Lecture3 part3 video
Summary
TLDRIn this lecture, the focus is on Newton's third law of motion, which explains the interaction of forces between objects, creating equal and opposite reactions. The concept is expanded to include gravity, with examples like the Earth and Moon illustrating mutual gravitational pulls. The gravitational constant, first measured by Henry Cavendish, allows for the calculation of celestial body masses. Surface gravity is discussed in relation to an object's mass and density, affecting an object's shape and ability to retain an atmosphere. The lecture concludes with escape velocity, a critical factor in space travel, determined by an object's mass and necessary for overcoming gravitational forces.
Takeaways
- đŽ Newton's third law of motion states that for every action, there is an equal and opposite reaction.
- đ The gravitational force between two objects is directly proportional to their masses and inversely proportional to the square of the distance between them.
- đ Newton's third law explains why the Earth and the Moon do not collide despite their mutual gravitational attraction; the Moon is in orbit around the Earth.
- đ The gravitational constant (G), crucial for calculating gravitational force, was measured by Henry Cavendish in 1798.
- đ The mass of celestial bodies like the Moon and the Sun can be determined using the gravitational constant and Newton's laws.
- đ Surface gravity is a measure of how strong the gravitational pull is at the surface of a planet or moon, affecting an object's weight and ability to retain an atmosphere.
- đ The Moon's surface gravity is about 1/6th of Earth's, which is why objects weigh less there and why the Moon lacks a substantial atmosphere.
- đ The Sun's immense mass results in a much stronger surface gravity compared to Earth, affecting the weight of objects and the behavior of its surrounding celestial bodies.
- đ Escape velocity is the minimum speed needed to break free from a celestial body's gravitational pull; Earth's escape velocity is approximately 11 kilometers per second.
- đ The concept of escape velocity is fundamental to space travel, determining the energy required to launch objects into space or reach other celestial bodies.
Q & A
What is Newton's third law of motion?
-Newton's third law of motion states that for every action, there is an equal and opposite reaction. When two objects interact, they create equal and opposite forces.
Why do two skateboarders move apart when one pushes against the other?
-According to Newton's third law, when one skateboarder pushes against the other, the second skateboarder pushes back with an equal and opposite force, causing both to move apart.
How does the mass of an object affect its interaction with forces?
-The mass of an object determines the force it exerts when interacting with another object. A larger mass results in a stronger force, while a smaller mass results in a weaker force.
What is the relationship between the Earth and the Moon according to Newton's law of universal gravitation?
-The Earth and the Moon exert gravitational forces on each other, with the force being directly proportional to their masses and inversely proportional to the square of the distance between them.
Why don't the Earth and the Moon collide despite their mutual gravitational pull?
-The Earth and the Moon do not collide because the Moon is in orbit around the Earth, maintaining a balance between the gravitational pull and its orbital velocity.
What is the gravitational constant, and who measured it?
-The gravitational constant, denoted as G, is a small number that was measured by Henry Cavendish in 1798. It is approximately 6.67 Ă 10^-11 m^3 kg^-1 s^-2.
How does the gravitational constant help in measuring the mass of celestial bodies?
-Once the gravitational constant is known, it can be used in conjunction with Newton's law of universal gravitation to calculate the mass of celestial bodies by observing their gravitational effects.
What is surface gravity, and how does it relate to the mass and radius of a celestial body?
-Surface gravity is the force of gravity experienced at the surface of a celestial body. It is determined by the mass of the body divided by the square of its radius.
Why does the Earth have an atmosphere while the Moon does not?
-The Earth has a stronger surface gravity than the Moon, which is sufficient to hold onto atmospheric particles and prevent them from escaping. The Moon's lower surface gravity cannot retain an atmosphere due to the Sun's energetic radiation.
What is escape velocity, and how does it relate to the mass of a celestial body?
-Escape velocity is the minimum speed needed to break free from a celestial body's gravitational pull. It is higher for larger, more massive bodies and lower for smaller ones.
