00:00:00
hi welcome to astro 101 the sun and it's
00:00:02
neighbors
00:00:03
this is already class seven in today's
00:00:06
class we're going to be looking at one
00:00:07
of the most
00:00:08
challenging topics that we cover all
00:00:10
semester in fact
00:00:11
today's lecture and the one before us
00:00:13
really are the
00:00:15
kind of the hardest things to understand
00:00:16
i think we're going to be able to do it
00:00:18
um if we if we pay attention and while
00:00:21
they're
00:00:22
challenging it's they're also really
00:00:24
cool the fact that there's these things
00:00:26
that we see in the world
00:00:27
that we can actually understand to
00:00:29
introduce today's topic i've got a
00:00:31
special guest
00:00:32
ah sofia hey dad good morning hey guys
00:00:35
so i'm here at crescent beach it is one
00:00:39
or i guess just after two o'clock and it
00:00:40
is currently low tide
00:00:42
hello so i'm here at crescent beach at
00:00:45
about 7 30 a.m and as you can see it is
00:00:48
currently high tide
00:00:50
so i guess uh you'll be here later this
00:00:53
afternoon
00:00:53
so you say alrighty then bye guys all
00:00:56
right well i gotta go
00:00:58
um bye sophia
00:01:01
all right that's very cool um sophia
00:01:03
left us
00:01:04
with this really interesting video of
00:01:08
um crescent beach
00:01:11
at low tide and at high tide
00:01:14
at low tide you can see the water is way
00:01:16
out there and all this
00:01:18
is basically dry whereas at high tide
00:01:20
the waters come in and this is all
00:01:23
flooded in fact in crescent beach
00:01:26
the water levels rise by a couple of
00:01:28
meters and so the water level comes from
00:01:31
out there all the way
00:01:32
in and we can see this difference
00:01:34
between high tide
00:01:36
and low tide and we you can look up
00:01:38
online these tables that tell you when
00:01:40
it's going to be high tide when it's
00:01:41
going to be low tide
00:01:42
but it took a very long time
00:01:45
to figure out what is it that causes
00:01:48
this phenomena
00:01:49
where the water level is way out here at
00:01:50
low tide way in here
00:01:52
just half a half a day later um
00:01:56
or quarter day later six six hours later
00:01:58
at high tide
00:01:59
um galileo who we've talked about before
00:02:03
thought he had an under an explanation
00:02:05
he thought it was because of the
00:02:07
motion of the earth as this moon moved
00:02:10
around the earth
00:02:11
would cause the oceans to slosh around
00:02:13
and he was convinced this is a great
00:02:15
evidence
00:02:15
for the fact the moon orbited the earth
00:02:20
no that's not the case that is not what
00:02:21
causes tides today we're going to find
00:02:23
out
00:02:24
let's but before we do that we need to
00:02:26
go and go ahead and review
00:02:29
what we covered last class that was a
00:02:30
long class lots of difficult ideas
00:02:33
let's review them again just to make
00:02:35
sure we see what's going on is to start
00:02:37
with newton's
00:02:38
first law now newton's first law
00:02:41
says if we recollect an object in motion
00:02:46
remains in motion unless acted upon by
00:02:48
an outside force
00:02:50
in other words if something is moving it
00:02:52
stays moving
00:02:53
in the same direction at the same speed
00:02:56
unless you apply a force to it
00:02:58
that's newton's first law so in the
00:03:00
picture here we have the
00:03:01
figure skater and he is sliding along
00:03:03
the ice in his very low friction skates
00:03:05
and he will just keep on moving
00:03:07
not speeding up not slowing down unless
00:03:10
a force is applied to him newton's first
00:03:13
law
00:03:13
if it's moving it stays moving if it
00:03:16
changes direction or speed
00:03:18
it's because there is a force applied to
00:03:20
it which brings us to newton's
00:03:21
second law newton's second law says
00:03:24
something accelerates or something
00:03:26
changes speed
00:03:28
if there's a force applied to it the
00:03:29
larger the force
00:03:31
the more quickly the speed changes
00:03:35
newton's second law also says that the
00:03:38
heavier something is
00:03:39
the less quickly it accelerates so we
00:03:42
have the picture here of the little boy
00:03:43
pushing grammar
00:03:45
small force um relatively large mass
00:03:48
therefore
00:03:49
not a very quick acceleration if you
00:03:51
switch it around put the boy in the cart
00:03:53
and grandma pushes then it'll accelerate
00:03:54
quite quickly
00:03:55
so more force more acceleration
00:03:59
more mass less acceleration because in
00:04:01
the equation here
00:04:02
the force is divided by the mass the
00:04:04
bigger the mass the less the
00:04:06
acceleration
00:04:07
nothing accelerates unless you apply a
00:04:09
force
00:04:11
okay excellent newton's second law
00:04:14
so we looked at some examples of that um
00:04:17
you know
00:04:17
this example here is something is
00:04:18
pushing something so you can imagine
00:04:21
um you know the engine in your car
00:04:23
turning the wheels and making the car
00:04:24
speed up
00:04:27
speeding up is a form of acceleration
00:04:28
but remember also changing direction
00:04:31
is a form of acceleration remember
00:04:33
velocity
00:04:34
is speed and direction combined together
00:04:37
into one thing
00:04:39
acceleration is change in velocity so a
00:04:42
change
00:04:42
in the speed or the change in direction
00:04:45
or both
00:04:46
which brought us to this little demo
00:04:47
here where my beautiful wife spins
00:04:49
uh a ball on a string over her head and
00:04:53
the ball goes in a circle
00:04:55
because the string is applying a force
00:04:58
to the ball
00:04:59
the string causes the ball to accelerate
00:05:02
into a circle
00:05:03
and so we see that here the string is
00:05:04
applying a force to the ball but then
00:05:06
when she lets go of the string the
00:05:07
string no longer applying a force the
00:05:09
ball just travels in a straight line
00:05:10
into the trees
00:05:12
kerfump okay so
00:05:17
newton's second law
00:05:21
a force causes acceleration the speed
00:05:25
and the direction
00:05:26
never change unless you apply a force if
00:05:28
