4.3-Conservation Laws in Astronomy

In the centuries since newton first stated his laws…

Art that they are not arbitrary at all, but instead reflect deeper aspects of nature known as conservation laws

Three most important conservation laws for astronomy

Conservation of momentum, of angular momentum, and of energy

In the centuries since newton first stated his laws…

Art that they are not arbitrary at all, but instead reflect deeper aspects of nature known as conservation laws

Three most important conservation laws for astronomy

Conservation of momentum, of angular momentum, and of energy

Law of conservation of momentum

The principle that, in the absence of net force, the total momentum of a system remains constant

• As long as there are no external forces, the total momentum of interacting objects cannot change; that is, the total omentum is conserved

• Can gain or lose momentum only if some other objects momentum changes by a precisely opposite amount

Why is the law of conservation of momentum implicit in newtons laws?

• Newtons second law tells us that when one pool ball strikes another, it exerts a force that changes the momentum of the second ball

• at the same time, newtons third law tells us that the second ball exerts an equal and opposite force on the first one – which means that the first balls momentum changes by precisely the same amount as the second Pauls momentum, but in the opposite direction

• Combined momentum of the two balls remains the same both before and after the collision

• External forces are accelerating the balls

Ex of conservation of momentum: rockets

• How do you fire a rocket engine, the total momentum of the rocket in the hot gases it shoots out the back mistake the same

• Other words, the amount of forward momentum the rocket games is equal to the amount of backward momentum in the gas that shoots out the back

• That is why forces between the rocket and the gases are always equal and opposite

The perspective of conservation of momentum, newtons first law…

• Makes perfect sense

• No net force acts on an object, there is no way for the object to transfer any momentum to or from any other object

• in the absence of a net force, and objects momentum must therefore remain unchanged – which means object must continue to move exactly as it has been moving

Current understanding of the universe…

conservation of momentum is an absolute law that always holds true

• ex: walls even when you jump up into the air. Legs propel you skyward, they are actually pushing earth in the other direction, given earths momentum and equal and opposite kick. However, earths huge mass renders its acceleration undetectable. During your brief flight, the gravitational force between you and earth pulls you back down, transferring your momentum back to earth. The total momentum of you and earth remains the same at all times

What keeps the planet rotating an orbiting the sun?

The law of conservation of angular momentum

The law of conservation of angular momentum

The principle that, in the absence of net torque, twisting force, the total angular momentum of a system remains constant

• Long as there is no external torque, the total angular momentum of the set of interacting objects cannot change

• Individual object can change its angular momentum only by transferring some angular momentum to or from another object

• astronomical objects can have angular momentum due to both rotation and orbit

Earths orbit around the sun

Simple formula tells us first angular momentum at any point in its orbit: angular momentum = M x V x R

• Where m is earths mass, v is its orbital velocity, and r is the radius of the orbit, by which we mean it's distance from the sun

• Because there are no objects around to give or take angular momentum from earth as it orbits the sun, earths orbital angular momentum must always stay the same

• Explains to key facts about earths orbit

Two key facts about earths orbit

1. Needs no fuel or push of any kind to keep orbiting the sun – it will keep orbiting as long as nothing comes along to take angular momentum away

2. Because earths angular momentum at any point in its orbit depends on the product of its speed an orbital radius (distance from the sun) call Mom earths orbital speed must be faster when it is near to the sun (the radius is smaller) lower what is farther from the sun (and the radius is larger)

Earths second fact

Is what Keplers second law of planetary motion states. The law of conservation of angular momentum tells us why Kepler's law is true

Why does earth keep rotating?