Why is it difficult to launch objects from Jupiter compared to the Earth?
-Jupiter has a much larger mass than Earth, resulting in a higher escape velocity. This means more energy and rocket fuel are required to launch objects from Jupiter's surface into space.
Outlines
đ Newton's Third Law and Gravity
The lecture segment delves into Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. This principle is illustrated through the example of two kids on skateboards pushing against each other, resulting in both moving apart due to the mutual forces. The concept is extended to gravity, explaining how objects with mass exert gravitational forces on each other. The Earth and the Moon are used as an example to demonstrate how they pull on each other without colliding due to the Moon's orbital motion. The segment also touches on the universal law of gravitation, which is dependent on the masses of the objects and the square of the distance between them. The gravitational constant 'G', first measured by Henry Cavendish, is crucial for calculating the force of gravity and, by extension, the mass of celestial bodies. The lecture concludes with a mention of how these principles relate to phenomena like tides and the ability to measure the mass of objects in orbit.
đ Surface Gravity and Its Effects
This paragraph explores the concept of surface gravity, which refers to the strength of gravity at a planet's surface. It explains how surface gravity affects an object's weight and the ability of a celestial body to maintain a spherical shape and retain an atmosphere. The Earth's surface gravity is used as a baseline, with comparisons made to the Moon, where surface gravity is one-sixth that of Earth, and to Jupiter and Saturn's moon Titan, which have different surface gravity effects due to their respective masses and distances from the Sun. The formula for surface gravity is introduced, highlighting its dependence on an object's mass and radius. The paragraph also discusses the relationship between surface gravity and escape velocity, which is the minimum speed needed to break free from a celestial body's gravitational pull. The significance of escape velocity in space travel is emphasized, particularly in the context of launching from Earth and the challenges of leaving larger planets like Jupiter.
đ Escape Velocity and Space Travel
The final paragraph of the script focuses on escape velocity, defining it as the speed required for an object to escape a celestial body's gravity without further propulsion. It explains that larger objects have higher escape velocities due to their greater mass. Earth's escape velocity is given as approximately 11 kilometers per second, a speed that requires significant energy to achieve. The concept is contrasted with black holes, where the escape velocity exceeds the speed of light, making escape impossible. The paragraph also discusses the practical implications of escape velocity for space travel, including the challenges of launching from Earth and the increased difficulty of leaving larger planets like Jupiter. The segment concludes with a teaser for upcoming lectures, which will cover modern astronomy, the study of the universe through light, and advancements in physics and telescope technology.
Mindmap
Keywords
đĄNewton's Third Law of Motion
đĄForce
đĄMass
đĄGravity
đĄOrbit
đĄTides
đĄSurface Gravity
đĄEscape Velocity
đĄAtmosphere
đĄSpherical Shape
Highlights
Newton's third law of motion involves equal and opposite forces when two objects interact.
The interaction between objects results in both objects moving apart due to the reaction force.
The mass of objects affects the outcome of force interactions, with lighter objects moving more easily.
Newton's law of universal gravity describes the force between two objects based on their masses and the distance between them.
The moon and Earth exert equal and opposite gravitational forces on each other, preventing them from colliding.
Tides are influenced by the gravitational interaction between the Earth and the moon.
The gravitational constant 'G' was measured by Henry Cavendish, allowing for the calculation of masses of celestial bodies.
The Greeks' understanding of the relative sizes of celestial bodies was enhanced by the inclusion of the gravitational constant.
Kepler's third law, when modified with Newton's law of gravity, can be used to calculate the mass of objects in orbit.
Surface gravity is determined by an object's mass and radius, affecting how much weight is experienced on its surface.
Objects with sufficient mass and density have enough surface gravity to form spherical shapes.
The Earth's strong surface gravity allows it to hold an atmosphere, unlike the moon with its weaker gravity.
Escape velocity is the speed required to break free from a celestial body's gravitational pull.