you apply a force then the speed or the
00:05:30
direction can change with no force
00:05:32
it'll travel in a straight line neither
00:05:34
speeding up nor slowing down
00:05:36
okay so newton's third law
00:05:39
for every force there is always an equal
00:05:42
equal an opposite
00:05:43
reaction force so if you push on
00:05:45
something it pushes back
00:05:47
we talked about the astronaut out in
00:05:48
space who pushes against her
00:05:50
spacecraft she moves away from the
00:05:52
spacecraft but at the same time the
00:05:53
spacecraft moves away from her
00:05:55
because she is lighter she moves faster
00:05:57
because the spacecraft is heavier it
00:05:58
moves slower
00:05:59
but every time you push something on
00:06:01
something it pushes back
00:06:03
to every force there was always an equal
00:06:05
and opposite
00:06:07
reaction force newton's third law
00:06:10
so we took these three laws
00:06:14
and we tried to understand from them how
00:06:16
we can understand the behavior of
00:06:18
objects in the solar system so we looked
00:06:21
at this um i had this little story here
00:06:22
we have
00:06:23
we launched a satellite at 33 000
00:06:25
kilometers per second
00:06:26
from 500 kilometers above the surface of
00:06:28
the earth to see what happens and the
00:06:29
answer is
00:06:30
it goes out and it goes it follows
00:06:34
an elliptical orbit the shape that it's
00:06:36
following it turns out
00:06:37
is an ellipse and it speeds up when it
00:06:40
gets close to the earth
00:06:42
and then slows down again as it gets
00:06:43
further away
00:06:45
the center of the earth is at one focus
00:06:47
of the ellipse and there's another focus
00:06:48
of the ellipse out here
00:06:51
why is an ellipse that's a
00:06:54
weird question let's let's first try to
00:06:56
understand
00:06:57
how i did the simulation what did i do
00:07:01
to make the simulation work well what i
00:07:03
did is i took
00:07:04
first of all newton's law of gravitation
00:07:07
a force equals the mass of the first
00:07:11
object
00:07:12
the earth times the mass of the second
00:07:14
object my
00:07:15
satellite divided by the distance
00:07:18
squared
00:07:18
times this little number g and then we
00:07:22
say
00:07:22
in this thing so f is the force
00:07:26
m is the mass there's mass of the first
00:07:28
object mass of the second object
00:07:30
r is the distance between them between
00:07:33
the center of the satellite and the
00:07:34
center of the earth
00:07:36
and a is acceleration the change in
00:07:40
velocity and then so i take this law
00:07:43
and i then add to it newton's second law
00:07:45
of motion
00:07:46
which says a the change in velocity
00:07:49
is equal to the force divided by the
00:07:51
mass the mass of the
00:07:53
um satellite now something i want to
00:07:58
yeah okay something i'll actually want
00:08:00
to look at right now before we continue
00:08:02
with this
00:08:02
remember last class i dropped the hammer
00:08:05
and it accelerated downwards and
00:08:06
accelerated downwards at 10 meters per
00:08:08
second
00:08:08
per second and that i said that except
00:08:12
for air resistance anything you drop
00:08:14
will accelerate that quickly that's at
00:08:17
first kind of a weird idea because you
00:08:18
would say well look
00:08:19
the heavier the hammer is the larger the
00:08:22
force
00:08:23
so a larger force should make a bigger
00:08:25
acceleration
00:08:26
yes but we're dividing it by the mass of
00:08:30
the hammer
00:08:32
so a bigger mass of the hammer makes a
00:08:34
smaller acceleration and in fact
00:08:36
the mass in the force exactly cancels
00:08:38
the mass in the acceleration
00:08:40
and so the acceleration does not depend
00:08:42
on the mass of the object that's kind of
00:08:43
cool
00:08:44
that that's really actually that's
00:08:47
actually really neat
00:08:49
well there it is okay so the fact that
00:08:51
everything falls at the same speed
00:08:52
ignoring every spare friction
00:08:54
is a natural consequence of the force of
00:08:57
gravity
00:08:57
and newton's second law okay anyway
00:09:00
going back to our orbit
00:09:02
we have the object which is a force
00:09:05
being applied on the object that equals
00:09:08
g the tiny number
00:09:09
times the mass of the earth times the
00:09:12
mass
00:09:13
of the satellite divided by the distance
00:09:15
between them
00:09:16
between the centers squared okay
00:09:19
i calculate that and then i say the
00:09:22
speed will change
00:09:24
by each time step the speed will change
00:09:27
by
00:09:28
the force sorry the velocity not the
00:09:30
speed the velocity will change
00:09:32
but the force divided by the mass so i
00:09:35
can take my particle and i say okay it's
00:09:36
going in this direction
00:09:37
so each time step i'll move it forward
00:09:40
by however however fast it's going
00:09:43
and then i will change the speed by
00:09:45
whatever the acceleration is
00:09:46
and then go to the next time step and
00:09:49
recalculate
00:09:50
so we have the force from gravity
00:09:54
pulling it this way we have the speed
00:09:56
going that way i move it forward in time
00:09:58
to the next place
00:09:59
because it's going this direction i move
00:10:00
it this direction and then i change the
00:10:02
speed
00:10:03
by by this equation change the velocity
00:10:06
by this equation not to speed
00:10:08
and then and then and then step on so
00:10:10
let's see how this goes
00:10:11
we go into the future later on we have
00:10:14
the force now is in this direction
00:10:16
again toward the center of the earth the
00:10:17
speed is in this direction i know what
00:10:18
to do and how to i know how to step it
00:10:20
forward and how to change the speed
00:10:21
the velocity i know how to change the
00:10:22
acceleration and i keep stepping forward
00:10:25
at this point you see that the the force
00:10:28
has a component
00:10:29
going this way to try and make it curve
00:10:31
but also a component in this direction
00:10:33
it's not pointing exactly sideways
00:10:36
anymore it's a little bit back
00:10:38
the force is also is is causing the
00:10:40
satellite to change direction
00:10:42
and to slow down if we go even later we
