The following is a
compilation of interesting facts or information about the moon that I
found on my walk to chodesh. Most of this I did not know and I
suspect the average person on the street most likely would not know
either. As such most people should find the following moon
information interesting. A lot of it is approximate. Except
for the two months quoted, a lot of values were determined using
models that are approximate. Probably nothing should be quoted from
here as exact. Anyone wanting more exact information should probably
go to an actual astronomy site. For everyone else, enjoy!
The synodic month of 29.53 days
month is 29.53059 days (29 days, 12 hours, 44
minutes, 2.8 seconds) and is measured from New Moon to New Moon.
The sidereal month of 27.32 days
orbital period in a non-rotating frame of reference (which on average
is equal to its rotation period) is about 27.32166 days (27 days, 7
hours, 43 minutes, 11.6 seconds). This is known as a
sidereal month and
is measured by observing how long it takes the Moon to pass a fixed
on the celestial sphere.
Why are these two months different? If it takes the moon 27.32 days to orbit the earth, then why does it take approximately 29.53 days to go from new moon to the next new moon?
Note the following diagram [nothing to scale]:
The earth moves 29.1 degrees around the sun in one synodic month
Orbit of earth about sun nearly circular
eccentricity of the Earth's orbit is currently about 0.0167, meaning
that the Earth's orbit is nearly circular, the semiminor axis is
98.6% of the semimajor axis.
eccentricity of an ellipse, usually denoted by ε
or e, is the ratio of the distance between the two foci, to the
length of the major axis or e = 2f/2a = f/a. For an ellipse the
eccentricity is between 0 and 1 (0<e<1). When the eccentricity
is 0 the foci coincide with the center point and the figure is a
The angle of travel for the earth about the sun was found by approximating the degrees given the synodic month of 29.53 days as follows:
An approximate value for the sidereal month can be determined using the synodic month by working out one orbit of 360 degrees given the extra 29.1 degrees about the earth needed for the moon to complete a synodic month as follows:
Similarly the difference in days between the two months can be determined by finding the time for the moon travelling 29.1 degrees about the earth as:
orbit of earth about sun not elliptic or circular
moon does not orbit the exact center of the Earth, but a point on a
line between the center of the Earth and the Moon, approximately
1,710 km below the surface of the Earth, where their respective
masses balance. This is the point about which the Earth and Moon
orbit as they travel around the Sun.
As such, technically the orbit of the earth would be along a slightly wobbly path as the centre-of-mass of the earth-moon system follows the elliptic path of orbit. For the above calculations the earth orbit path was approximated as circular.
scale usually not correctly shown
synodic month not exactly 29.53 days
Through 2011 the synodic
month length ranged from 29.34 days up to about 29.76 days.
From year to year this range probably won't change very much but consider the following quote:
of perturbations in the orbits of the Earth and Moon, the actual time
between lunations may range from about 29.18 to about 29.93 days. The
long-term average duration is 29.530589 days (29 d 12 h 44 min 2.9
This gives a worst possible range of 0.75 days or 18 hours. This may be extreme and for 2011 only about a 10 hour range occurred. Still this may mean that a close watch on the synodic month lengths should be given each year for those who are interested in the lunar months.
don't we have a solar eclipse every new moon?
The Moon is a cold, rocky body about 2,160 miles (3,476 km) in diameter. It has no light of its own but shines by sunlight reflected from its surface. The Moon orbits Earth about once every 29 and a half days. As it circles our planet, the changing position of the Moon with respect to the Sun causes our natural satellite to cycle through a series of phases:
The phase known as New Moon can not actually be seen because the illuminated side of the Moon is then pointed away from Earth. The rest of the phases are familiar to all of us as the Moon cycles through them month after month. Did you realize that the word month is derived from the Moon's 29.5 day period?
To many early civilizations, the Moon's monthly cycle was an important tool for measuring the passage of time. In fact many calendars are synchronized to the phases of the Moon. The Hebrew, Muslem and Chinese calendars are all lunar calendars. The New Moon phase is uniquely recognized as the beginning of each calendar month just as it is the beginning on the Moon's monthly cycle. When the Moon is New, it rises and sets with the Sun because it lies very close to the Sun in the sky. Although we cannot see the Moon during New Moon phase, it has a very special significance with regard to eclipses.
eclipse of the Sun (or solar eclipse) can only occur at New
Moon when the Moon passes between Earth and Sun. If the Moon's shadow
happens to fall upon Earth's surface at that time, we see some
portion of the Sun's disk covered or 'eclipsed' by the Moon. Since
New Moon occurs every 29 1/2 days, you might think that we should
have a solar eclipse about once a month. Unfortunately, this doesn't
happen because the Moon's orbit around Earth is tilted 5 degrees to
Earth's orbit around the Sun. As a result, the Moon's shadow usually
misses Earth as it passes above or below our planet at New Moon. At
least twice a year, the geometry lines up just right so that some
part of the Moon's shadow falls on Earth's surface and an eclipse of
the Sun is seen from that region.