The Earth's escape velocity is approximately 11 kilometers per second, a significant challenge for space travel.
Objects with higher mass, like Jupiter, have higher escape velocities, making it difficult to leave their gravitational influence.
The concept of escape velocity is crucial for understanding how objects can be launched into space or orbit.
Transcripts
all right everyone welcome to the last
part of lecture 3 we are in this Bart
going to talk about Newton's third law
of motion and some of the consequences
having to do with gravity so lute up on
the first law in the second law the
third law of motion Newton's third law
has to do with the forces and how
objects interact with forces when two
objects interact they create we're known
as equal and opposite forces so imagine
you had two kids on two skateboards okay
one kid pushes against the other but
you'll notice that even if just one kid
pushes against the other they both go
apart and the reason for this is this
one kid pushes against the other and
because Newton's certain law Newton's
third law of motion the other object
pushes back with an equal and opposite
force this is true for any two objects
if I push on a wall it pushes back on me
with equal and opposite force by push on
a chair it pushes back on me with equal
and opposite force although when I push
on a chair the chair moves and I don't
that's because the chair has less mass
than I do when I push in the wall I move
in the wall doesn't that's because the
wall has more mass than me now this
applies to Newton's third law well sorry
to Newton's law of universal gravity
remember Newton's law says the force of
gravity between two objects is the mass
of those two objects combined divided by
the distance squared but let's say over
here we have the moon and over here we
have the earth okay if the earth is
pulling on the moon well Newton's third
law says the moon is also pulling on the
earth
they're tugging towards each other the
only reason they don't hit each other is
because the moon is in orbit and go back
to the previous lecture to talk about
orbits
things that go around something else
without ever hitting them now the moon
pulls back on the earth as much as the
earth pulls on the moon this actually we
will talk about this later has to do
with things like tides and tides in the
ocean I have to do this kind of gravity
now gravity remember the formula is
force is equal to some kind of constant
G times mass times mass divided by
distance radius squared so this is just
meant to be a mass so two masses on top
but there's also this gravitational
constant G now Newton was not able to
measure the gravitational constant it
wasn't until a couple hundred years
later and in 1798 when a scientist named
Henry Cavendish measured this it's a
very small number that's why it was so
hard to measure it was so small six
point six seven times 10 to the negative
11 it's a very small number but once you
know what that number is what the
gravitational constant is you can then
measure the mass of objects so now
remember back in the Greeks the Greeks
understood how big the Sun was compared
to the earth and how small the moon was
compared to the earth so the Sun is a
hundred times bigger the moon is one
quarter of the size of the earth but
once you can plug the actual
gravitational constant into the
equations having to do with acceleration
orbit's you can actually measure the
mass of these objects and what we
learned is the moon is actually only
180th
of the mass of the Earth and the Sun is
more than 300,000 times the mass of the
Earth so if you used Kepler's third law
modified using Newton's law of gravity
you can actually figure out the mass of
objects in their orbits this leads to
another idea that we call surface
gravity now surface gravity is basically
how strong is the gravity on the planet
you're standing so here on the earth we
experience one earth surface gravity and
you weigh what you weigh but if you were
standing on something different say if
you were standing on a different planet
or say the moon well if you're on the
moon surface gravity is 1/6 of what it
is here on the earth which means you
weigh one-sixth of what you do here on
the earth on the Sun you would weigh
more Jupiter you would weigh more
although technically both of those don't
really have surfaces but this idea of
surface gravity how strongly gravity
affects the surface of planet does it's
determined by the weight so it sorry it
determines the weight of stuff that
stands on the surface but it also
influences whether or not that surface
is spherical and shape objects that are
big enough have enough internal gravity
enough service gravity that they're
pulled into spherical shapes and that's
the kind of thing we call a dwarf planet
we will talk more about that later
but anything the spherical shape is
called a planet unless it's huge call
the star but
also influences whether or not an object
can have an atmosphere so the earth the