00:10:44
go out here
00:10:46
the force is pulling this way it's
00:10:47
causing the satellite to slow down the
00:10:50
force is pulling toward the earth
00:10:52
and also causing it to change direction
00:10:54
and because it's so much further away
00:10:56
the force is much less so the further
00:10:58
away you are
00:11:00
the less the force the less the
00:11:03
acceleration
00:11:04
but to get out there gravity had to be
00:11:07
slowing it down so when it gets out here
00:11:08
it's going much slower because gravity's
00:11:10
been slowing it down the whole way
00:11:11
and now gravity will cause it to speed
00:11:13
up again until it finally gets in
00:11:14
close to the earth so this is how my
00:11:18
little program
00:11:19
works that uses newton's second law and
00:11:22
newton's law of gravitation
00:11:24
to make those orbits that i showed you
00:11:26
and uh
00:11:27
i mean it's a really really simple uh
00:11:30
differential equation solver relatively
00:11:32
speaking there's much much better ones
00:11:33
but
00:11:34
this worked a little python program um
00:11:38
i mean i'd love to teach you
00:11:39
differential calculus right now uh
00:11:41
vector calculus rather but teaching
00:11:43
vector calculus
00:11:45
probably out of scope of um
00:11:48
astral 101 but this kind of math i'm
00:11:52
talking about newton had to invent it in
00:11:54
order to do this kind of work so it's
00:11:56
it's
00:11:57
pretty pretty great um now that we know
00:11:59
it it's like oh yeah that's kind of easy
00:12:01
ish
00:12:02
i don't know all right so orbits you
00:12:04
take these two equations
00:12:06
you apply them step by step by step and
00:12:08
you can reproduce
00:12:10
the orbit of a satellite around the
00:12:13
earth
00:12:14
you find that it is an ellipse you find
00:12:17
that the earth is at the center is that
00:12:19
one of the focuses and that the other
00:12:21
focus is somewhere in space
00:12:24
this nowhere here in this mass that goes
00:12:27
into this orbit
00:12:28
do we say anything about it being an
00:12:30
ellipse nowhere in this mass
00:12:32
do we say anything about where the
00:12:33
focuses are it just
00:12:35
that's just how
00:12:39
it works so why isn't it an ellipse
00:12:44
because it's a natural consequence of um
00:12:47
acceleration being proportional to the
00:12:49
square of the distance from the mass
00:12:52
very it's very interesting uh it it's
00:12:55
just that's just the way it works
00:12:58
it's a natural consequence of these
00:12:59
rules where did these rules come from
00:13:07
well there they are
00:13:10
they came from the mind of god
00:13:13
okay instant review quiz when
00:13:16
in the highly eccentric orbit of a comet
00:13:20
is the speed of the comet
00:13:23
the greatest the speed not the velocity
00:13:25
the speed when is the speed
00:13:27
the greatest four possibilities here a
00:13:31
it's always the speed is always the same
00:13:33
b
00:13:34
when the comet is furthest from the sun
00:13:36
c when the comet is approaching the sun
00:13:38
coming in towards the sun
00:13:40
d when the comet is closest to the sun
00:13:43
or
00:13:43
e when the comet is moving away from the
00:13:46
sun
00:13:47
when is the speed of the comet
00:13:50
the greatest okay we can think back to
00:13:53
this this is actually
00:13:56
this is kepler's second law isn't it
00:14:00
when is the speed the greatest do you
00:14:03
remember
00:14:08
d when the comet is closest to the sun
00:14:11
that's when the speed is greatest
00:14:14
okay next question
00:14:17
when in the highly eccentric orbit of a
00:14:19
comet is the angular momentum of the
00:14:22
comet the greatest remember going back
00:14:24
to last class the idea of
00:14:25
angular momentum when is the angular
00:14:27
momentum of the comet
00:14:29
the greatest option a it's always the
00:14:31
same
00:14:32
because angular momentum is conserved or
00:14:34
b when the comet is furthest from the
00:14:37
sun
00:14:38
when the comet is approaching the sun
00:14:39
when the comet is closest to the sun
00:14:41
or when the comet is moving away from
00:14:43
the sun well the answer is a
00:14:45
right angle momentum is conserved it's
00:14:48
always the same so a good that one's
00:14:51
easy
00:14:52
all right next question when in the
00:14:53
highly eccentric orbit of a comet
00:14:56
is the force due to gravity between the
00:14:59
comet and the sun
00:15:00
the greatest when is the force due to
00:15:03
gravity
00:15:03
between the comet and the sun the
00:15:06
greatest
00:15:09
well it's the universal law of
00:15:10
gravitation so the force is always the
00:15:12
same
00:15:13
or when the comet is furthest
00:15:16
from the sun or when the comet is
00:15:19
approaching the sun
00:15:21
or when the comet is moving away from
00:15:24
the sun
00:15:26
or when the comet is closest to the sun
00:15:27
what do you think
00:15:30
when is the force of gravity between the
00:15:31
comet and the sun the greatest let's
00:15:33
remember remind ourselves about the
00:15:34
equation
00:15:35
force equals g then it's got the two
00:15:39
masses multiplied
00:15:40
divided by the distance squared
00:15:44
so the masses aren't changing in this in
00:15:46
this problem right the masses are always
00:15:48
the same and g is always the same but
00:15:49
the distance is changing
00:15:51
because it's a highly eccentric orbit is
00:15:52
going from close to far
00:15:55
you divide the force by the distance
00:15:57
squared
00:15:58
so a bigger distance is a smaller force
00:16:01
so a smaller distance is a larger force
00:16:02
the answer
00:16:04
the force must be greatest when the
00:16:06
comet is closest so it must be
00:16:08
d when the c so when the objects are
00:16:11
close together
00:16:12
there's a large force when they're
00:16:13
further apart it's a small force
00:16:16
so when the comet is closest to the sun
00:16:18
is when the force is greatest
00:16:22
which leads us to our last little
00:16:24
instant review quiz question
00:16:25
when in the highly eccentric orbit of a
00:16:27
comet is the comet's acceleration
00:16:30
the greatest i mean the same
00:16:33
things here furthest approaching closest
00:16:35
