As I said, there is more moving parts in 
our model of the cosmos. 
There are more things that do not remain 
fixed on the celestial sphere, and just 
rotate with it, but yet, rise and set so 
are off the earth. 
And the next most conspicuous one after 
the sun, is our moon. 
like the sun, 
the moon moves along the celestial 
sphere. 
It's not fixed. 
for the same reason, the moon orbits the 
Earth. 
It orbits the Earth in the same sense 
that the Earth orbits the sun. 
And the same sense that, therefore, the 
sun appears to orbit the Earth, 
moving towards the east along the 
celestial sphere. 
But the moon orbits the Earth much 
faster. 
The moon completes a complete orbit 
around the earth in what is called a 
sidereal month which is 27 and a 
one-third days. 
that means that it's right ascension 
increases by 48 minutes per day. 
Compare this to the sun's measly four 
minutes. 
In other words the moon takes a month to 
orbit the earth. 
The sun takes a year to orbit the earth. 
A month is a twelfth of a year, four 
minutes is a twelfth of 48. 
The mathematics adds up. 
Now, as the moon orbits the Earth, it 
also rotates about its axis. 
We'll discuss next week why that is. 
But this means that we are always seeing 
the same side of the Moon as it rotates 
around us. 
there's the same side of the Moon that 
faces us. 
This means that while there is no such 
thing as the dark side of the Moon, there 
certainly is such a thing as the far side 
of the Moon. 
There are parts of the Moon that are 
never visible from Earth, and, those were 
first, 
Seen, or. 
Indirectly seen by human eyes. 
When the Soviet lunar space craft first 
orbited the moon. 
So this is why. 
When we look up at the moon, every time 
we see it. 
It has this familiar, look. 
We're always seeing the same side of the 
moon. 
Now, the, moon, therefore, moves to the 
east along the celestial sphere by 48 
minutes a day. 
The sun moves to the east along the 
celestial sphere by four minutes a day, 
which means the moon moves faster to the 
east along the celestial sphere. 
The moon moves 44 minutes per day farther 
than the sun does. 
Which means moonrise relative to sunrise 
is delayed by 44 minutes a day. 
because the moon and sun are in this 
race, it takes the moon a little bit 
longer to complete a full rotation of the 
celestial sphere relative to the sun. 
To come to the same relative position as 
the sun. 
that takes what is called a synodic 
month, which is about 29 and a half days. 
This is the time say, from the moon being 
in alignment with the sun. 
And then the moon, running ahead of the 
sun, and catching up with the sun, 29 
one-half days later. 
As usual this takes a little bit longer 
than the 27 days that it takes the moon 
to complete a sidereal rotation. 
For the same reason that a solar day is 
longer than a sidereal day. 
The difference being more significant 
here because we're talking about a month 
rather than a day. 
now, the position of the moon relative to 
the sun controls two things. 
One is, when during the day it rises and 
sets? 
If the moon is at the same right 
ascension as the sun, then it rises at 
sunrise and sets at sunset because it's 
in the same direction in the sky as the 
sun is. 
Whereas, if the moon say is twelve hours 
away from the sun, it's 180 degrees away 
at right ascension, the moon will rise at 
sunset and set at sunrise. 
So, rising and setting times of the moon 
change throughout the synodic month. 
And, in addition to this of course, the 
moon's appearance in the skies changes. 
It goes through phases, and the best way 
to see this is the following interesting 
simulation. 
The best way to understand, how the 
moon's position relative to the sun gives 
us the phases of the moon is to just do 
it. 
And to just do it, you need a source of 
light. 
You can use a light bulb, or if you 
prefer, you can just use, the sun. 
Just go outside if you can't find a light 
bulb. 
Anything round. 
I have a white styrofoam ball here to 
play the role of the moon. 
And your head, to play the role of Earth. 
the view from your eyes will give you the 
view as seen by people on that side of 
earth facing the moon of what the moon 
looks like. 
And then, you simply turn around to 
perform a complete lunation. 
to give you a sense of what this looks 
like in case you're not going to do it 
yourself, though I strongly recommend it. 
what we have here is a, on the left side 
of the screen you'll see a setup of in 
the studio of me holding a moon and 
turning around in the relative 
configuration. 
Whereas on the right side you'll see the 
image of a gopro camera that's mounted to 
the Moon, so it shows you the image of 
the Moon as I see it. 