Admittedly we only needed the last paragraph but there was a wealth of information here that just could not be missed. Curiously though this site has the orbit of the moon as the synodic length, not the sidereal. A simple mistake.
and month are cognates
month is a unit of time,
used with calendars,
which was first used and invented in Mesopotamia, as a natural period
related to the motion of the Moon;
The traditional concept arose with the cycle of moon
phases; such months
(lunations) are synodic
and last approximately 29.53 days.
are words that have a common etymological
origin. The word derives from the Latin cognatus
The time it takes the Moon to go through
all its phases is about a month, and that was so important to our ancestors that they created the period of time we call a month.
Maybe you've even noticed that the word month is like the word moon.
month generally defined as being from new moon to new moon
mean synodic month (New Moon to New Moon)
New Moon phase is uniquely recognized as the beginning of
each calendar month
month is 29.53059 days (29 days, 12 hours,
44 minutes, 2.8 seconds) and is measured from New Moon to New Moon.
Month: The period between successive new moons (29.531 days).
month. the period of a complete revolution of the moon around the
earth, as the period between successive new moons (synodic month),
equal to 29.531 days
month was originally defined as the time between one new
moon to the next, a period now called the synodic
Sometimes other phases of the moon are mentioned but the most common is the new moon.
Synodic month is one moon day
students get confused about the geometry of the orbit of the Moon
because they have heard this term "the dark side" of the
Moon (besides being a famous---at least to us old timers---album by
Pink Floyd). If you examine the figures above about how the phases of
the Moon change, you see that for at least one half of the lunar
orbit, each spot on the Moon has daylight. That is there are 14.75
days when the Sun is visible each orbit, and 14.75 days each orbit
when the Sun is not visible. At any one time (just like on the
Earth!!!), there is one half of the Moon which is in darkness, and
one half which is in the sunlight. It is true that the Moon spins
much more slowly than the Earth, but the Moon has "days"
and "nights". It is just that these days and nights are
14.75 Earth days long! So the far-side of the Moon which we cannot
see is not the "dark side", it is the far-side. At full
Moon, the far-side is completely dark. But at New Moon, the far-side
is fully illuminated (as seen from the Sun!).
What is the point of this quote? We only see one side of the moon. Why? Because the moon is also rotating on its axis. The time the moon has to do “one orbit” about its axis takes the same time as one synodic month. The following picture shows this more clearly:
The 1 Earth day at the beginning is included in the 29.53 days. Note the little yellow spot on the moon. Now as the moon orbits the Earth after one synodic month the little yellow spot moves too. Note the extra moon added for the 3rd Earth position for the synodic month. This is just showing the moon at the opposite side of the Earth. This of course would be half way through the synodic month but for comparison showing it here in the 3rd Earth position. The importance of this is that you can see that the Moon is actually rotating about its own axis as it also rotates about the Earth. Now consider the yellow moon spots on the New Moons. If you were standing on these yellow spots on the moon it would be mid-day. In other words the New Moon to New Moon is mid-day to mid-day for the yellow spot position. What this means is that the New Moon to New Moon has covered exactly one Moon day. What we call the synodic month is no more than the day for the Moon. The synodic month IS one Moon Day. Another way to think of this is that one moon day is equivalent to 29.53 earth days.
rotates approximately 360.986 degrees to complete one earth day
rotates approximately 389.1 degrees to complete one moon day or
Some Bible info on New Moon
the new moon, month, monthly
new moon, the day of the new moon, the
calends of a lunar month which was a festival of the ancient Hebrews.
(2) a lunar month,
beginning at the new moon.
moon, month. 1. new
moon = day, time, of new moon, as religious
festival. 2. month
(as beginning with new moon, lunar month; …
kho'-desh; from 2318; the new moon; by impl. a
month:--month(-ly), new moon.
Month, monthly, new moon. Although this word
properly means “new moon,” it is commonly used as an equivalent
to our word “month” because the month began when the thin
crescent of the new moon was first visible at sunset. The Hebrew
calendar used a lunar month fitted into a solar year. This was done
by adding an extra month approximately once every three years because
it was about eleven days less than the solar year. In early Israel
the first of each month, or new moon, was determined by observation
and proclaimed officially by the blowing of trumpets. The month was
considered to be thirty days (note Gen 7:11; cf. 8:3-4), unless the
new moon was observed earlier.
Most Christian festivals are timed according to the lunar month
a calendar based on the variations of the phases of the Moon as seen from Earth.
The lunar year contains 12 synodic months, these consisting of 29.5305882 days, the synodic month being defined as the time interval
(synodic period) between new moons. Therefore, the lunar year of 354.3672 days is about 11 days shorter than the solar year of 365.24219 days.