moving away
00:16:36
or both b and d
00:16:41
so is it when it's furthest away when
00:16:44
it's coming toward it
00:16:46
it's kind of falling in toward the
00:16:49
sun or when it's kind of scooting moving
00:16:51
out away from the sun maybe the
00:16:52
acceleration be like slowing down
00:16:54
the quickest or when it's closest
00:16:58
when it's spinning around with that's
00:16:59
crystalline as close as we know it's
00:17:00
moving the fastest
00:17:02
but where is the acceleration the
00:17:05
greatest
00:17:08
well there's a few ways we can think
00:17:09
about this one way is we can remember
00:17:13
the last question which said that the
00:17:15
force
00:17:16
is the greatest when it's close and then
00:17:18
remember
00:17:20
newton's second law that says the
00:17:22
acceleration
00:17:23
depends on the force the bigger the
00:17:25
force the bigger acceleration
00:17:27
that would say that the biggest
00:17:29
acceleration
00:17:30
is when the force is the biggest and
00:17:32
that would say that it is when
00:17:34
the comet is closest to the sun
00:17:40
now it's interesting when the comet is
00:17:42
closest to the sun
00:17:44
that's when it's moving the fastest but
00:17:45
also it's kind of when the speed is
00:17:47
changing
00:17:48
the least the speed is not changing when
00:17:50
it's closest to the sun
00:17:53
but the direction is changing very
00:17:55
rapidly and remember acceleration
00:17:57
is a change in velocity in other words a
00:17:59
change in speed
00:18:00
or direction and so the force of gravity
00:18:03
is the strongest one is closest to the
00:18:05
sun
00:18:05
therefore the acceleration is largest
00:18:08
when it's closest to the sun
00:18:09
and what's happening there is the
00:18:10
direction is changing rapidly
00:18:12
when it's close to the sun so the answer
00:18:14
there is
00:18:15
c all right are we starting to
00:18:17
understand
00:18:18
how newton's laws cause orbits
00:18:23
you have the object moving you have the
00:18:25
force of gravity pulling on it changing
00:18:27
its direction
00:18:28
and it just moves along and as it moves
00:18:29
the force is continuously trying to
00:18:31
change the direction
00:18:32
and the faster the further away it is
00:18:36
the less the force the closer it is the
00:18:37
greater the force as it moves away
00:18:39
there's force pulling it back so it
00:18:41
slows down when it's
00:18:42
when it's coming toward it the force is
00:18:44
accelerating it forward and
00:18:46
continuing to cause it to curve so in
00:18:48
the end you end up
00:18:49
with an ellipse why is it an ellipse and
00:18:51
not some other shape
00:18:53
because the answer is an ellipse okay
00:18:57
there we go moving on
00:19:00
the next thing we talked about was free
00:19:02
fall remember this question
00:19:04
we have our astronaut floating in space
00:19:07
and we ask why is the astronaut floating
00:19:11
and not falling to the earth remember
00:19:14
there's still the force of gravity
00:19:15
acting on him
00:19:17
in fact he's only about five percent
00:19:20
lighter
00:19:21
than he would be on the surface a five
00:19:22
percent less force of gravity therefore
00:19:25
five percent less weight
00:19:26
not mass but wait
00:19:29
so why is he floating and not falling to
00:19:31
the earth
00:19:32
the answer is because he is
00:19:36
in orbit like his spacecraft the thing
00:19:39
we just talked about he is moving
00:19:40
forward gravity is pulling him toward
00:19:42
the earth
00:19:43
and so he's turning but he's going fast
00:19:46
enough that he never hits the earth he
00:19:48
just keeps
00:19:48
curving around it like the spacecraft in
00:19:50
our little calculation we did
00:19:52
so he is orbiting at the same speed of
00:19:55
his spacecraft
00:19:57
so he feels weightless he feels
00:20:00
that he's just responding to whatever
00:20:02
gravity he wants him to do
00:20:04
so he feels like he has no weight he is
00:20:06
an orbit like his spacecraft
00:20:08
he's traveling at around 26 000
00:20:10
kilometers per hour in this case
00:20:11
so the force required to make him go in
00:20:13
a circle is the same as the force of
00:20:16
gravity
00:20:18
pretty cool all right free fall
00:20:22
whenever the only thing acting on you is
00:20:24
the force of gravity
00:20:26
then we say you are in free fall it
00:20:28
feels like you're falling
00:20:30
even though he's not going toward the
00:20:31
center of the earth he
00:20:33
the only thing acting on him is gravity
00:20:35
therefore he feels weightless
00:20:40
i can explain this slightly and a
00:20:41
different way a bit if you've ever been
00:20:43
to the amusement park and gone those
00:20:44
spinny rides
00:20:45
and they push you back against the uh
00:20:48
the wall
00:20:49
that pushing back it feels just like
00:20:51
gravity
00:20:52
now imagine you're on a spinny thing but
00:20:55
you're spinning at just the right rate
00:20:57
so that the force of spinning of
00:21:01
being turned into a circle equals the
00:21:03
force of gravity and they exactly cancel
00:21:05
then you would feel weightless that's
00:21:07
what's happening to him
00:21:08
he's going around the earth at 26 000
00:21:11
kilometers per hour
00:21:13
the force of gravity pulling him down
00:21:16
exactly equals the force required to
00:21:19
make him go in a circle
00:21:20
and therefore he is weightless and he's
00:21:21
going in a circle that's pretty cool all
00:21:24
right
00:21:25
free fall
00:21:28
now on to our new topic for the day
00:21:31
we're going to take these same ideas
00:21:32
we've been talking about about force
00:21:34
and apply them to trying to understand
00:21:37
where the heck tides come from so let's
00:21:40
start here
00:21:40
here we have the earth looking down at
00:21:42
the north pole here we have the moon
00:21:44
looking down at the north pole of the
00:21:45
moon
00:21:46
we have the force of gravity force
00:21:49
equals
00:21:49
gm1 m2 over r squared m1 is the mass of
00:21:53
the earth
00:21:54
m2 the mass of the moon r
00:21:57
is the distance between the centers of
00:21:59
the
00:22:00
planets that's the force on the whole of
00:22:03
the earth acting on
00:22:05