When the demonstration begins, the moon 
is, in between the sun and the Earth. 
It's on the line between sun and Earth. 
And so, the illuminated side of the moon, 
as we can see in this beautiful picture, 
faces the sun, 
and therefore, faces away from the Earth. 
I see the dark side of the, the moon. 
And then moon will be nearly invisible. 
As turn to my left to the east. 
slowly, the western side of the moon will 
become illuminated. 
And we'll see a growing crescent, until 
after I've turned 90 degrees. 
We'll see a waxing quarter moon. 
Since the moon is now six hours, or 90 
degrees to the east of the sun, it will 
rise six hours after the sun. 
In other words, the waxing quarter moon 
rises about at noon and sets about at 
midnight. 
As I continue to turn to the, the east, 
the illuminated part of the moon will 
grow and become gibbous until at last, 
when I am twelve hours away from the sun. 
I will see a full round moon illuminated. 
we're going to have to switch cameras at 
some point, to give you the full view, 
because of studio limitations. 
Don't get confused by that. 
Twelve hours to the east to the sun, the 
full moon rises as sunset and sets at 
sunrise. 
And so the full moon is the only moon 
that is really up all night and only 
during the night and you'll note that to 
give us a view of the full moon, I had to 
tilt the moon's orbit I'm holding way 
above my head, we'll get back to that in 
a second. 
As I continue to turn to the east now the 
western part of the moon is losing the 
sunlight. 
I see the eastern part of the moon 
illuminated. 
It is a waning gibbous moon. 
And then when I reach 90 degrees to the 
sun again I have a waning quarter moon. 
The waning quarter moon which is six 
hours to the west of the sun will 
therefore rise six hours before the sun. 
In other words rise about at midnight, 
set about noon. 
This is the moon we see in the morning. 
Finally, as I continue turning to the 
east, the moon becomes closer to the sun 
in the sky. 
only the eastern edge of the moon is 
illuminated. 
I find a waning crescent moon. 
And after a full synodic orbit is passed, 
the moon is back in line with the sun. 
And again, I see only the dark side of 
the moon. 
And we're back to new moon. 
So what I hope you saw and I do encourage 
you to do it yourself. 
It's really fun and you can show it to 
your 
friends and family, 
is that over the course of a senotic 
month as the Moon orbits the Earth 
relative to the Sun the shape of the 
visible part of the Moon changes in the 
sky, 
as well as because of the relative 
position of Moon and Sun the rise time. 
So the New Moon when the Sun and the Moon 
are roughly at the same right ascension 
and the Moon is completely dark in the 
sky rises at sunrise and sets at sunset. 
the waxing quarter moon, when the moon is 
about six hours of right ascension to the 
east of the sun, rises six hours after 
the sun. 
So the waxing quarter moon rises at noon 
and sets around midnight, and is visible 
all afternoon. 
The full moon, where the moon is twelve 
hours of right ascension ahead of the 
sun, 
in other words on the opposite side of 
the sky. 
The full moon is the only time that the 
moon rises at sunset and sets at sunrise. 
And the waning quarter moon, where the 
moon is 
six hours to the west of the sun, or 
eighteen hours to the east, the moon 
being six hours to the west of the sun, 
rises six hours before the sun. 
In other words, rises about at midnight 
and sets about at noon. 
And the waning moon is visible all 
morning. 
So when you see the moon in the daytime, 
you should not be surprised. 
But should you ever see a full moon at 
noon, something has gone terribly wrong, 
so. 
Both the phases and the periodic change 
in moon rise and set times are completely 
understood in terms of this model where 
the moon reflects sunlight and what we 
see depends on the angle between the 
moon, the sun and the earth. 
You can stimulate this, you can go to the 
stimulation page of the University of 
Nebraska Lincoln and get less freedom 
version but I encourage you to construct 
take a light pall and a. 
Ball of some sort and make yourself a 
moon. 
So, this describes the moon's motion and 
the changes in the phase. 
you notice that at new moon and at full 
moon, I had to sort of adjust the moon. 
I was moon, orbiting the moon about my 
head, not in a horizontal orbit but in a 
tilted orbit, so that it went below the 
sun at new moon, and way high above the 
sun at full moon. 
So, this brings up the question of, what 
is the moon's declination? 
Indeed, the moon roughly orbits the Earth 
along the ecliptic. 
But it deviates from the ecliptic by five 
degrees. 
for comparison, the sun and the moon are 
about the same size in the sky. 