Earth isn't transferring any of the angular momentum of its rotation to another object, it keeps rotating at the same rate. (in fact, earth is very gradually transferring some of its rotational angular momentum to the moon, and as a result earths rotation is gradually slowing down)

Conservation of angular momentum also explains why…

We see so many spinning discs in the universe, such as the discs of galaxies like the Milky Way and discs of material orbiting young stars

• ex-ice skater spinning in place: because there is so little friction on ice, the angular momentum of the ice skater remains essentially constant. When he pulls in his extended arms, he decreases his radius – which means his velocity of rotation must increase. Stars and galaxies are both born from clouds of gas that start out much larger in size. These clouds almost inevitably have some small net rotation, though it may be imperceptible. Like the spinning skater as she pulls in her arms, they must therefore spin faster as gravity makes them shrink in size

The law of conservation of energy

The principal that energy (including mass – energy) neither created nor destroyed, but can only change from one form to another

• like momentum and angular momentum, energy can't appear out of nowhere or disappear into nothingness

• Objects can gain or lose energy only by exchanging energy with other objects

• Because of this law, the story of the universe is a story of the interplay of energy and matter: actions involves exchanges of energy or the conversion of energy from one form to another

Planetary interiors cool with time…

Because they radiate energy into space, and that the sun became hot because of energy released by the gas that formed it

Play the laws of conservation of momentum, angular momentum, and energy…

Can I understand but most every major process that occurs in the univ

In essence, energy is what?

what makes matter move

• Is this statement is so broad, they often distinguish between different types of energy

• ex: Energy we get from the food we eat, the energy that makes our cars go, and energy and light bulb emits

• we can classify nearly all types of energy into three major categories

Kinetic energy

• Energy of motion, ½mv² (m is objects mass and v is its speed)

• ex: Falling rocks, orbiting planets, and the molecules moving in the air

Radiative Energy

• energy carried by light; the energy of a photon is Planck’s constant times its frequency, h x f

• All light carries energy, which is why light can cause changes in matter

• ex: light can alter molecules in our eyes – thereby allowing us to see – or warm the surface of a planet

Potential Energy

• Energy stored for later conversion into kinetic energy; includes gravitational potential energy, electrical potential energy, and chemical potential energy

• ex: of rock perched on a ledge has gravitational potential energy because it will fall if it slips of the edge, and gasoline contains chemical potential energy that can be converted into the kinetic energy of a moving car

Energy can be converted…

From one form to another, but it can never be created or destroyed, an idea embedded in the law of conservation of energy

Regardless of which type of energy we are dealing with…

we can measure the amount of energy with the same standard units

• Americans, the most familiar units of energy or calories, which are shown on food labels to tell us how much energy our bodies can draw from the food

  • A typical adult needs about 2500 calories of energy from food each day

• In science, the standard unit of energy is the joule

• One food calorie is equivalent to about 4184 joules, so the 2500 cal use daily by typical adult is equivalent to about 10 million joules

Although there are only three major categories of energy, we sometimes…

divide them into various sub categories

In astronomy, what is the most important subcategory of kinetic energy?

thermal energy

Thermal energy

The collective kinetic energy, as measured by temperature, of the many individual particles moving randomly within a substance like a rock or the air or the gas within a distant star

All objects contain…

Thermal energy even when they are sitting still, because the particles within them are always jiggling about randomly

• These random emotions can contain substantial energy: if you ever parked car due to the random atoms is much greater energy of the car moving at highway speed

How are temperature and thermal energy different?

• He measures the total kinetic energy of all the randomly moving particles in a substance

• Richard measures the average kinetic energy of the particles

• Popular object, a higher temperature simply means that the particles on average have more kinetic energy and hence are moving faster (measured in kelvin-the kelvin scale does not have negative temperatures, because it starts from the coldest possible temperature, known as absolute zero)

Turn off energy depends on temperature…

Because a higher average kinetic energy for the particles in a substance means a higher total energy

But thermal energy also depends on what?

The number and density of the particles

Ex of thermal energy depending on the number and density of the particles

• You quickly thrust your arm in and out of a hot oven and a pot boiling water

• The air in a hot oven is much higher in temperature than the water boiling in a pot

• The boiling water would scold your arm almost instantly, well you could safely put your arm into the oven air for a few seconds

• the reason Is density

• Both cases, because the air or water is hotter than your body, molecules stroking your skin transfer thermal energy to molecules in your arm

• Higher temperature in the oven needs the air molecules strike your skin harder, on average, and the molecules in the boiling water

• How does the density of the water is so much higher than the density of air (water has far more molecules in the same amount of space) many more molecules strike your skin each second in the water

• Each individual molecules that strikes your skin transfers a little less energy in the boiling water than in the oven, the sheer number of molecules hitting you in the water means that more thermal energy is transferred to your arm-that's why the boiling water causes a burn almost instantly

the environment in space provides another example of what?