the whole of the moon but what if i say
00:22:08
i don't want to talk about yeah
00:22:09
so the gravitational attraction between
00:22:11
the earth and the moon applies a force
00:22:13
okay but what if i don't want to talk
00:22:15
about just the force
00:22:17
of gravity on the center of the earth
00:22:20
let's imagine
00:22:21
i think about you know uh a bit of rock
00:22:24
here on the edge um
00:22:26
just on this side of the earth i'm just
00:22:27
going to imagine just a little mini
00:22:29
sphere
00:22:30
of rock right it's part of the earth but
00:22:33
i'm going to say what's the force
00:22:34
of gravity on that rock from the moon
00:22:38
well it's closer so a given chunk of
00:22:42
rock
00:22:44
will have a larger force than a chunk at
00:22:47
the same mass at the center of the earth
00:22:50
from the moon because it's closer so
00:22:51
here it's closer there's a larger force
00:22:53
applied to a chunk of rock here
00:22:55
than a chunk of rock there if the trunk
00:22:57
is rocking the same size
00:22:59
the fact that the rocks are all
00:23:00
connected together doesn't really matter
00:23:01
right we're saying what's the force of
00:23:02
gravity on this bit of the earth
00:23:04
force of gravity in this bit of the
00:23:05
earth is stronger than the force of
00:23:06
gravity on this bit of the earth
00:23:08
because it's closer to the moon the
00:23:10
force of gravity from the moon
00:23:12
on this chunk of rock is larger than the
00:23:14
force of gravity from this chunk of rock
00:23:16
which will cause that chunk of rock to
00:23:18
be pulled this way
00:23:19
compared to the center well how about
00:23:23
back here what about a chunk of rock out
00:23:26
here a long way
00:23:28
further from the moon well it's further
00:23:30
away
00:23:31
so there will be a smaller force applied
00:23:33
to a chunk of rock
00:23:35
further from the moon
00:23:39
so the force of gravity from the moon is
00:23:42
less here
00:23:43
than here and greater here than here
00:23:49
so what's that gonna do well this is
00:23:52
pulling away from here and this is
00:23:54
pulling away from here
00:23:55
so it's gonna take the entire earth and
00:23:58
stretch it
00:24:01
in the direction of the moon right this
00:24:03
is pulling
00:24:04
harder than here so this pulls away from
00:24:06
here so this this point stretches away
00:24:07
from this point
00:24:08
and then this point stretches away from
00:24:10
that point so this stretches away from
00:24:12
there
00:24:13
and this stretches away from there so
00:24:15
the whole earth gets
00:24:17
squished up now the earth is going to
00:24:19
move due to the average force on the
00:24:21
whole earth unless the earth breaks
00:24:23
but if the earth doesn't break then all
00:24:25
that's going to happen is the earth is
00:24:26
going to get
00:24:27
stretched and the same thing
00:24:32
will happen to the moon now this course
00:24:33
doesn't happen right away right
00:24:35
um it turns out that uh rock
00:24:38
and the earth's mantle this thing stuff
00:24:40
to make earth is made of doesn't bend
00:24:41
very quickly it kind of
00:24:43
you push a force and it goes okay
00:24:46
so this bending into a blob like this
00:24:50
doesn't happen right away it takes time
00:24:52
before it bends to its natural shape
00:24:56
so what do we do with this well the
00:24:58
earth is rotating
00:25:00
and it's rotating too quickly for the
00:25:03
rock and the mantle to really respond
00:25:04
much
00:25:05
so here's the earth spinning around it's
00:25:07
trying to squish out like this toward
00:25:09
the earth toward the moon
00:25:10
because of this differential force but
00:25:12
by the time it starts to move
00:25:14
the earth is rotated and it tries to
00:25:15
move different way and it's rotating to
00:25:16
try to move a different way
00:25:18
so you end up with the shape of the
00:25:19
earth barely changing
00:25:23
that's rock and the mantle but what if
00:25:26
instead the whole earth were covered in
00:25:29
a large ocean
00:25:32
well if the whole earth was covered in a
00:25:33
large ocean well the ocean
00:25:36
would move the ocean would stretch out
00:25:39
compared to the moon
00:25:42
they'd have time to ocean would have
00:25:43
time to flow they'd respond
00:25:46
so what we find is that in fact the
00:25:48
oceans on earth do respond to the tidal
00:25:50
forces from the moon
00:25:51
so the oceans do squeeze out and it gets
00:25:53
the oceans are thicker on this side
00:25:56
oceans are thicker toward the moon or
00:25:57
just oceans are thicker away from the
00:25:58
moon
00:25:59
and they're thinner um in this direction
00:26:03
because of the force from the moon now
00:26:04
something funny about this picture
00:26:05
you'll notice
00:26:06
i drew it i drew it tipped
00:26:11
that's because the earth is turning and
00:26:14
friction with rotating earth causes the
00:26:16
tidal bulge to lag behind
00:26:18
so it's not quite lined up with the moon
00:26:19
it's lagging behind a bit
00:26:21
just because of friction between the
00:26:23
earth
00:26:24
and the oceans so the earth is turning
00:26:27
the oceans are responding to the force
00:26:28
from the moon
00:26:29
but because it's turning it lags so you
00:26:31
get you get these tidal bulges
00:26:34
lagging behind um the direction pointing
00:26:36
at the moon
00:26:37
if you notice there's a there's a tidal
00:26:38
bulge back here and a tidal bulge up
00:26:40
here remember
00:26:42
this part is being pulled away from this
00:26:43
part this part is being pulled away from
00:26:45
this part
00:26:45
so the whole earth gets stretched you
00:26:47
don't just get a blob
00:26:48
on the side facing the moon you get a
00:26:50
bulge on the side
00:26:52
away from the moon because of this
00:26:54
differential force
00:26:55
where the back pulse not as hard as the
00:26:57
middle pull is not as hard
00:26:59
as the front so the whole thing gets
00:27:00
stretched out now i'm saying it with
00:27:02
words
00:27:04
you may think i don't really get that
00:27:06
that's okay the only way to really
00:27:08
understand it
00:27:08
i think is to do the proper math do the
00:27:11
proper
00:27:12
integrations which we're not going to do