A true lunar calendar quickly gets out of step with the seasons and is often replaced by a luni-solar calendar in which every third or
fourth year contains 13 as opposed to 12 lunar months, a leap month being intercalated (added) as required. Islamic, Jewish, Hindu,
Buddhist, and all Christian festivals except Christmas itself are timed according to the lunar calendar.
Yet just as vital an influence on the calendar is the fact that the Christian Church grew up in the Roman Empire, which followed a calendar
controlled by the sun.
In 325CE the Council of Nicaea established that Easter would be held on the first Sunday
after the first full moon occurring on or after the vernal equinox. From that point forward,
the Easter date depended on the ecclesiastical approximation of March 21 for the vernal equinox.
Easter is delayed one week if the full moon is on Sunday, which decreases the chances of it
falling on the same day as the Jewish Passover. The council’s ruling is contrary to the
Quartodecimans, a group of Christians who celebrated Easter on the day of the full moon,
14 days into the month.
Moon phases not the same length
This is the view from the Southern Hemisphere. The Moon is rotating clockwise and the line of shadow/light appears to rotate anti-clockwise. From the Southern Hemisphere the line dividing the dark and light parts of the face of the Moon travels from left to right. As θ travels from zero to 2π we see that the full cycle of phases is taken:
θ = 0 New Moon
We can determine the formula for x1 in terms of θ mathematically as
where r is the radius of the Moon. A corresponding velocity formula for x1 as it moves across the face of the Moon can be found as:
The radial rate of change here is different to the radial velocity of the Moon. This is because this calculation is independent of how fast the Moon is rotating itself about its axis. We simply have the phases during the synodic month of 29.53 days. That's it.
As the shadow line gets to the extreme edges [θ approaches 0 and π] the speed will actually drop to zero instantaneously and then increase again with maximum speeds attained at π/2 and 3π/2. These are the radial positions for the First and Last Quarters. The slowest speeds [of zero km/hr] will be attained at the instantaneous points of the New and Full Moons. The mathematics of this gives us an amazing result. The longest phases are the New and Full Moons. All the other phases are shorter!
percentage of illumination of face of moon
The models investigated
were rectangular, trapezoidal, parabolic, and exact using spherical
coordinate geometry. They all yielded the same formula solution. To
simplify the mathematics we will consider the model dimensions about
1 or similar for calculating ratios and only the simplest model is
covered here. The rectangular model is here shown:
The light rectangular
area is (1 − x1)h
, the total rectangular area is 2h. Then the percentage
illumination is approximately:
new moon not same as astronomical new moon
to the Mishnah and Tosefta, in the Maccabean, Herodian, and Mishnaic
periods, new months were determined by the sighting of a new
crescent, with two eye witnesses required to testify to the Sanhedrin
to having seen the new lunar crescent at sunset. The practice in the
time of Gamaliel II (c. 100 CE) was for witnesses to select the
appearance of the moon from a collection of drawings that depicted
the crescent in a variety of orientations, only a few of which could
be valid in any given month.
molad is the time of the moon's "birth." There is a point
in the moon's orbit in which it is positioned directly between the
earth and the sun, making it invisible to anyone standing on earth's
surface. The molad occurs when the moon has moved far enough from
this position that a thin crescent of its illuminated surface becomes
visible, marking the start of a new Jewish month.
Chodesh, the new month, is marked by the appearance of the first
sliver of the new moon in the sky above Jerusalem in Israel.
It is clear from these quotations that to the Jewish mind, the new moon occurs when the first sliver of the waxing crescent becomes visible. The following snapshot from a Jewish site shows this clearly:
The Jewish new moon is not the same as the astronomical new moon which is completely dark.
Jewish Calendar does not correctly follow the lunar months
The Jews are aware of these length discrepancies and readily admit them:
Different versions of the new moon day
Various reasons for keeping the new moon day
Gen 1:16 And God made the two great lights, the greater light to rule the day, and the lesser light to rule the night; he made the stars also.
Moon orbits the Earth - or more accurately the Earth and Moon revolve
around a common barycentre - at a centre-to-centre distance of
384,000 km. The Sun, some 150,000,000 km away, is 1,400,000 km
across. It is an almost unbelievable coincidence that from the
surface of the Earth, the Sun and the Moon appear more or less
exactly the same size - around 32 arc minutes. It is this fact which
allows us to see the Sun’s corona during a solar eclipse. No other
combination of bodies anywhere in the Solar System give rise to this
1. The Oxford Interactive Encyclopedia. Developed by The Learning Company, Inc. Copyright (c) 1997 TLC Properties Inc. All rights reserved.
2. L.W.Cowie and John Selwyn Gummer, The Christian Calendar: A complete guide to the seasons of the Christian year, 1974, Weidenfeld and Nicolson, London, pp. 7,8.
Last revised: 18 Sep 2016.