate the orbit of the Moon around the Earth, and the small circles indicate the Moon at four different positions in its orbit. The diagonal line on the Moon indicates the location of a crater on the Moon.

In the left-hand diagram (A-B-C-D), the Moon does not rotate around its own axis, so the different Moons are only shifted but not rotated with respect to one another. As seen from the Earth (in the middle of the large circle, but not shown), the crater is sometimes at the near side of the Moon, and sometimes at the far side of the Moon. When the Moon has returned to position A, then the crater has returned to its original position, too, as seen from Earth, so as seen from Earth the crater rotates around the axis of the Moon in the same time that the Moon takes to orbit around the Earth.

In the right-hand diagram (E-F-G-H), the Moon always shows the same side to the Earth (because the stripe always points at the Earth) and rotates around its own axis (which sticks straight out of the picture), as is perhaps easier to see from the four moons at the bottom right, which have the same orientation as in the top right-hand diagram with the lunar orbit. When the Moon has orbited once around the Earth, then the Moon has rotated once around its axis.

In general, if a moon rotates in the same direction in which it orbits around its planet, then the number of times that people on the planet see the moon rotate around its axis (i.e., see the same crater return to the middle of the disk of the moon) plus the number of times that people near the far-away star see the moon rotate is equal to the number of orbital periods that the moon has completed (as seen from the star).

If the moon rotates opposite to the direction in which it orbits around its planet, then the number of rotations as seen from the planet *minus* the number of rotations as seen from the star is equal to the number of orbital periods.

If the moon does not rotate at all (compared to the stars), then the number of rotations as seen from the star is zero, so then both cases yield the same result, namely that the observers on the planet see a number of rotations equal to the number of orbital periods.

We always see the same side of the Moon, so the Moon must rotate around its axis in the same time that it takes for the Moon to orbit once around the Earth. This is called a 1:1 spin-orbit resonance.

It takes on average exactly the same amount of time for the Moon to rotate once around its axis as it takes for the Moon to orbit once around the Earth (and in the same direction), namely 27 days 7 hours 43 minutes. For example, when the Moon has completed one quarter of its orbit around the Earth, then it has also rotated by 90 degrees around its axis (compared to the stars), so that we still look at the same side of the Moon.

The Moon rotates around its axis at a fixed speed, but the speed at which the Moon orbits around the Earth is not always the same. The Moon goes somewhat faster through some parts of its orbit, and somewhat slower through other parts of its orbit. Also, sometimes the North Pole of the Moon is tilted a little towards us, and sometimes the South Pole (just like for the seasons on Earth), and sometimes the Moon is a little closer to Earth and sometimes it is a little further away. All in all the Moon seems to do some nodding (yes) and shaking (no), and also some growing and shrinking, but you can only tell if you take pictures of the Moon day by day and compare them carefully. You can see this, for example, on the "Astronomy Picture of the Day" of 10 August 2003, at //antwrp.gsfc.nasa.gov/apod/ap030810.html.

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The astronauts of the Apollo 8, and Apollo 10 through 17 missions have seen the far side of the Moon with their own eyes. Three astronauts went on each mission, but three of the astronauts each went on two missions, so in total 24 astronauts have seen the far side of the Moon so far. See //nssdc.gsfc.nasa.gov/planetary/lunar/apollo.html for more information about the Apollo missions.

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## 28. Names of Full Moons

There appear to be quite a few specific names for Full Moons in various seasons or months, but they are folklore names and have no official standing. There is no official list of Full Moon names. This means that anyone can invent a new name for a particular Full Moon (or any other phase of the Moon, for that matter). In fact, a particular Full Moon can have very different names in different cultures. For example, it is highly unlikely that the name "Sturgeon Moon" was used of old in areas where the sturgeon is not known.

I imagine that most specific names for full moons point to an activity that can be done or a foodstuff that can be obtained or an animal that can be seen at the time of that full moon, but you can only get the real story behind the name from the person or people who invented the name.

I had not heard of a Sturgeon Moon before, but could readily find references to it using a popular search engine. The most definite-sounding explanation was at //www.pburch.net/lunarcal.html which says that the Sturgeon Moon is the 11th full moon after the Harvest Moon, which itself is the full moon closest to the beginning of autumn. Usually, the Sturgeon Moon is the last full moon before the Harvest Moon.

Full moons with their own names are usually tied to the seasons. Each one has a slightly different character from the other ones, and not just because of the change in agricultural activities throughout the year. The full moon is opposite the Sun in the sky, so the path through the sky that the Sun follows in the summer is followed by the full Moon in the winter, and vice versa. Outside of the tropics, the summer Sun gets high in the sky, but the winter Sun stays low. Therefore, the winter full moon gets high in the sky, but the summer full moon stays low. Several factors conspire to make the winter full moon stand out more: the sky is darker, the night is longer, the moon gets higher (hence brighter) and remains above the horizon for longer.