00:27:14
because we're not doing math in this
00:27:15
class
00:27:16
so i kind of tried to explain to you how
00:27:20
this squeezing action works to really
00:27:23
understand it you have to do the math
00:27:25
so all you need to know all you need to
00:27:28
know
00:27:29
is that there's a bulge on both sides of
00:27:30
the earth because of the moon
00:27:32
on the side facing the earth moon and
00:27:34
the side away from the moon
00:27:35
and that the um
00:27:39
the bulge lags because of the spinning
00:27:41
of the earth those are things you need
00:27:42
to know
00:27:43
exactly why it is it comes from the
00:27:46
force of gravity it comes from newton's
00:27:47
laws it comes from
00:27:49
models of friction but um and inertia
00:27:52
and viscosity but uh
00:27:57
those are much more complicated topics
00:27:59
because you actually need to do the math
00:28:00
to really understand them
00:28:01
so just kind of get the basic idea you
00:28:03
can
00:28:04
think about it all right i kind of get
00:28:07
it
00:28:07
that's that's good enough okay that's i
00:28:10
guess that's good enough
00:28:13
so this leg applies a force
00:28:16
on the earth causing its rotation to
00:28:19
slow down there's a there's a force
00:28:20
being applied
00:28:21
because the thing is turning the moon is
00:28:25
pulling on it and then it's kind of
00:28:27
dragging against it so that dragging
00:28:30
forms a force that actually is trying to
00:28:33
slow the earth's rotation
00:28:36
down i mean it's a huge effect
00:28:39
in fact when the earth was first formed
00:28:41
the rotation period was only 14 hours a
00:28:43
day was
00:28:44
14 hours long when the earth was first
00:28:46
formed
00:28:47
but now billions of years later because
00:28:48
of this force from the moon continuously
00:28:50
applying a force on the rotation of the
00:28:52
earth
00:28:52
the earth has slowed down to the point
00:28:54
where a day is now 24 hours
00:28:58
that's cool what that means
00:29:02
is that the rotation of the earth is
00:29:03
getting slower and will continue to get
00:29:05
slower and slower and slower
00:29:07
and if the sun wasn't going to blow the
00:29:10
earth up
00:29:10
in a few billion years in billions of
00:29:13
years the earth's rotation would finally
00:29:15
stop and the earth would always be
00:29:18
the same side of the earth would always
00:29:20
be facing the moon in the same way
00:29:22
that the same side of the moon is always
00:29:24
facing the earth in
00:29:26
fact that's what happened to the moon
00:29:28
now the earth
00:29:29
is much more massive than the moon the
00:29:31
force of gravity
00:29:32
the tidal forces on the moon are much
00:29:35
larger than the tidal forces
00:29:37
um on the earth from the moon the title
00:29:40
forces from the
00:29:41
earth on the moon are much larger than
00:29:43
tidal forces of the moon
00:29:44
on the earth and the moon is much
00:29:47
smaller much lighter much easier to
00:29:48
speed up and slow down
00:29:50
consequently the rotation of the moon
00:29:53
has stopped relative to the earth it is
00:29:56
now
00:29:56
tidally locked so the faint same side of
00:29:59
the
00:30:00
earth always faces same side of the moon
00:30:02
always faces the earth
00:30:03
it does it no longer spins relative to
00:30:07
the
00:30:07
earth that's because of this tidal
00:30:09
effect the force
00:30:11
the tidal forces causing the moon to be
00:30:13
elongated
00:30:14
for it to turn would require that rock
00:30:16
to being continuously being squeezed and
00:30:18
unsqueezed and that takes energy
00:30:20
that produces friction and it would it
00:30:22
slowed down
00:30:23
the rotation of the moon until finally
00:30:26
the same side of the moon
00:30:27
always faces the earth tidal locking
00:30:30
so that wow there was this mystery we
00:30:33
had
00:30:34
why is the rotation of the moon exactly
00:30:36
right so the same size of the moon
00:30:37
faces the earth it's because of this
00:30:40
tidal force
00:30:41
the same effect that's that made the
00:30:43
earth do that
00:30:44
is making uh made the moon do that is
00:30:47
slowly making the earth do that
00:30:49
oh that's oh that's cool well there it
00:30:52
is
00:30:53
now we know same side of the moon always
00:30:55
faces the earth because of
00:30:57
tidal forces
00:31:00
cool all right review instant review
00:31:03
quiz
00:31:04
in this model that i showed you how many
00:31:07
tides are there
00:31:08
in a day is there one tide
00:31:12
when you're facing the moon or is there
00:31:15
one tide
00:31:16
one high tide a little after you're
00:31:19
facing the moon because of that leg
00:31:21
or is there two one when you're facing
00:31:24
the moon and one
00:31:25
on the opposite side because there's two
00:31:27
bulges
00:31:28
or is it d2 a little after you're facing
00:31:32
the moon because the leg and then around
00:31:35
12 hours later
00:31:36
well it's d right there's there's two
00:31:40
tides there's two high tides there's the
00:31:42
one
00:31:44
sort of facing the moon and the one sort
00:31:46
of facing opposite the moon
00:31:47
but they are um lagged from each other
00:31:50
because of
00:31:51
um that friction effect the same effect
00:31:55
that's slowing down the earth so it
00:31:57
it the day gets longer and longer and
00:32:00
which cause the moon to stop uh rotating
00:32:04
relative to the earth all right there we
00:32:06
go it's the review quiz complete
00:32:10
okay so the idea called tidal locking
00:32:13
friction with rotating earth causes the
00:32:14
tidal bulge
00:32:15
to lag behind this leg applies a force
00:32:18
on the earth causing its rotation to
00:32:19
slow down
00:32:20
rotation periods of 14 hour okay we
00:32:22
already did all this it's weird
00:32:26
now
00:32:35
okay well it turns out you might be
00:32:37
asking yourself well doesn't the sun
00:32:39
also provide a gravitational force on
00:32:41
the earth after all
00:32:42
the earth is orbiting around the sun
00:32:45
surely
00:32:46
the sun must provide a gravitational
00:32:49
force on the earth and therefore
00:32:51
the sun presumably would cause
00:32:54
tides on the earth and the answer is yes
00:32:57
it does
00:32:58
