Astro 101 Class 7: Tides

00:44:05
https://www.youtube.com/watch?v=E7kONCIMXz4

Résumé

TLDREn esta clase, se exploran las leyes de Newton y su aplicación en fenómenos astronómicos, particularmente en el movimiento de cometas, satélites y mareas. Las mareas son causadas por las fuerzas gravitacionales de la Luna, las cuales estiran la Tierra, afectando los niveles de agua en diferentes áreas y creando mareas altas y bajas. Este estiramiento desequilibra la rotación de la Tierra, ralentizándola, fenómeno que también explica por qué la misma cara de la Luna siempre mira hacia la Tierra, conocido como bloqueo de marea. Se comprobó que Newton desarrolló un modelo para predecir estos movimientos, aunque fue necesario el desarrollo de la teoría de la relatividad de Einstein para ajustar las anomalías, como la órbita de Mercurio. La clase destaca la evolución del conocimiento científico y cómo los modelos científicos son reformulados para brindar explicaciones más precisas de nuestro universo, abriendo la puerta a nuevas teorías y descubrimientos.

A retenir

  • 🌊 Las mareas se forman por la diferencia de fuerza gravitacional de la Luna sobre la Tierra.
  • 🌕 El bloqueo de marea explica por qué solo vemos una cara de la Luna.
  • 🚀 Newton formuló leyes que modelan el movimiento celeste con precisión.
  • 🌌 La relatividad de Einstein ajusta anomalías en las leyes de Newton.
  • 🔄 La rotación de la Tierra se desacelera por efectos de marea.
  • 🌞 El Sol también afecta las mareas, aunque menos que la Luna.
  • 📈 Las simulaciones de órbitas usan las leyes de Newton.
  • 🛰️ La aceleración y dirección están influenciadas por fuerzas gravitacionales.
  • ⚖️ Las leyes de Newton son fundamentales pero tienen limitaciones.
  • 🧠 El conocimiento científico evoluciona con nuevas teorías.

Chronologie

  • 00:00:00 - 00:05:00

    En la clase de Astro 101 de hoy, se introducen los temas de las mareas y las leyes de Newton. El enfoque inicial se centra en explicar las diferencias entre las mareas altas y bajas, cuestionando la explicación errónea de Galileo sobre el fenómeno de las mareas causado por la Luna. Se menciona que el video proporcionado muestra ejemplos reales de mareas en Crescent Beach, y se destaca la dificultad de entender el tema, pero también su relevancia y asombro.

  • 00:05:00 - 00:10:00

    Se revisan brevemente las leyes de Newton para establecer una base para entender el comportamiento de las mareas. La Primera Ley de Newton describe cómo un objeto en movimiento permanece en movimiento a menos que una fuerza externa actúe sobre él. Se ilustra con ejemplos simples como un patinador sobre hielo. La Segunda Ley explica la relación entre la fuerza aplicada y el cambio de velocidad, y se utiliza para explicar cómo objetos de diferentes masas aceleran de manera distinta. La Tercera Ley de Newton aborda las fuerzas de reacción iguales y opuestas, ejemplificada por un astronauta empujando contra su nave en el espacio.

  • 00:10:00 - 00:15:00

    La explicación de las mareas se basa en estas leyes de Newton, detallando cómo la gravedad de la Luna afecta la Tierra. Se describe cómo diferentes partes de la Tierra experimentan fuerzas de gravedad variables debido a la proximidad a la Luna, llevando a una "estiramiento" del planeta. Se introduce el concepto de las fuerzas diferenciales para explicar cómo esto genera un efecto de estiramiento en los océanos de la Tierra, resultando en las mareas. Se menciona que la rotación de la Tierra y la fricción influencian este fenómeno, provocando un retraso en el alineamiento del abultamiento con la Luna.

  • 00:15:00 - 00:20:00

    La clase continúa analizando el fenómeno de la "bloqueo de marea", donde la fricción causada por las mareas eventualmente desacelera la rotación de los cuerpos celestes, aplicable tanto a la Tierra como a la Luna. Se explican conceptos como la marea de primavera y la marea muerta, dependiendo del alineamiento del sol, la Tierra y la Luna. Se detalla cómo las fuerzas de marea afectan las órbitas satelitales alrededor de otros planetas y cuerpos, y cómo las fuerzas gravitacionales interfieren con las aceleraciones de estos objetos. Se realizan cuestionarios instantáneos para reforzar el concepto de aceleración y fuerzas gravitacionales.