earthĂs has a strong enough gravity that
we can hold on to an atmosphere
atmosphere of particles do not escape
the earth because the surface gravity of
the earth is high enough that those
particles are held on to because of
gravity but the moon our moon it's
smaller than the earth as a lower
surface gravity and the particles are
not held on so the moon does not have an
atmosphere it's the same distance from
the Sun that we are right but it doesn't
have an atmosphere because service
gravity is too low and the sunlight is
too energetic and it blows away any gas
the moon might have around it whereas
the earth because of a higher surface
gravity is able to hold onto those gases
and that's why we have an atmosphere now
there are other objects like our moon
the same size that are further from the
Sun so for example one of the moons of
Saturn is a moon called Titan Titan is
about the same size as our Moon
but Titan does have an atmosphere a
relatively thick atmosphere made mostly
of nitrogen now Titan can hold on to its
atmosphere
because while its surface gravity is the
same as our moon it is much further away
from the Sun so it gets less energy from
the Sun and so the particles of gas
don't have enough energy to escape so
things get a little bit complicated but
service gravity basically describes how
much an object will weigh how much all
weigh on an object and that has depends
it depends on the object's mass and its
density and so big objects strong
surface gravity small objects relatively
weak
if there is a formula for this the
surface gravity depends on the mass of
the object divided by its radius squared
and again we're talking about the
surface so it is the object's radius for
the earth the surface gravity about 9.8
meters per second squared the moon and
if you divide the Earth's gravity by the
moon's gravity you get about five point
six which means that the on the moon you
weigh about one-sixth of what you do
here on the earth Jupiter / Earth you
get about three so on Jupiter you weigh
about three times more than you do on
the earth this idea also is related to
the idea of escape velocity now escape
velocity let's say you're on the earth
if you want to throw something up into
the air well you can throw it up and if
you threw something up in the air I
threw them in the air it would go up
into the air and then come back down but
there is a speed at which would be
through an object up into the air it
would never come back down now it will
always slow down as it goes up but at
this velocity it will never come back
this is called escape velocity the
bigger an object is by mass the larger
the escape velocity so if you're trying
to launch something off the surface of
the earth into space
well if you're trying to go to Mars you
have to get escape velocity if you're
only going to the moon well you don't
have to get quite escape velocity
because again the moon is in Earth's
orbit so it's still part of the Earth's
gravity but you have to get close this
is why we build giant rocket ships
because escape velocity from the earth
turns out to be a pretty big number it's
around 11 kilometers per second that's
something like seven
half miles per second that's fast it
takes a lot of energy to get out now
there are things in space like black
holes where the escape velocity is
literally greater than the speed of
light which means nothing can escape but
the earth 11 km/s things can escape we
can get away from the Earth's gravity
larger objects have greater escape
velocities which for instance is why we
can't go to Jupiter and go into Jupiter
and then get things out of Jupiter
because getting to Jupiter is easy but
any things away from Jupiter they have
to have a really high escape velocities
okay so if you were to for instance go
into Jupiter
well to get out you would need a lot of
rocket fuel that's hard to do so escape
velocity we use it all the time when we
talk about getting to other objects like
the moon or other planets or even
getting into orbit around the Earth so
like space stations and whatnot in orbit
around the Earth you don't have to quite
be going to escape velocity to get there
because you haven't escaped the Earth's
gravity but you do have to be going fast
again from the earth escape velocity 11
kilometers per second it's pretty fast
it's pretty fast and again you could do
this calculation pretty simply I'm not
gonna ask you guys to do it but or to do
the actual math but it's a pretty simple
calculation to do more mass higher
escape velocity
okay and this is how we get away from
the earth it's the only way we can see
if the earth is to actually get to a
velocity where we can escape the Earth's
gravity all right now in the next couple
of lectures we're going to be talking
about moving towards modern astronomy
and about how we now study the universe
so light and more modern ideas about
physics and telescopes so stay tuned
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