the sun also causes tidal forces on the
00:33:00
earth
00:33:01
the sun is much more massive so you'd
00:33:03
think well maybe it's going to provide
00:33:05
larger tidal forces but it's much
00:33:07
further away
00:33:08
so maybe you'd conclude that it provides
00:33:10
much smaller title forces
00:33:11
it turns out that um the further away
00:33:16
component overwhelms the larger
00:33:19
mass of the sun component so it ends up
00:33:22
that the
00:33:23
tides from the sun are smaller than the
00:33:26
tides from the moon
00:33:27
but in the same kind of order when
00:33:31
the earth when the moon the earth
00:33:35
and the sun in that direction are all
00:33:36
lined up in other words when you're on a
00:33:38
full moon
00:33:38
or a new moon because it can be over
00:33:40
here or over there
00:33:42
when you're all lined up in a full moon
00:33:44
or a new moon
00:33:45
the tidal forces from the moon and the
00:33:48
tidal forces from the i should say sun
00:33:50
tide emerges from the moon and from the
00:33:51
sun add together
00:33:54
this is called a spring tide
00:33:59
on a full moon and a new moon the tidal
00:34:01
forces from the moon
00:34:02
and the earth add together you get a
00:34:05
spring tide
00:34:10
when the on a quarter moon when the sun
00:34:13
is down here
00:34:14
down below looking up this way and a
00:34:17
quarter moon
00:34:18
the tidal forces from the sun partially
00:34:20
cancel
00:34:21
the tidal forces from the moon this is
00:34:23
called a neap tide it's a smaller tide
00:34:27
so the sun is trying to make tidal
00:34:30
bulges
00:34:30
aligned this way but lagged because of
00:34:32
the rotation of the earth
00:34:34
the moon is trying to make tidal bulges
00:34:36
aligned this way
00:34:38
the moon beats the sun but the sun makes
00:34:40
the tides smaller
00:34:42
so you get small tides during a quarter
00:34:45
moon
00:34:46
and you get large tides during a full
00:34:49
moon
00:34:50
that's the theory anyway let's see what
00:34:53
you
00:34:53
actually get here we have tide tables
00:34:57
for tofino british columbia so this is
00:34:59
on the
00:35:01
west coast of vancouver island so you're
00:35:03
just right on the edge of the pacific
00:35:04
ocean
00:35:05
and what you find is that near a
00:35:09
new full moon or near a new moon you get
00:35:11
large tides
00:35:13
during the quarter moon you get smaller
00:35:15
tides
00:35:16
you also see you get two tides per day
00:35:19
one so you get one high tide in the
00:35:21
daytime here and one high tide at night
00:35:23
day night day night all along that's
00:35:27
pretty cool um just like we said it
00:35:30
should be
00:35:31
so this really does appear to be the
00:35:33
explanation for tides
00:35:35
now there's some weird things going on
00:35:37
slightly
00:35:38
it turns out that this model we just
00:35:41
gave gave gives the tidal levels for the
00:35:44
kind of the whole earth but when you
00:35:45
have water flowing up and down channels
00:35:47
and up and down
00:35:48
inlets and and things that
00:35:51
flow kind of messes up this easy
00:35:53
calculation because it get even more lag
00:35:55
and more weird delay so if you look at a
00:35:57
tide table for somewhere
00:35:58
that's more inland maybe up a inlet or
00:36:00
something you won't get this nice double
00:36:02
bumps like this it'll look a little bit
00:36:04
different that's just because the water
00:36:06
takes time to flow and it kind of
00:36:07
bounces around a bit
00:36:08
it's much more complicated to calculate
00:36:10
but this this
00:36:11
this story really does apply to the
00:36:14
rising and lowering of the
00:36:15
ocean as a whole when you have a
00:36:19
full moon or a new moon you get large
00:36:21
tides when you have a quarter moon
00:36:23
you get smaller tides that's because the
00:36:25
tides from the
00:36:28
sun cancel out the tides from the uh
00:36:31
moon to some level
00:36:32
all right so we're almost done here
00:36:35
finally
00:36:36
we can go ahead and look at this plot we
00:36:37
this the simulation we saw
00:36:39
last class now remember this last class
00:36:41
we were looking at how
00:36:42
um charon
00:36:46
is orbiting around pluto but not around
00:36:49
the center of pluto's
00:36:50
orbiting around a spot kind of in
00:36:52
between pluto and charon
00:36:54
because the mass of cheron is kind of
00:36:58
almost large compared to the mass of
00:36:59
pluto so it actually orbits around this
00:37:01
spot right there
00:37:03
we also noticed that the same side of
00:37:06
charon
00:37:06
always all the same side of pluto always
00:37:08
faces charon
00:37:09
and the same side of charon always
00:37:11
spaces pluto before we didn't really
00:37:13
understand why that is but now we do
00:37:15
it's this tidal locking if charon were
00:37:18
to be rotating compared to
00:37:19
pluto that squeezing of the shape of
00:37:22
charon
00:37:23
due to pluto would be significant and it
00:37:25
would they would you're trying to make
00:37:27
this oblong shape and as it turned
00:37:29
it would be like break the rock and bend
00:37:31
it and that would take energy
00:37:33
that presumably was happening at one
00:37:35
point in the in the life of pluto and
00:37:36
charon
00:37:37
but that rotating gradually slowed down
00:37:41
charon's rotation until finally the same
00:37:43
side always faces pluto
00:37:44
and exactly the same thing pluto the
00:37:46
charon trying to bend pluto
00:37:49
pluto originally was probably rotating
00:37:51
compared to charon
00:37:52
but then finally because of millions and
00:37:55
billions of years of this rotation
00:37:57
it just dissipated the energy until
00:37:59
finally it rolled to a stop
00:38:00
so the same side of charon always faces
00:38:03
same side of pluto always faces cheer on
00:38:04
the same side of cheron always faces
00:38:07
pluto
00:38:09
so in the last two classes we've looked
00:38:11
at how newton's laws
00:38:12
can be used to describe the behavior of
00:38:15
many many things in the universe
00:38:17
from falling haber hammers to the orbit
00:38:20
of charon around pluto
00:38:21
we can use it to understand um tides we
00:38:24
can understand
00:38:25