Since the seasons are opposite on opposite sides of the equator, local names for full moons that are tied to the seasons apply to months that are half a year apart on opposite sides of the equator. For example, the Harvest Moon is tied to the beginning of autumn (when the harvest is in full swing), which corresponds to September - October in the northern hemisphere but to March - April in the southern hemisphere.

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## 29. The Name of the Daytime Moon

As far as I know there is no special name for a Moon that is seen during the daytime, because it is the very same Moon that can also be seen at night. If it is not Full Moon or New Moon, then at any given moment the Moon can be seen from some places where it is day and from some other places where it is night.

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## 30. Full Moon Around the World

There is just one Moon around the Earth, so all people who see the Moon see the same Moon, and if the Moon happens to be full at that time, then all people who see the Moon see the same Full Moon.

At any time, you can see only half of the sky, because you cannot see through the ground. At night, the Sun is in the other half of the sky, which you can't see because the ground blocks your view of it. Someone who is at the exact opposite side of the Earth from you sees exactly the opposite half of the sky than you. If the Sun is above the horizon for you, then the Sun is below the horizon for this other person, and vice versa, and the same for anything else in the sky. So, if you can see the Moon (whether it is full or not), then this other person cannot see the Moon, and vice versa.

So, you cannot see the Full Moon at the same time as someone at the exact opposite side of the Earth, but the Moon that both of you see at different times is the same Moon, and if the Moon looks full to you, then it will also look full to the other person twelve hours later.

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In some newspapers and other publications times of Full Moon are shown to the nearest minute. Those times are then (probably) the timea at which the ecliptic longitude (a certain celestial coordinate) of the Moon differs exactly 180 degrees from the same coordinate of the Sun, as seen from a standard location (perhaps your national observatory, or even the center of the planet). Because not all places on Earth are in the same time zone, it is possible for such a moment of Full Moon to fall into different dates at different locations on Earth (for example, at 23:15 on 12 March in the Netherlands, which corresponds to 0:15 on 13 March in Egypt, assuming a one-hour time difference between Egypt and the Netherlands), even though it is really the very same moment of time.

However, the average person sees little difference between the Full Moon and the Moon one day earlier or later, so if the Moon looks full at a certain date from one location, then it looks full at the same date also from any other location on Earth.

The answer to the question therefore depends a bit on how precise you wish to capture the time of Full Moon. If you want to be accurate to the minute, then there is a chance of not more than 50 percent that a given Full Moon falls on different dates as seen from two different locations on Earth. If you only care about how full the Moon looks at first glance, then there is no practical difference between Full Moons seen from different locations on Earth.

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## 31. The Brightness of the Moon

How bright the Moon appears to be in the sky depends on a lot of things. The brightness changes with the season, with the phase of the Moon (e.g., full or new), with the height of the Moon above the horizon, and - very importantly! - with the condition of the atmosphere (e.g., the weather).

There are at least two measures for how bright the Moon appears to be in the sky. The total brightness is the amount of light that comes from the lunar disk as a whole. This is measured, for example, as a magnitude. The surface brightness is the brightness per solid angle, or the amount of light that comes from a small piece of the Moon that fills the whole field of view of your telescope. This is measured, for example, as a number of magnitudes per square degree.

The brightness of the Moon depends at least on the following factors:

1. the distance of the Moon from the Earth. This varies during a month between about 5% above and below average, with occasional deviations up to 7%. Because of this, the total brightness of the Moon can vary between about 11% above and below the average, with occasional deviations up to about 15%. The surface brightness is not affected by this.
2. the (spatial) distance of the Moon from the Sun. This varies during the year between about 1.7% above and below the average (least in January, greatest in June). This causes variation in the total and surface brightnesses of the Moon between 3.4% above and below average.
3. the distance of the Moon in the sky from the point exactly opposite the Sun (which we'll refer to as the antipode). Because of the "opposition effect" a few degrees kan make a large difference. At 5 degrees from the antipode, the total and surface brightnesses are already 10% less than at the antipode (excluding the effect of the shadow of the Earth). This distance itself has two contributions:
1. the ecliptic latitude of the Moon, which is the distance of the Moon above or below the ecliptic (the path of the Sun). This deviates from 0° by up to about 5.5° each month, which yields a reduction in brightness (both total and surface) of 11%.
2. the distance, in time, from the moment of Full Moon. The Moon moves by about 12 degrees in the sky each day (relative to the Sun), so if the moment of Full Moon happens to be near noon, then it is easily 6 hours before or after Full Moon when you see the Moon, which means the Moon is about 3 degrees further away from the antipode, which yields a reduction in brightness (total and surface) of 6%.

These two effects can together yield a distance of 6 degrees from the antipode, and a reduction in brightness of 12%.