And both of them are about half a degree, 
so that the moon is, 
distant from the sun by up to ten times 
their radius. 
And so typically the moon passes well 
below or above the sun when its for 
example a new moon 
And so we have these two circles, now the 
ecliptic and the orbit of the moon around 
the Earth, the tilt between them is five 
degrees. 
The analog of the equinoxes, the hinges 
at which these two circles are hinged, is 
now called the nodes and the line 
connecting them, the line of nodes. 
And so the moon is at most five degrees 
away from the sun, which means among 
other things that as the sun moves north 
and south along the ecliptic, the by 23.5 
degrees in the summer. 
North and 23.5 degrees south in the 
northern winter. 
the moon, which is at most five degrees 
away from the sun pretty much follows the 
ecliptic. 
So the moon too, is higher in the sky in 
the summer, and lower in the sky in the 
winter. 
But. 
It generically is not exactly the same as 
the sun. 
It is only at exactly the same 
declination of the sun when it is along 
the line of nodes, just as the sun is on 
the celestial equator at the equinoxes. 
So twice in each of it's rotations about 
the Earth, the Moon lies along the lines 
of nodes. 
And in that case the Earth, the Sun and 
the Moon are in the same plane. 
Interesting things happen, of course, 
when the moon is in the line of nodes. 
And, it is either full or new. 
Let's see what happens then. 
In our first limation, I kept the moon 
way north, or up in this image from the 
sun when it was full and way south of the 
sun when it was new. 
what we're going to do now is see what 
happens to the full moon when the line of 
nodes is aligned with the direction to 
the sun. 
In other words the moon when it is twelve 
hours away in right ascension from the 
sun, is it exactly the sun's declination. 
And we start our demonstration with the 
waxing gibbous moon. 
And it waxes until it, is becoming full. 
And then, what we see is that, from the 
eastern side of the moon, a fuzzy shadow 
covers the surface of the moon. 
Of course, this is the shadow of my head. 
it would not be as shaggy were it the 
real Earth. 
But this is exactly the geometry for a 
total lunar eclipse. 
The Moon enters the shadow from. 
The west moving east and therefore it 
moves out of the shadow starting with its 
eastern edge first so when you see a 
lunar eclipse take place and then the 
moon uncover you're literally watch the 
moon orbit around the earth. 
About two weeks later or two weeks 
earlier, the Moon is now at the Sun's 
right ascension, we're getting a new Moon 
and the Moon is still at the same 
declination as the Sun and we'll see what 
happens. 
We pick up the story with a waning 
crescent Moon. 
The Moon moves in front of the Sun. 
When it is at the Sun's right ascension 
and declination the Moon in fact is 
obscuring the Sun. 
And remember we are on the day time side 
of the Earth. 
This is mid-day because it is a new Moon, 
we shouldn't be able to see it at all. 
In fact we don't. 
But then we don't see the sun either, we 
get complete darkness, in the middle of 
the day, and as the moon continues to 
move to the east, then we see this weird 
glow on the moon. 
This is an artifact of a shiny Gopro 
camera but even this is instructed. 
The lens of the camera is still eclipsed. 
But the bits of the camera on the right 
hand side are already shining in the 
light. 
And they're, you can see their reflection 
of that off the moon. 
This is what would happen if people 
living a few thousand kilometers to the 
west of you. 
Erected a huge shiny tower on earth, 
during a total solar eclipse, you might 
see the reflections from that shiny tower 
on the surface of the moon. 
And then, as the moon continues to move 
east, the sun is again revealed and it's 
bright mid-day. 
What did the model show us? 
Well, the moon's orbit is tilted five 
degrees with respect to the sun's orbit, 
the ecliptic. 
And so there are two points along the 
moon's orbit at which it is on the 
ecliptic. 
Now, as the sun orbits the earth or the 
earth orbits the sun there's going to be 
two times a year where the direction of 
this line of nodes coincides with the 
direction of the sun because the sun 
makes a complete circle and, at two 
antipodal points along the circle it 
coincides with the line of nodes. 
This gives us twice during an average 
year something called and eclipse season. 
And, the alignment is, need not be 
absolutely perfect because neither the 
sun nor the moon are point like objects. 
But there are two sort of one, one and a 
halve month periods, 
during each year. 
And in those one, one and a half month 
periods, eclipses may occur. 
May occur that is, when the moon is 
either full or new. 
