AST101 part 2

Newton: Speed

The rate of change of position.

Newton: Velocity

Speed and direction

Newton: Acceleration

Rate of change of velocity

Newton’s first Law:

An object in motion remains in motion unless acted upon by an outside force

Newton’s second law:

Acceleration is proportional to Force and inversely proportional to mass

F = mA

• More Force means more acceleration

• More Mass means less acceleration

Newton’s third law:

For every force, there is always an equal and opposite reaction force.

Momentum

Mass times Velocity

p = mV

In close system, momentum is conserved

Angular Momentum:

Mass times velocity times distance

w = mVr

In a closed system, angular momentum is conserved

Angular Momentum and Orbits:

Distance is large — Speed is small

Distance is small — Speed is large

Newton’s Universal Law of Gravitation

There is a force between any two objects in the Universe.

• force is proportional to: product of the masses of each object

• force is inversely proportional to the square of the distance.

Newton’s Universal Law of Gravitation — cont.

The force depends on M1 times M2.

• Double the mass of either object = double force

• Half the mass of either object = half force

• Double distance = reduce force by d²

• Half distance = reduce by d²

Acceleration Due to Gravity

Near the Earth, with no air resistance, all objects would speed up by 10m/s every second.

Freefall

Only force acting on an object is gravity

Freefall in space — orbit

Travelling around 26,000 km/h – force required go in a circle is the same as the force of gravity.

Orbits

Velocity highest closest to center of mass — perihelion, biggest angle to orbit

Velocity lowest farthest from center of mass — aphehelion, smallest angle to orbit

Moon’s gravity on earth

Tides — moon

The varying gravitational force squeezes both the Earth and the moon

• oceans respond to tidal forces from the moon

• friction with rotating earth causes tidal bulge to lag behind

• applies force on earth, causing rotation to slow down (14h to 24h)

Tidal locking

same face always facing

Tides — sun

The Sun also causes tidal forces on the Earth!

• 2 tides

• facing moon and facing sun

Spring tide

In a full moon or new moon, tidal forces from the moon and the earth add

• twice a month

• largest tides

Neap tide

If quarter moons, Tides from sun cancel moon’s tides

• twice a month

• smallest tides

Tides summary

There are two high tides and two low tides per day!

Distances

Diameter of earth = 12k km (1 earth unit)

Diameter of the sun = 1.3 million km (129 earths) 

Distance from earth to sun = 1 AU

Masses

Mass of earth = 5.97x10^24kg 1 earth unit

Mass of sun = 333k earths

The sun is white, not yellow

Atmosphere scatters light from the sun 

• In daytime sun is white

Why is the sunset red?

Unscattered red light 

• When red light hits the atmosphere, it passes right through 

• Gone through a lot of air = dimmer

Cross section of the sun

• Core

• Radiative zone

• Convective zone

• Photosphere

• Corona

Plasma

At high temps, electrons are stripped away from the nucleus = this state is called plasma

Where is the energy coming from? NOT BURNING

Nuclear Fusion in the sun

Converting 4 protons = 2 positrons (positively charged electrons) + 2 neutrinos + 2 gamma rays + 1 helium nucleus

• lower mass than starting — released as energy

E = mc²

A lot of energy from a small bit of mass

Fusion is hard.

The positive charge on the protons makes them repel each other

• Needs high temperatures (millions of degrees)

  • Needs high speeds

• Also needs high density — more collisions

Core is 160 times denser than water

Pressure, Temperature, and Density

Higher temp = higher speed, higher pressure

Higher density = higher pressure

Hydrostatic equilibrium in the sun 

Force of pressure in the sun is the same as the force of gravity — sun is stable

• more density

• more fusion

• higher temp

• higher pressure

• core expands

• density drops

• equilibrium restored

Nuclear fission

• Neutrons can hit an atom’s nucleus 

• Becomes unstable

• Split the atom

• Total mass is less than start

• Releasing energy and other neutrons

• Chain reaction

Structure of the sun

• Core: fusion, 10mil C, 100X density of water

• Radiative: hot but calm, few million C, density of water

• Convective: hot air rising, cooling, then falling (brings heat to surface), hundreds of thousands C, density of styrofoam

The Surface of the Sun

Bright regions: Hot plasma rises from below

Darker regions: cooler plasma sinking

(convection)

Sunspots

Sunspots are cooler spots on the surface of the Sun.

(4000 C rather than 5500 C)

Sunspots and Solar Flares

UV Lightshows very hot plasma around sunspots

• The filaments follow Magnetic field lines

• Sunspot activity is on an 11 year cycle — correlates with radioactivity from solar flares

How do we know? Vibrations

The Sun vibrates, kind of like a bell

• Observations of vibrations on surface show the interior structure of the Sun

• Vibrations match what is predicted by the models

How do we know? Neutrinos

The models predict a flux of Neutrinos from the core of the sun.