  • 00:20:00 - 00:25:00

    La discusión se mueve hacia las fuerzas de las mareas solares, destacando cómo éstas, aunque menores comparadas con las lunares, también afectan el nivel del mar, creando una marea compuesta en conjunciones específicas del Sol y la Luna. Se analiza la importancia de estos conceptos en tablas de mareas reales, como las de Tofino, Columbia Británica. Se explica cómo las variaciones en los niveles del mar pueden diferir debido a condiciones geográficas específicas y la complicación del flujo de agua en áreas de canales e inlands.

  • 00:25:00 - 00:30:00

    La clase finaliza vinculando estas ideas con conceptos más grandes de la física, como el uso de las leyes de Newton para explicar la conducta de objetos celestiales. Se concluye con una mirada hacia cómo las acciones de los cuerpos masivos pueden afectar su propia rotación y la de sus satélites a través de fricción y fuerzas de marea, introduciendo la importancia del tema tanto en fenómenos globales como locales alrededor de planetas como Plutón y Caronte.

  • 00:30:00 - 00:35:00

    Se revisa cómo las leyes de Newton se pueden aplicar para predecir una amplia gama de fenómenos en el universo, desde objetos cotidianos en movimiento hasta órbitas de cuerpos celestes, resaltando la revolución científica que estas leyes impulsaron. Se plantea la complejidad añadida de las predicciones de Einstein con la relatividad general, que corrigen y amplían el marco newtoniano, dando paso a predicciones como agujeros negros y ondas gravitacionales, áreas donde las leyes de Newton no ofrecen descripciones adecuadas.

  • 00:35:00 - 00:44:05

    Por último, se discute cómo la ciencia y nuestras comprensiones evolucionan al enfrentar anomalías en los datos, lo que lleva al desarrollo de nuevas teorías como la relatividad. Se reconoce las limitaciones actuales en ciertas áreas, como la energía oscura y el universo temprano, mientras se anticipan descubrimientos futuros. La clase concluye anunciando la continuación con el estudio del Sol y la luz en próximas sesiones.

Afficher plus

Carte mentale

Mind Map

Questions fréquemment posées

  • ¿Por qué la clase de hoy es considerada una de las más desafiantes del curso?

    Se considera desafiante porque cubre temas complejos como las leyes de Newton y sus aplicaciones astronómicas, las cuales requieren comprender conceptos abstractos.

  • ¿Cómo contribuye la Luna a las mareas en la Tierra?

    La Luna ejerce una fuerza gravitacional que causa mareas al crear una diferencia de fuerza en distintos puntos de la Tierra, estirándola y creando mareas altas y bajas.

  • ¿Qué es el bloqueo de marea?

    El bloqueo de marea es el fenómeno por el cual un cuerpo celeste siempre muestra la misma cara a otro debido al efecto de las fuerzas de marea que han ralentizado su rotación.

  • ¿Cómo afectan las leyes de Newton a las órbitas de los cuerpos celestes?

    Las leyes de Newton explican cómo las fuerzas gravitacionales afectan la aceleración y dirección de los cuerpos celestes, determinando sus trayectorias orbitales.

  • ¿Cómo afecta el Sol a las mareas terrestres?

    El Sol también crea fuerzas de marea en la Tierra, pero su efecto es menor que el de la Luna debido a la mayor distancia, aunque se suman en fases de luna nueva y llena.

  • ¿Qué demuestra la diferencia en las mareas solares y lunares?

    Demuestra cómo la combinación de fuerzas gravitacionales de diferentes cuerpos celestes puede afectar fenómenos como las mareas, resultando en mareas de primavera y de sicigia.

  • ¿Qué papel juega la fricción en la rotación de la Tierra respecto a las mareas?

    La fricción entre la Tierra y su océano debido al movimiento de marea causa que la rotación de la Tierra se desacelere gradualmente.

  • ¿Por qué se utilizan las leyes de Newton para simular órbitas?

    Porque explican cómo las fuerzas afectan el movimiento y dirección de los cuerpos celestes, permitiendo predecir trayectorias usando dichas leyes.

  • ¿Qué fenómeno nuevo explica la teoría de la relatividad de Einstein respecto a las leyes de Newton?

    La teoría de Einstein explica las discrepancias en las leyes de Newton, como la órbita de Mercurio, introduciendo conceptos como la curvatura del espacio-tiempo.

  • ¿Cuáles son algunas limitaciones de las leyes de Newton?

    Las leyes de Newton fallan bajo condiciones extremas de gravedad, como cerca de agujeros negros o cuando se trata del universo temprano, donde la relatividad general es más precisa.

Voir plus de résumés vidéo

Accédez instantanément à des résumés vidéo gratuits sur YouTube grâce à l'IA !
Sous-titres
en
Défilement automatique:
  • 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
Tags
  • Newton
  • gravedad
  • mareas
  • relatividad
  • bloqueo de marea
  • rotación de la Tierra
  • satélites
  • cometas
  • astronomía
  • Einstein