So that it is at the correct part of its 
orbit, 
at the right ascension, either of the sun 
or opposite that of the sun, 
and now at the right declination. 
So twice a year we have an eclipse 
season. 
And during an eclipse season, you have 
usually between two or three eclipses. 
One of one kind and flanking it two weeks 
on either side. 
Two of the other kind. 
So you could can have a solar eclipse 
flanked by two lunar eclipses. 
Or a lunar eclipse flanked by two solar 
eclipses by the time, the next eclipse of 
either type would have occurred the next 
new moon for example. 
the sun is now to far from the line of 
nodes and you no longer get an eclipse. 
So typically no more than three per 
season and this should happen twice per 
year. 
In fact like everything else that is 
tilted the line of nodes wobbles. 
In other words the tilt between. 
The moons orbit and the ecliptic is 
always five degrees but its orientation 
wobbles and as is with the case with the 
earth it actually wobbles to the west 
Because it is orbiting to the east and so 
the two persesses to the west very slowly 
to the west once every eighteen point six 
years or so and this just means the 
eclipse year the year during which two 
eclipse seasons happen. 
is a little bit shorter than the full 
orbital year of the Earth. 
Only 346.6 days. 
And so, during each of those two eclipse 
seasons a newer full Moon might lead to a 
solar or a lunar eclipse. 
so new moon during eclipse season means 
the moon is in front of the Sun and at 
the right declination so you can have a 
solar eclipse. 
A full moon means the. 
Earth is between the moon and the sun, 
and the Earth's shadow will obscure the 
moon, just as my shaggy head obscured the 
moon in our model. 
Now, we need to get a handle on the 
relative sizes and distances of things to 
understand the difference of the two 
phenomena. 
So, the moon and the sun are almost 
precisely the same size, in angular 
terms, in the sky. 
If you think about it, the sun is much 
larger than the moon. 
From our small angular proximation, we 
know that it is much farther. 
The ratio of their sizes is almost 
precisely the ratio of their distances. 
So that both the moon and the sun appear 
in the sky to be about the same size. 
An interesting coincidence. 
What this allows is, when you have 
perfect alignment during new moon, the 
moon is able to completely obscure the 
sun. 
When you superpose two discs of the exact 
same size in the sky. 
But this requires perfect alignment. 
So perfect, that in fact, it will only 
obtain for a small region on Earth, if 
you move a little bit away from that 
region on Earth. 
Then the alignment is no longer perfect. 
The alignment is only perfect at one 
point on Earth. 
And when I say one point, I mean, a 
region on Earth, 
whose size is up to about 250 kilometers, 
that's a very small part of a planet with 
a radius of 6400 kilometers. 
And in that region where the moon's 
shadow completely obscures the sun, you 
get what is called a total eclipse. 
And we have here a beautiful time series 
of a a total eclipse. 
Notice that as time progresses in this, 
the moon seems to obscure the sun from 
the left. 
Whereas in mine, and then leave the sun 
to the right, whereas in my model, this 
was happening the other way around. 
The reason is that this eclipse in 2001 
was observed near Zimbabwe, and, near 
Zimbabwe, you're in the southern 
hemisphere, which means, east and west 
are still the same, but looking, since 
the sun is, now to your north, 
The, the moon entering the sun from the 
west moving to the east is now from the 
left to the right. 
So north to the southern hemisphere 
viewers this time it makes sense to you. 
The moon is coming from the west to the 
east across the surface of the sun, it 
obscures the sun completely for a few 
minutes and then. 
Is seen to move away and what we're 
watching again is the moon orbiting the 
earth although also this place Zimbabwe 
is being moved along the surface of the 
earth by the earth's west to east 
rotation and moves out of the shadow as 
we'll see in a moment and 
noteworthy, when the moon completely 
obscures the sun, 
a region around the sun that appeared 
completely dark before, is suddenly seen 
to be 
brilliantly luminous. 
This is called the corona, the crown of 
the sun. 
It is not visible when, we see the, the, 
the, the sun itself, or the sun's disc, 
because the sun's disc is so bright that 
it blinds us to the, brilliants of the 
corona. 
But once you obscure the sun's disc, you 
can see that the region around the sun's 
disk is illuminated when we talk about 
the sun, we'll try to understand what 
this glowing crown is and how to observe 
it away from eclipses. 