4. the height of the Moon in the sky. Part of the moonlight is absorbed or scattered when it travels through the atmosphere of the Earth, and the more slanted the rays of moonlight are (i.e., the closer the Moon is to the horizon), the more air it has to pass through, and the more light gets absorbed or scattered. I have no accurate numbers for how much effect this has, but when the Moon is low in the sky then it is at least a factor of 2, and probably even more. The height of the Moon in the sky has the following contributions:
1. the geographical latitude of the observer. The smaller the latitude (north or south), the higher the Moon can get.
2. the declination of the Moon. The Full Moon is (almost) exactly opposite the Sun, so the declination of the Full Moon is greatest at the beginning of winter and least at the beginning of summer, and the Full Moon can get on average about 46 degrees higher in the sky in winter than in summer. The ecliptic latitude of the Moon counts for this as well.
3. the distance, in time, to the transit of the Moon (when the Moon is highest in the sky). If $$b$$ is the geographical latitude then the Moon can get at best (at the beginning of winter) to 119 − $$b$$ degrees height, and at worst (at the beginning of summer) no higher than 61 − $$b$$ degrees. For $$b$$ = 51 degrees (about right for the Netherlands, Belgium, and southern Canada) the limits are 10 degrees and 68 degrees.

5. the colors of moonlight that are watched. Blue light is scattered more easily than red light, and the different colors of light are also probably absorbed by different amounts by dust in the air. In practice, this is only important when the Moon is low in the sky.
6. the condition of the atmosphere (smog, dust, clouds). This obviously has great influence, and especially near the horizon.

For the greatest total brightness of Full Moon, you need the following combination of factors: watch the Moon just before or after a lunar eclipse (i.e., closest to the antipode of the Sun but without getting into the shadow of the Earth), around local midnight, around the end of December, seen from 23° north latitude, from great elevation.

The same factors are important for the greatest surface brighness, except that the distance of the Moon from the Earth is not important there.

If you are interested in the greatest contrast of the brightness of the Moon with the sky itself, then you are interested in the surface brighness of the Moon and in the brightness of the sky. The brightness of the sky is greater when there is more scattered light, which is when the Moon is low in the sky, and when it is closer to sunrise or sunset. For the greatest contrast with the sky you should watch the Full Moon high in the sky, in the middle of the night, in winter (so the Moon is highest in the sky and the Sun furthest below the horizon, so both of them scatter the least amount of light into the sky).

If you watch the Moon at a fixed height above the horizon, then all factors related to the height of the Moon in the sky play no role anymore. In that case, for the surface brightness of the Full Moon, only the distance from the Earth to the Sun and the condition of the atmosphere remain as factors, with the latter probably being more important than the former. The season is then irrelevant, except where it influences the weather.

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## 32. Conjunctions of the Moon with a Planet

The Moon has a conjunction with any given planet about once every 27 1/3 days. If you want a precise date and time of something related to the Moon, then you should consult an astronomical almanac or planetarium program, because the motion of the Moon cannot be caught with sufficient accuracy in simple formulas. However, if you are content with an estimate that may be a day or two off, then you can find enough information in these web pages to do the calculations:

Check the relevant Planetary Phenomena Page to determine by how many hours the planet leads or lags the Sun. This can be a negative number. Multiply that number by 29.5/24 = 1.23 to find the estimated number of days after New Moon that the conjunction occurs. This, too, can be a negative number, and then the conjunction is before New Moon. Earlier on this page I explained how you can find the dates of New Moon, and then you have all information that you need.

For example: When is the conjunction of the Moon with Jupiter nearest to the end of December 2003? Jupiter then leads the Sun by about 7.5 hours, so the Moon is then near Jupiter about 7.5/24×29.5 = 9 days before New Moon. It is New Moon around 23 December 2003, so the conjunction with Jupiter is then near 14 December 2003, and again about every 27 1/3 days later.

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## 33. Is the Moon Heating Up?

The Moon receives almost all of its heat from the Sun, so if the Sun were getting steadily brighter, then one would expect the Moon (and also the planets) to get hotter. However, the only obvious feature that has been detected in the variation of the brightness (the amount of emitted energy) of the Sun is a tendency to rise and fall with the number of sunspots visible on the Sun (and with other measures of solar activity), which happens in a rough cycle of about 11 years. No clear long-term increasing or decreasing tendency has been detected so far. If the Solar System is a bit warmer at some time due to solar activity, then we expect it to cool down again later, when the solar activity subsides as usual. See //en.wikipedia.org/wiki/Solar_variability

To my knowledge, nobody measures temperatures on the Moon on a regular basis. I don't think there are any thermometers active on the Moon at the moment (2007). One can deduce the temperature from measurements of infrared radiation coming from the Moon, but those are difficult to make from Earth, and any such measurements obviously do not include the far side of the Moon.

The temperature on the Moon varies with the time of day and with the location on the Moon, like it does on Earth, but the lunar day is a lot longer than the Earth's day, so any given spot on the Moon can heat up longer when the Sun is up, and can cool down longer when the Sun is down. The temperature on the Moon can vary between about −200 and +120℃.

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Last updated: 2017-12-28