Lecture3 part3 video

Summary

In 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

• 🔴 Newton's third law of motion states that for every action, there is an equal and opposite reaction.
• 🌍 The gravitational force between two objects is directly proportional to their masses and inversely proportional to the square of the distance between them.
• 🌕 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.
• 📏 The gravitational constant (G), crucial for calculating gravitational force, was measured by Henry Cavendish in 1798.
• 🌟 The mass of celestial bodies like the Moon and the Sun can be determined using the gravitational constant and Newton's laws.
• 🌐 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.
• 🌑 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.
• 🌞 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.
• 🚀 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.
• 🌌 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 × 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

00:00

📚 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.

05:03

🌐 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.

10:04

🚀 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.

Keywords

💡Newton's Third Law of Motion

Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction. This fundamental principle is central to understanding how forces interact in the physical world. In the script, the law is illustrated with the example of two kids on skateboards pushing against each other, resulting in both moving apart due to the equal and opposite forces exerted. This law is crucial for comprehending the mutual gravitational attraction between celestial bodies like the Earth and the Moon.

💡Force

Force is a push or pull upon an object resulting from its interaction with another object. In the context of the video, force is discussed in relation to Newton's laws of motion, particularly the third law, which deals with the forces between objects. The script uses the example of a person pushing against a wall or a chair to demonstrate how forces are reciprocal; the wall or chair pushes back with an equal and opposite force.

💡Mass

Mass is a measure of the amount of matter in an object and is an intrinsic property that determines the strength of its gravitational attraction. The video script mentions mass in relation to Newton's law of universal gravitation, where the gravitational force between two objects is directly proportional to the product of their masses. The script also contrasts the mass of the Earth, Moon, and Sun to explain their gravitational interactions.

💡Gravity

Gravity is the force that attracts two objects with mass towards each other. The script explains gravity through Newton's law of universal gravitation, which quantifies the gravitational attraction between two masses and how it decreases with the square of the distance between them. The concept is further elaborated upon with the discussion of how gravity influences tides and the ability of planets to hold onto their atmospheres.

💡Orbit

An orbit is the curved path that an object in space takes around another object due to the force of gravity. The script refers to orbits when discussing how the Moon, despite the gravitational pull from the Earth, does not crash into it because it is in orbit. Orbits are a key concept in understanding the motion of celestial bodies and are influenced by both the mass of the objects and the distance between them.

💡Tides

Tides are the regular rise and fall of sea levels caused by the gravitational pull of the Moon and, to a lesser extent, the Sun. The script mentions that the Moon's gravitational pull on the Earth is responsible for the tides in the ocean. This phenomenon is a direct consequence of Newton's Third Law, as the Earth also pulls on the Moon with an equal and opposite force.

💡Surface Gravity

Surface gravity refers to the force of gravity experienced at the surface of a planet or celestial body. The script explains that surface gravity is determined by the mass of the object and its radius, and it affects how much weight an object has on that surface. It also influences the shape of celestial bodies, as larger objects with more mass tend to be pulled into a spherical shape due to their own gravity.

💡Escape Velocity

Escape velocity is the minimum speed needed for an object to break free from the gravitational influence of a celestial body without further propulsion. The script discusses how the escape velocity of Earth is approximately 11 kilometers per second, which is the speed required to launch a spacecraft into space without it falling back to Earth. This concept is crucial for space travel and understanding the energy requirements for leaving a planet's gravitational pull.

💡Atmosphere

An atmosphere is a layer of gases surrounding a planet or other celestial body. The script explains that the Earth's atmosphere is held in place by its strong surface gravity, preventing the gases from escaping into space. In contrast, the Moon, with its lower surface gravity, does not retain an atmosphere. The presence or absence of an atmosphere can significantly affect the conditions on a celestial body's surface.

💡Spherical Shape

A spherical shape is a nearly perfect ball shape that celestial bodies tend to take due to their own gravity. The script mentions that objects with enough mass and internal gravity will be pulled into a spherical shape. This is why planets and dwarf planets are often spherical, as their self-gravity is strong enough to overcome any other forces that might distort their 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

earthís 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