A more common phenomenon than this 
beautiful totality is when the new moon 
occurs, the line of nodes are not exactly 
aligned with the sun and so the moon is a 
little bit south or a little bit north of 
the sun, and then the moon would have 
passed below or above the sun. 
Above if it were south since we're in the 
southern hemisphere, and below, if north, 
or the other way in the northern 
hemisphere. 
And then you will find a partial eclipse 
where not the full surface of the sun is 
obscured. 
But only, some fraction thereof. 
And this is far more common, because it 
requires a less sensitive alignment to 
give you a sense of, 
what the, the shadow of the moon on the 
earth looks like. 
here's a beautiful image taken from the 
Mir spacecraft on August eleventh, 1999. 
And, this is an image of earth, 
and what we're seeing on Earth is the 
moons shadow. 
So, the moon's shadow as I said, obscures 
the, the moon can obscure the entire sun 
in this inner circle of a radius of about 
250 kilometers, up away, we see this 
partial shadow. 
These are regions where if you look up, 
you can see part of the sun, but, some 
fraction of the sun is obscured by the 
moon. 
You can see around it a little bit, and, 
so, this is called the Penumbra or 
Partial Shadow. 
People here see a total eclipse, people 
here see a partial eclipse. 
And, now remember, that underneath. 
This, shadow. 
This earth is rotating so that this 
shadow is effectively moving along the 
earth at some 1000 kilometers per hour 
and so each, individual location only 
gets a short period of totality. 
Now. 
This is what happens if alignment is 
perfect and if the moon and the sun are 
indeed exactly the same size in the sky. 
How can they change? 
Does the moon shrink? 
No, but the moon's orbit around the earth 
is not completely circular. 
The moon is sometimes a little closer to 
earth, and sometimes a little farther, 
when. 
Complete alignment occurs and the moon is 
on the. 
Farther part of its orbit, it's just a 
bit farther from Earth. 
Since its size didn't change, its 
apparent size in the sky is a little bit 
smaller. 
it's then smaller than the sun in the 
sky. 
And we get what is called an annular, 
annular eclipse. 
because you seen an annulus of sun, a 
ring of sun surrounding the moon. 
This shadow here is the moon. 
We see some of the, 
corona, and even some of the chromosphere 
around the sun but what we also see here 
is a little bit of a disc of the sun, the 
photosphere as it's called and the moon 
not completely obscuring it in this 
beautiful image of an annular solar 
eclipse. 
This is what happens when alignment, 
during eclipse season occurs at new moon. 
During full moon, what happens is that 
the earths shadow prevents sunlight from 
hitting the moon and the moon becomes 
dark. 
The moon as I said, is moving to the 
east, it enters earth's shadow from the 
west. 
Again, the eclipse can be total or 
partial and 
Depending on the quality of the 
alignment. 
And, you can get a penumbral eclipse, 
where the moon is only in partial shadow. 
In other words, where, from the moon, you 
can see some part of the sun. 
But, some of the sunlight is blocked by 
the Earth. 
Just as pieces of the Earth were in 
partial moonshadow. 
then the moon just slightly dims. 
It's kind of hard to even notice it. 
But when you get a total eclipse, 
when some part of the moon's surface is 
completely obscured from the sun, 
then this is the beautiful image you see. 
Now this, I'm not sure, surprise you. 
I mean, perhaps some sunlight is reaching 
over here. 
Maybe I didn't time this photo to precise 
totality. 
But where is the light coming from that 
allows us to see the moon this side of 
the moon at all. 
This side of the moon is, in fact, in 
total Earth shadow, you cannot see 
sun, the sun, from this area of the moon. 
What you can see in the sky is a bright, 
glowing Earth. 
Remember, the Earth is bigger than the 
moon, so it, handily obscures the sun. 
It's much easier to arrange a total lunar 
eclipse than a total solar eclipse. 
And also, a solar eclipse, a lunar 
eclipse, when it occurs, is visible, 
since the moon is dark, to anybody on 
Earth who can see the moon. 
So whenever it occurs during your 
nighttime, you can see the moon eclipse. 
It's a far less delicate arrangement than 
the solar eclipse which only blocks out 
the sun for a small fraction of the 
earth. 
but the source of this red illumination 
of the moon. 
the answer is here on the slide. 
Comes from light defracting through 
Earth's atmosphere. 
Why light defracting through the Earth's 
atmosphere would give the moon this 
famous wine red color is something we'll 
have to investigate. 