These Neutrinos are measured!

Emission

All the light came from some sort of emission

Reflection

• Light bounces off something that is reflective (straight lines) – in one direction

• Reflection doesn't have to be 100%, can be partial reflection

Scattering

Scattering is reflection in all directions (rough surface)

• Only a certain wavelength (colour) is scattered

• Things have colour because of the wavelength that is scattered (or coloured emission)

• Every other colour got absorbed

Absorption

For black objects, all colours of light are absorbed

• If you can see it, it's not black

Light colours vs dark colours

• Light – all get reflected, some more than others

• Dark – everything absorbed, some more than others

• White – all get reflected equally

Transmission

• Light comes along some object, goes through, and comes through the other side 

• Semi-transparent (some colours get absorbed) vs transparent

White light from the sun is colour of every wavelength

• If the sun was orange the beam would be orange 

• White objects reflect all light equally

How do screens make their colours?

By adjusting RGB, can get emissions of different colours

• White – All colours on

• Black – all lights off

• Yellow – red and green

• Cyan – green and blue 

• Purple – red and blue

Waves

Wavelength: distance between peaks

Amplitude: height of peaks

Frequency: how often the peaks arrive

Light is an Electromagnetic wave (what is purple)

ALL light (in a vacuum)

• Travels at 300,000 km/s 

• Same speed 

• The wavelength or frequency determines the colour 

  • Shorter wavelength – bluer

  • Longer wavelength – redder

  • Purple? – red light sensors have a leak for sensitivity to blue light

Electromagnetic spectrum

Thermal Radiation

Anything that is ‘warm’ glows

The temperature of the object effects its spectrum

• hot things brighter

• hot things peak at a shorter wavelength

Planck spectrum

Intensity x Wavelength

Hot Gas Emssion

• When low pressure gas is excited, it glows with distinct colours 

• Excite electrons, forming plasma, calms down, emit light

Hot Gas Emssion — emission lines

Much of the light comes out in specific colors – called emission lines

• each element has its own pattern

Energy Levels

Different transitions give light of different colors!

Absorption lines and Emission lines

Thermal radiation from?

From a hot dense source

Emission line spectra

From hot low density gas

Absorption line spectra

From cool low density gas with a hot source behind it

Understanding the Sun’s Spectrum

The Sun’s spectrum is continuum plus absorption lines

• Continuum is due to opaque, high density hot interior (blackbody)

• Absorption lines are due to cooler gas in the photosphere

Examples of Spectra: The sun from space

Stars (like the Sun): Mostly a continuous spectrum, but with emission and absorption lines

Examples of Spectra: The sun from Earth

The Earth’s atmosphere has huge absorption lines from greenhouse gasses - Especially in the infrared

The Moon’s spectra

Reflection of the Sun’s thermal spectrum

Thermal emission from the warm rock

• No atmosphere, so no absorption lines

Nebula

Nebula produce emission lines

• lines used to determine composition

The spectrum of Mars from space

• hot gas above main atmosphere

• red light from sun scattered

• CO2 atmosphere

• Mar’s thermal spectrum

Light can tell us about it’s source!

Temperature:

• location of the peak of spectra

• emission and absorption lines

Density:

• emission/absorption lines

• width of the lines

Composition:

• each atom has unique lines

Doppler Effect

Sound is a presure wave, Pitch is frequency

• Source is coming towards = pitch (freq) is higher

• Source is going away = pitch (freq) is lower

Doppler Effect for light

Moving away = redshift

Moving toward = blueshift

Molecular clouds

In galaxies

• Mix of gas and dust

• ¾ hydrogen

• ¼ helium

• Traces of other elements

• Appears black because the dust blocks light

Can we see inside molecular?

Molecular clouds are very cold (-260celcius)

• Measured spectrum and see peak 

• Sub-millimetre light 

• Very dim and cold

• Not visible to the eye

Step 1: Molecular Cloud

Mix of gas and dust

Step 2: Protostar

Blobs of denser and hotter matter

Attract more matter due to higher gravity

AND higher pressure in the center

• Higher density = higher pressure

• Higher temp = higher pressure

More gas gets pulled in, core becomes = denser, hotter = eventually enough for fusion