The difference between temperature and heat

• Surprisingly, the temperature in low – earth orbit can be several thousand degrees

• However, Astronauts working outside in earth orbit are at much greater risk of getting cold than hot

• reason: extremely low density: although the particles striking an astronaut spacesuit may be moving quite fast, there are not enough of them to transfer much thermal energy

How do astronauts become cold in space?

You may wonder how the astronauts become cold given that the low density also means the astronauts can't transfer much of their own thermal energy to the particles in space. It turns out that they lose their body heat by emitting thermal radiation

What two types of potential energy are important in astronomy?

Gravitational potential energy and mass-energy

Gravitational potential energy

Energy that an object has by virtue of its position in a gravitational field; an object has more gravitational potential energy when it has a greater distance that it can potentially fall

• An objects gravitational potential energy depends on its mass and how far can fall as a result of gravity

• An object has more gravitational potential energy when it is higher and less when it is lower

Ex of gravitational potential energy

• If you throw a ball up into the air, it has more potential energy when it is high up then when it is near the ground

• He must be conserved during the balls flight, the balls kinetic energy increases when its gravitational potential energy decreases, and vice versa

• By the ball travels fastest (has the most kinetic energy) when it is closest to the ground, where it has the least gravitational potential energy

• The ball is, the more gravitational potential energy it has in the slower the ball travels (less kinetic energy)

An object very close to earth surface…

Gravitational potential energy of MGH, where m is its mass, g is the acceleration of gravity, and h is ist height above the ground

Before a star forms…

• its matter is spread out in a large, cold cloud of gas

• Most of the individual cast particles are far from the centre of this large cloud and therefore have a lot of gravitational potential energy

• Who is Louis gravitational potential energy as the cloud contracts under its own gravity, and this lost potential energy ultimately gets converted into thermal energy, making the centre of the cloud hot

Einstein discovered what?

• that mass itself is a form of potential energy, often called mass– energy

• The amount of potential energy contained in mass is described by Einstein's famous equation- E =mc²

  • E is the amount of potential energy, m is the mass of the object, and c is the speed of light

• this equation tells us that a small amount of mass contains a huge amount of energy

Mass-energy

Potential energy of mass, which has an amount given by the famous formula E = mc²

Example of E=mc²

• A small amount of mass contains a huge amount of energy

• He released by a 1–megaton H–bomb, which could destroy a city out to a radius of about 10 km, comes from converting only about 0.1 kg of mass into energy

• Generates energy by converting a tiny fraction of its mass into energy through a similar process of nuclear fusion

What else can Einstein's formula tell us?

That mask can be converted into other forms of energy, it also tells us that energy can be transformed into mass

• This process is especially important in understanding what we think happened during the early moments in the history of the universe, when's all the energy of the big bang turned into the mass from which all objects, including us are made

• Scientists also use this idea to search for undiscovered particles of matter, using large machines called particle accelerators to create subatomic particles from energy

How do objects get their energy?

Because energy can't be created or destroyed, objects always get their energy from other objects

• Always tracing objects energy back to the big bang, the beginning of the universe in which all matter and energy is thought to have come into existence

Ex of tracing where energy came from

• You've thrown a baseball, it is moving, so it has kinetic energy

• This kinetic energy came from the motion of your arm as you threw it

• In turn your arm got its kinetic energy from the release of chemical potential energy stored in your muscle tissues

• Your muscles got this energy from the chemical potential energy stored in the food to eat

• The energy stored in the foods you ate came from sunlight, which plants convert into chemical potential energy through photosynthesis

• Radiative energy of the sun is generated through the process of nuclear fusion, which releases some of the mass – energy stored in the sons supply of hydrogen

• Yes – energy stored in the hydrogen came from the birth of the universe in the big bang

• Do you throw the ball, its kinetic energy will ultimately be transferred to molecules in the air or ground. It may be difficult to trace after this point, but it will never disappear