This is a picture actually taken at our 
observatory, in the, solstice eclipse of, 
December 2010. 
And so, this is 
Pretty image and lunar eclipses are 
easier to find and observe. 
I encourage you to enjoy them. 
A few more fun facts about the moon, 
while we're discussing the moon. 
So two well known 
things that people appear to observe. 
One is that when you see the moon rising 
or setting, it's near the horizon, it 
appears larger. 
This, it turns out, is a psychological 
illusion. 
Taking pictures of the moon with a 
camera, you can measure its angular size. 
And in fact, if anything, the strange 
optical effects make it appear a little 
bit smaller in the sky near the horizon. 
But there are various psychological 
theories, near, the comparison to other 
objects nearby, angular corrections. 
I'm not an expert on the psychology. 
But, it does appear to us that the rising 
full moon seems huge when it's on the 
horizon, and small when it's high in the 
sky. 
But, this is completely in our heads. 
On the other hand, there is this other 
famous illusion, where, which is called 
seeing the old moon in the new moon's 
arms. 
Which is, that when you see a crescent 
moon, 
where only a fraction of the moon is 
illuminated, then you can sometimes 
imagine to yourself that your mind 
completes the full disk of the moon, and 
you can see the part of the moon that is 
not illuminated by sunlight. 
And, 
this one is a physical effect. 
Here's a camera capturing it. 
Here's the illuminated side of the moon, 
so the sun is down that way. 
This side of the moon is dark, sunlight 
cannot reach it, and yet I see it, so 
there's sunlight hitting it, and there is 
a reason, of course, is that when the 
moon is a crescent, 
if you are on the moon, 
set up the configuration in your head, 
you would see that there would be a full 
Earth in the sky. 
And viewing the, the full Earth in the 
lunar sky means that there is bright 
Earth light illuminating the moon. 
So the light that is hitting the moon, by 
which we are seeing this moon is Earth 
light, in other words light that was 
emitted by the sun, reflected by the 
earth, 
hit the moon, reflected off the moon and 
came in the appeture of this camera. 
So the fact that you can see the dark 
part of the moon as a crescent is not 
psychological, it is true. 
You can only see this when the moon is a 
crescent basically because once the moon 
becomes too bright, it blinds us, it 
dazzles us and we can't see this. 
Also, 
the larger the illuminated part of the 
moon, the less of the face of the Earth 
is illuminated. 
Of course, when we have a full moon, then 
people on the moon would see a new Earth. 
The phases are complementary. 
And so for both of those reasons, we only 
see this when the moon is a crescent. 
So we've made some progress in 
understanding astronomical phenomenon. 
The way they change periodically. 
We've got the sun, we've got the moon. 
Let us close this discussion with some 
interesting relations between astronomy 
and time keeping. 
I've told you that units of time kept 
being defined in terms of the Earth's 
rotation and orbit. 
This is not a coincidence. 
We want our time to match what's going 
on. 
We want. 
Six a.m. 
On our clock to be solar sunrise, because 
that's the time we go out and plant, 
things, work in our fields. 
And so, our 24 hour days are adjusted to 
be the mean solar day. 
Are months that, twelve months into which 
we traditionally divide the year, are 
approximately lunar. 
the synodic lunar month is 29 and a half 
days. 
Our months are a bit longer than that. 
But, and this allows for the rare 
phenomenon of two full moons. 
Falling in the same month, which is what, 
colloquially, is called a blue moon. 
It's a rare phenomenon. 
It requires a full moon right at the 
beginning of the month, but it does 
happen. 
Our definition of a year is designed to 
match the orbit. 
A year is 365 days. 
the Earth, orbits the sun once. 
every 365.2564 days, a little over a 
quarter of a day, 
This is sidereal orbit, in other words, 
this is the time that it takes the Earth 
to return to the same position in the sky 
relative to the sun, or the time it takes 
the sun to return to the same position in 
our sky, relative to the stars. 
Hence, sidereal orbit. 
The first thing we observe is, that the 
year is not, unfortunately, an integral 
number of days. 
This is a problem. 
It means that, 
Since we, our days turn over every 24 
hours, that every four years 
You're timekeeping if you have a 365 day 
year. 
Then every four years, you are off by a 
day relative to the Earth's orbit. 
So who cares? 
Well, accumulate those days for 180 
intervals of four years. 
And now, you are off by 180 days which is 
half a year which means that now January 
corresponds to northern summer. 