use it to understand why the same face
00:38:27
of this moon is always facing the earth
00:38:30
and this was the start of a huge
00:38:33
revolution in science
00:38:35
where people began to believe that
00:38:38
we could really understand the behavior
00:38:40
of anything
00:38:41
in the universe and newton's laws of
00:38:44
motion
00:38:44
and later physics from them had became
00:38:47
incredibly successful
00:38:49
in understanding a huge wide range of
00:38:51
phenomena and by the 19th century
00:38:53
electromagnetism the laws of
00:38:55
electromagnetic magnetism came along the
00:38:57
laws of understanding how light behaved
00:38:59
and we kind of came to a point
00:39:02
where the assumption was that we really
00:39:04
understand the behavior of
00:39:06
everything now there's a limit to this
00:39:09
right we don't know
00:39:10
why f equals m a we don't know why the
00:39:13
acceleration is proportion of the force
00:39:15
divided by the mass we don't know why
00:39:17
the acceleration of a particle is
00:39:19
inversely proportional to the distance
00:39:21
um from a massive object i mean we can
00:39:24
say things but
00:39:25
why is it that way instead of some other
00:39:27
way we don't really know but
00:39:29
we know that if that is how the universe
00:39:32
behaves and it does
00:39:33
then we can predict the behavior of a
00:39:35
great many many things now
00:39:38
by the end of the 19th century there
00:39:41
were very few
00:39:42
things missing very few
00:39:45
experiments didn't quite match the data
00:39:47
one of them
00:39:48
was that the orbit of mercury
00:39:51
disagreed with newton's laws that is to
00:39:55
say
00:39:56
mercury's orbit was off just by this
00:39:59
tiny little bit
00:40:02
he's like what's small it is small
00:40:06
but there's no particular reason why
00:40:08
newton's laws shouldn't be
00:40:09
perfect lots of explanations maybe
00:40:11
there's another planet maybe the sun
00:40:13
isn't perfectly spherical
00:40:14
but none of these could be made to fit
00:40:16
the data
00:40:18
until finally in the early 20th century
00:40:21
another
00:40:22
extraordinarily famous physicist albert
00:40:24
einstein
00:40:26
proposed his theory of general
00:40:28
relativity which
00:40:30
supplants newton's laws of motion
00:40:34
and newton's sorry einstein's
00:40:38
view of the universe is very different
00:40:41
than
00:40:41
the view of the universe described in
00:40:44
newtonian
00:40:45
mechanics space-time is actually
00:40:49
bent by mass it's not a force it's a
00:40:52
warping of space-time
00:40:53
and so he would say the reason that the
00:40:56
orbit of mercury was off is because in
00:40:58
fact space near the sun is bent
00:40:59
and the distance is a little bit larger
00:41:01
than you thought it was
00:41:03
crazy weird ideas but if you take
00:41:07
einstein's description of what the way
00:41:09
the universe works
00:41:11
all of a sudden all these errors go away
00:41:13
and then it predicted other things it
00:41:14
predicted
00:41:15
gravitational waves being emitted by
00:41:18
spinning objects it predicted the
00:41:19
existence of black holes
00:41:21
places where gravity is so strong that
00:41:24
light can't even get out and in fact as
00:41:26
you get close to the black hole time
00:41:27
itself slows down
00:41:29
these crazy crazy objects objects which
00:41:32
have been
00:41:32
confirmed predictions that have been
00:41:35
shown to be true
00:41:36
so we now would say
00:41:41
newton's laws of motion well they're not
00:41:45
they're not right they're they're
00:41:48
wrong
00:41:52
they're wrong in that they don't always
00:41:54
predict
00:41:55
the behavior the universe will will
00:41:57
experience
00:41:58
they usually do except for in really
00:42:00
weird places where the gravitational
00:42:02
forces are enormous
00:42:03
like near the sun or near a black hole
00:42:07
will we then go and say that newton was
00:42:09
wrong or that his theories were of no
00:42:11
value no
00:42:12
no they're still very very useful if you
00:42:14
want to calculate what happens when you
00:42:15
kick a football newton's laws are great
00:42:17
you do not want to mess around with
00:42:19
the einstein equations because they are
00:42:21
so unbelievably complicated to use
00:42:24
but we also would say that it's an
00:42:26
incomplete theory
00:42:28
this is how things work in in physics
00:42:32
we come up with a description of the
00:42:34
behavior of the universe we do
00:42:35
experiments to test the description
00:42:37
until we find a discrepancy and then we
00:42:40
look for
00:42:42
a modification to the theory or a whole
00:42:44
new way of looking at it
00:42:45
that will explain this discrepancy and
00:42:48
so that we can
00:42:49
again say we have a model that fits all
00:42:51
the observations
00:42:52
we are now back into a place like we
00:42:54
were in the 19th century
00:42:55
where to a pretty impressive level
00:42:59
there isn't an experiment we can think
00:43:00
of where we could not at least in
00:43:02
principle calculate
00:43:04
what the outcome of the experiment would
00:43:06
be there's a small number of pla of
00:43:08
exceptions we don't know how to describe
00:43:10
the extremely extremely early universe
00:43:13
the first tiny fraction of a second when
00:43:15
the temperatures and densities were high
00:43:17
enough
00:43:17
we don't think we know how to calculate
00:43:19
what happens there there's this
00:43:21
mysterious thing in the universe we call
00:43:23
dark energy which causes causing the
00:43:25
universe's
00:43:25
expansion to speed up we don't really
00:43:28
know what causes that where it's from
00:43:29
what it's doing
00:43:32
but they're very very few
00:43:35
areas we just don't know how to
00:43:37
calculate them it's we're hopeful
00:43:39
that it is in searching out those
00:43:42
unexplained
00:43:43
areas that hopefully we can come up to a
00:43:46
new understanding how the universe works
00:43:47
science continues um we've been able to
00:43:50
accomplish a lot
00:43:52
but we we aren't done
00:43:55
looking forward to the next class when
00:43:56
we'll start looking at the sun and at
00:43:58
light
00:43:58
thank you very much