Step 3: Main Sequence Star

• Hydrostatic equilibrium in a star

• Star starts out with ¾ hydrogen and ¼ helium

• In the core, fusion is converting hydrogen into helium

• Helium content increases

Step 4: Hydrogen Shell burning Red Giant

• Core begins to cool and shrink

• Collapse stopped by degeneracy pressure – all atoms as close as they can get

• Inert helium core

• Hydrogen pulled inside starts to fuse – more energy than normal

• Star starts to expand into red giant

Step 5: Helium Core burning Red Giant

• Eventually, add enough helium from hydrogen shell burning to burn helium

• Helium into oxygen and carbon

• And also hydrogen shell burning

Step 6: Helium Shell burning Red Giant

• Inert carbon core provides enough pressure for helium shell burning

• And hydrogen shell burning

• Thousands of times more energy

• Star expands by a factor of 1000

Step 7a: planetary nebula

• Increasing energy coming out blows off the hydrogen and helium envelope

• Lit up by hot core = planetary nebula

• Can disperse and become new molecular clouds

Step 7b: White Dwarf

• What's left? Carbon and oxygen core

• White dwarf – extremely dense and inert

• Starts extremely hot – Cooools down for billions of billions of billions of years

• Final state is unknown

Terrestrial Planets

• Small

• Rocky

• Relatively thin or no Atmosphere

• Few moons

• Made from Heavy Elements

Jovian Planets

• Large.

• Gas + Liquid.

• Many moons.

• Mostly light elements

Observations

• inner planets rocky, outer planets gas/ice

• planet orbit in ecliptic plane

• planet orbit in same direction as sun’s rotation

• moon’s orbit most in same direction

Exceptions

• earth, saturn, and uranus are tipped

• venus rotates backwards very slowly

• triton (neptune moon) orbits out of plane and backwards

The Nebular Hypothesis

• As protostar forms, conservation of angular momentum makes it spin very fast

• Collisions between particles flatten the orbit — forming disk of gas and dust

• ALL young stars have this (shape varies)

• Small bits stick to larger bits

• Eventually gravity pulls them together to form planets

The Frost Line

The closer to the protostar, the hotter it is

• Distant disk is cold enough for light molecules (methane) to condense/freeze

• Near disk only heavy molecules (like metals) can condense

Frost line — cont.

• Disk is 98% hydrogen and helium

• 2% everything else

• Outside frost line, most of everything else can condense

• Inside frost line only metals — a lot less material

Terrestrial Planets form inside the frost line!

Heavy elements, small because less material

Jovian Planets form outside the Frost Line!

Rocks, metal, and ice

• Larger cores use gravity to accrete large gas envelopes

• Each planet has its own disk, which then forms moons

Not all planetesimals end up as parts of planets.

Inner solar system = rocky asteroids

Outer solar system = icy comets

The Heavy Bombardment Period (what shows lots of collisions)

Early on lots of planetesimals (asteroids and comets)

• Collisions frequent

• Surfaces of airless bodies (e.g. moon) show lots of collisions

• Far fewer planetesimals now

The Age of the Solar System

Radioactive materials decay into other elements

E.g. potassium-40 decays into argon-40 (1.25 billion years half life)

By looking at ratio of elements, can determine age

The age of earth

• Based on the ratio of Potassium-40 to Argon-40

• Earth’s oldest rocks are 4.55 Billion years old

• The Universe is about 3 times older than the Earth.

Where did the moon come from?

Moon is made of same stuff as Earth’s crust

• planet around the size of mars crashed into earth

• most material fell back down to earth

• small bit stayed = moon

Other exceptions from?

Tipped rotation = giant collisions

Venus rotating backwards = collisions?

Triton = probably got captured into neptunes orbit

Proplanetary disk inside frostline

• 0.2% metal (solid)

• 0.4% rock (solid)

• 1.4% hydrogen compounds (gas)

• 98% helium and hydrogen (gas)

Only metal and rock can from planetesmials

Proplanetary disk outside frostline

• 0.2%: Metal (Solid)

• 0.4%: Rock (Solid)

• 1.4%: Hydrogen compounds (Solid Ice)

• 98% helium and hydrogen (gas)

Metal, rock, and hydrogen compounds can form planetesimals

Creating Craters

Planetesimal striking surface with speed around 100,000km/h

• Vapourises rock and creates enormous explosion

• Crater is left

• Why so few craters on earth, mars, and venus?

Craters after heavy bombardment period

Large impact can damage the lithosphere

Molten lava leaks up, flooding crater

Leaves smooth surface

Future impacts create few new craters

Happened after heavy bombardment, before moon cooled enough (doesnt happen now)

Looking inside planets: Drill holes? X-rays?

• Deepest hole is 12km 

• Earth’s radius is 6371km

• X-rays cant penetrate rock

Looking inside planets: Sound waves

Using direction and timing of earthquakes, the interior of the planet can be probed – detected by seismometers