This is very inconvenient if you're 
trying to plan agriculture and we have a 
solution to this, right, this was 
discovered by Julius Caesar, or in his 
time, and it was his legislation that 
added leap years. 
Once every four years we add another day, 
making that year 366 days long. 
The average year is now 365 and a quarter 
days long, and now we never drift more 
than a day off from having our orbit 
match our calender. 
However, this is not completely precise 
enough. 
In fact what we want our calendar to 
match is the seasons. 
The seasons have to do with the relation 
between the earth's position relative to 
the Sun and not the stars, but the 
direction of the tilt of the celestial 
north pole or the terrestrial north pole. 
And remember that, that wobbles 
to the west, 
rather than to the east. 
So a, a complete rotation. 
Where, between solstice and solstice, or 
equinox and equinox, is a little bit 
shorter than the sidereal year, rather 
than longer. 
This is called the tropical orbit. 
The mean time between solstice and 
solstice is 365.2422 days. 
Remember that the precession is very 
slow, takes 26,000 years. So it's not a 
big effect over a year, but it does make 
the mean tropical year a bit shorter than 
365.25 days. 
This was understood in the sixteenth 
century and led to the correction from 
the Julian to the Gregorian calendar, 
correcting for the deviation between 
0.2422 and 0.25 required removing some of 
the leap years. 
That is why on 
Centuries that are not millennia, in 
other words years whose number divides 
100 but not 1,000, we do not add a leap 
year. 
We do not add a 29th day to February, 
those years are only 365 days long. 
The average year is a little bit less 
than 365 and a quarter days long. 
In fact it's close enough to this number 
on average that it will be a millennium 
before we have to make another 
correction. 
And so we definitely use astronomical 
phenomena to adjust our clocks and our 
calendars, not for any silly reason but 
because astronomical phenomena govern our 
life, 
and we need our, timekeeping to match 
that. 
It's quite an elaborate universe we're 
starting to build around us. 
We have the celestial sphere where the 
stars are fixed. 
we have a solar sphere that rotates 
relative to the celestial sphere about 
this tilted axis. 
So that the sun can move along the 
ecliptic. 
We have a lunar sphere tilted relative to 
the ecliptic around which the moon moves 
a little bit faster. 
Moreover, all these, tilted trajectories 
are also wobbling to the west, one very 
slowly, every 26,000 years. 
The moon's a little bit faster, every 2.6 
years. 
This is very elaborate, but it does 
explain everything we see. 
The alternations of day and night, the 
phases of the moon, eclipses, seasons. 
Almost everything. 
Let's go to Athens and see what we might 
have been missing. 
We're back to our favorite picture of the 
sky in Athens. 
And I've allowed the software to show us 
the ecliptic and we see the 23.5 degree 
tilt, relative to the celestial equator. 
We the, see the intersection of the 
ecliptic and the equator here at the 
prime meridian in Pisces. 
We still live in the age of Pisces and 
We see that the part of the ecliptic 
that's visible at night is mostly the 
part north of the equator. 
That's reasonable because, end of 
November, the sun is well south of the 
equator. 
The part of the ecliptic that lies south 
of the equator is what we see during the 
day. 
So far, so good. 
the other thing you'll notice. 
And I'm sure if you, tried to run your 
own simulation. 
And certainly, if you went outdoors, 
you will have realized by now that I 
fudged. 
I suppressed some things in the 
simulations I've been showing. 
In particular, the two brightest objects 
in the sky were omitted from my 
discussion up to now. 
One of these, the brightest of them is 
this waning gibbous moon, 
which we see here. 
A waning gibbous moon, remember, 
is a moon that is 
past full. 
And so, it rises after sunset, 
and at 9:00 p.m., we're still seeing it 
in the eastern sky, so we expected that. 
the moon happens to lie very close to the 
ecliptic right now. 
It could have deviated, remember, by as 
much as five degrees. 
we also have, the next brightest object 
in the sky is the beautiful planet, 
Jupiter. 
and we have not brought up planets. 
And once we allow that, we see that 
scattered along this ecliptic are a few 
others, non-star objects, 
Neptune, Uranus, and the asteroid, Ceres. 
And, if we look at this image over time. 
We would notice that, like the moon and 
the sun, the planets move as well, 
which means we're going to have to start 
next week by adding even more moving 
parts to our universe, and 
enriching what we know, 
and eventually leading us to a much, much 
deeper understanding.