a solar eclipse is an absolute delight
to behold and so i'm going to show you
the mathematics behind how we can
predict when they're going to happen
i'm recording this before the 2015
eclipse
but don't worry the information I'm
giving you now remain valid for at least
the next nine hundred and eighty-five
years
as you may have noticed the moon is not
transparent
this means that blocks the light from
the Sun and it casts a shadow occasion
that shadow moves across the earth and
if you're standing with a shadow fall's
your witness a total solar eclipse from
our point of view
the moon has moved in front of the Sun
and completely blocked its light for a
solar eclipse to work though
the moon has to be big enough to block
out the Sun and believe me this diagram
is not to scale
in reality the moon is 400 times smaller
than the Sun but in a fantastic cosmic
coincidence
it's approximately three hundred and
eighty nine times close-up on average
and that's close enough
it means from our point of view the moon
is almost exactly the same size as the
Sun in the sky
this means it will line up and it will
completely block the disc of the Sun if
the moon with any smaller or any further
away
it wouldn't be big enough from my point
of view to cause total solar eclipses
but of course it could be bigger and it
could be closer and would still get
eclipses but fantastically because the
apparent size of the moon matches
exactly the apparent size of the sun's
photosphere the bright surface of the
sun it blocked out the bulk of the light
from the Sun but it doesn't block the
Sun Thank atmosphere as you can see from
this photograph taken in a total solar
eclipse the Sun has a very faint
atmosphere with fantastic structure in
it this is normally swamped by all the
photons coming from the rest of the Sun
only because our eclipses line up so
well
do we ever get to see it we are
incredibly lucky that from our point of
view the size of the moon matches
exactly the size of the Sun
I mean the probability of that happening
is literally astronomical
it may look like the Sun the Moon move
around randomly in the sky but that's
not the case
eclipses occur based on the some
earth-moon system the earth orbits
around the sum and the moon orbits
around the earth and its when those two
orbits come into alignment and bring the
moon between the Sun and the earth that
we get a solar eclipse
although i should point out of course
once again that diagram was in no way to
scare in fact there's pretty much
nothing in this video
that's to scale to illustrate what
happens during a solar eclipse here i
have the earth and you're going to be
the Sun so your line of sight of the
rays of sunlight coming out of your face
or whichever part of your body you shoot
the Sun shines out of and then it hits
the earth except of course when the moon
gets in the white as it orbits around
the earth
it causes eclipses and the moon orbits
the earth every 29.5 3059 days and so
there you have it
this is why we get a solar eclipse every
29 days 12 hours 44 minutes and three
seconds
unfortunately it's not that simple of
course physics isn't that simple
there's actually more than one type of
lunar month poor exactly the same orbit
so for a start
the moon doesn't go around the earth in
a circle actually follows an ellipse
which means at different points
the moon is different distances from the
plant and its closest point it's 360
3396 kilometers away from the earth and
its greatest distance its 405,000 504
now the month i mentioned before the
29.5 three days
that's the time the moon takes to be
from the point where its closest to the
Sun back to being closest to the Sun
again a different month is 27.5 five
days and that's the time the moon takes
from being at the closest point to the
earth back to being at the closest point
to the earth and the difference there is
almost two days and the reason for that
two day discrepancy is because the
elliptical shape orbit
during the movies 21.5 five-day lap
around the earth the earth hasn't stood
still
it's orbiting the Sun it will have gone
for about 30 degrees of its orbit which
means even though the moon is back at
the same point relative to the earth
it's no longer the same point relative
to the Sun it has to go a little bit
further to go between Sun and the earth
once more and that's where the expert
two days comes from but it's not always
the same amount of time because the
moon's elliptical orbit tracks with the
earth
the direction is pointing changes
relative to the Sun so different points
in the year it takes more or less time
for the moon to once again go between
the Sun and the earth that time I gave
you before the 29.5 three days
that's just an average but it's okay we
can factor this all in we can do the
calculations on the elliptical orbit of
the moon as the earth goes around the
Sun and we can calculate how often the
moon goes between the Sun and the earth
unfortunately it's not that simple yep
there was a third type of lunar month so
you're the son here we have the earth
the earth is orbiting around you in a
fixed plane
the man however orbits around the earth
in a different plane
its orbit is tilted at 5.1 degrees from
the earth orbit around the sun and this
is why we don't get an eclipse every
single month
the moon has to both be going between
the Earth and the Sun as well as either
going down through the Earth's all that
or coming back up again and that is our
third type of lunar month
the amount of time between the moon
going down through the Earth's orbit
- when we get back to the same . and
there is 27 . - 12 21 days the shortest
month yet and this explains why eclipses
are so rare we only get just over to a
year in fact we average 238 solar
eclipses per century but now we've got
everything sorted we can calculate when
they are unfortunately it's not that
simple
remember them
and elliptical orbit around the Earth
but that doesn't stay still
either it actually drift by 40 points 7
degrees every year so it rotates once
every eight point eight five years
yes the moon's orbit orbits and so the
two points where it crosses the earth or
but drift around the earth over the
course of eight point eight five years
and only when the moon goes between the
Earth and the Sun while one of these
nodal points is also between the Earth
and the Sun will we get a solar eclipse
unfortunately it's not that simple
any second now unfortunately it's not
that simple
there's so much more to take into
account the Earth's orbit of course
that's not a circle
it's no lips as well and a lip that also
moves it rotates once every 20 and a
half thousand years and the u.s. gravity
is a nice and tidy all know
for a start the earth is in a perfect
sphere it's an oblate spheroid on top of
that it's covered in water and the title
drag messes with everything and then
there's the gravity between the moon and
the Sun so far already take into account
the gravity between the Sun and the year
and then separately between the Earth
and the moon but of course it's a
gravitational pull between the moon and
the Sun in fact the mutual gravitational
attraction between the Sun and the moon
is over twice that between the Earth and
the moon
the direction the moon is traveling
relative to the Sun makes a big
difference on its speed and that is
constantly changing in fact every single
number i have given you in this video
every direction every speed every angle
every time they're all only
approximations their averages the whole
system is constantly changing it is a
wonder we have eclipses at all
what this means is we can't make any
meaningful proper long-term predictions
about solar eclipses but for the
reasonably near future we can and NASA
have gone through all of the years
between negative 1999 and positive three
thousand they have analyzed all 60 1841
lunar months that's from New Moon to New
Moon and they've checked all eleven
thousand eight hundred and ninety-eight
eclipses and put all the data up on
their website but to the undrained I
just watching it happening
we're back to a random movement of the
Sun and the moon in the sky and
occasionally they happen to cross but
then out of all this chaos
another cosmic coincidence steps forward
to save the date
just like the moon's apparent size
happens to match the sun's apparent size
there is one special combination of the
three different types of Luna
and that happens to line up perfectly
if you take 220 three new moon months so
from closest to the Sun the closest to
the Sun and you compare that to 239 of
the month between the closest point of
the earth to the closest point of the
earth and then you compare those two 242
of the months between when the moon goes
through the Earth's orbit back to win
our next goes through the earth orbit
all three of those are pretty much
exactly the same length of time they all
come out spot on 18 years 11 days and
eight hours
and so it means if out of all this
random movement you somehow have a solar
eclipse
you know that 18 years 11 days and eight
hours later we will have had an integer
number of all the different types of
months in bold and so we will return to
pretty much exactly the same geometry
there will be another very similar
eclipse 18 years 11 days and eight hours
later
it's called the sarah cycle and allows
us to predict when eclipses are going to
happen in the reasonably near future
except of course unfortunately it's not
that simple
thanks you're welcome
in 2009 july twenty second i was lucky
enough to witness the total solar
eclipse when the moon shadow came across
the Pacific Ocean through Japan across
mainland China and then out through
India because of the Saros cycle
I know I can enjoy the next equivalent
to clips in 18 years 11 days and eight
hours time and it will look like this in
the year 2000 27 on august second
except those eight hours are about a
third of the day and so the Earth's
rotation won't line up everything else
will
but the earth will have spun about
another third of a rotation so the
eclipse will actually happen over here
and then another Sarah cycle later in
2045 on august 12
it will be another third of a rotation
across and it will go through America
and this cycle can also be worked
backwards before the 2009 eclipse is one
in 1991 then 1973 1955 1937 1919 and
1901 you notice that over time the
eclipses are actually working their way
up the planet and that is because of the
slight mismatch of the Saros cycle with
the rotation of the moon's an elliptical
orbit around the Earth and it means that
the eclipses gradually drift further and
further north
this particular Sarah cycle Sarah cycle
136 actually began on the fourteenth of
june in the year 1360 on that day there
was an eclipse right down near the South
Pole is now gradually been working its
way up across the planet and the very
last one will occur on the thirtieth of
july in the year two thousand six
hundred and twenty-two right up at the
North Pole
there are currently 41 active Sarah
cycles working their way up or down the
planet
so there you have it the maths and solar
eclipses is an absolute mess because
orbits are really complex
cated however we do know solar eclipses
are amazing to watch if you can go and
see one do of course be safe and don't
blind yourself
and bear in mind that they're not gonna
be around forever partly because the
moon is gradually moving further away
because of that title drag actually
drifts about 3.7 centimeters throw away
from the earth every year which means it
about point six billion years it will be
too far away to cast a shadow on our
planet but apart from that we have no
idea what the orbits will be like that
far in the future according to our best
simulations in the next five billion
years
there's a one-percent chance that
mercury will leave its orbit and either
crash into Venus or the Sun in fact
there was a nonzero chance that in three
point three six billion years the
gravitational force from Jupiter were
not mercury out of its orbit in turn
will impact on Mars that within slam
into the earth
so you know enjoy eclipses while you can
for more math behind solar eclipses and
all sorts of diagrams and calculations
and plots and things that I can possibly
fit in this video's google checkout
NASA's five millennium canon of solar
eclipses i'll put a link to it in the
comments below is based on the fantastic
work of thread s been ax and genius
where you just want to see more videos
of me talking about math
some of them a lot shorter and there's
much more mathematically certain then
just click on the move
that's now orbiting me
yeah
