Origin of Solar System Origin of Solar System

Key Concepts: Lecture 18: Solar System Formation, LightFormation of the Solar System: the Nebular HypothesisLight: wave-like behaviorLight: particle-like behaviorLight: Interaction with matter - Kirchoff’s LawsOrigin of Solar System• Planets orbit the Sun in same direction (counter-clockwise ifviewed from above the Earth’s north pole) and in nearly the sameplane.• Most planets and the Sun also rotate in roughly this same direction,although planets can be tilted, occasionally by large angles.• Most moons orbit around their parent planet in this same direction• Solar system is differentiated– Terrestrial planets: high densities, small to moderateatmospheres, slow rotation, 0 to few moons– Jovians: low densities, thick atmospheres, fast rotation, manymoons• Asteroids are very old – primitive unevolved material - commonage of oldest solar system material: 4.6 billion years.• Comets are also very old: primitive icy fragments from Oort Cloudor Kuiper BeltOrigin of Solar System• Observations of the differentmembers of the solar systemplace constraints on theoriesof its formation– motions– chemical composition– ageOrigin of the Solar System:Nebular Hypothesis(originally due to Kant & Laplace)• Slowly rotating interstellar cloudof gas & dust• Gravitational contraction– disk flattens– conservation of angularmomentum• Sun forms at center of nebula

Conservation of MomentumMomentum = mass x velocityOther examples of conservationof angular momentumReview Newton’s Laws of Motion (Lecture 9).Newton’s 1st Law implies momentum is conserved (i.e. isunchanging) if there are no forces acting on an object.Newton’s 2nd & 3rd Laws imply that if a force is applied theoverall momentum is also conserved (i.e. unchanged) sincethere is always an opposite force of equal strength.Conservation of Angular MomentumAngular momentum ! mass x rotation rate x radius 2An object of constant mass will spin faster as it contractsIce skater video….Origin of the Solar System• All cold interstellar gas we seetoday has some small dust grains.We think the pre-solar nebulawould have started with these also.• Growth of these grains to largersizes and eventually to formPlanetesimals• Gravity collects planetesimals toform Protoplanets• Formation of Jovians: Largeprotoplanets sweep up gas• Formation of Terrestrials: Smallerprotoplanets, in a warmerenvironment, not able to retainlarge amounts of Hydrogen gas

Origin of the Solar System• Planets form in disk ofgas and dust near centerof nebula.We can see other solar systems forming• See star formation section later in course- Orbits are all in same direction andplane. They are approximately circular.- Change in composition of planets isdue to changes in local temperature indisk: planets are forming viacondensation and accretion and disk iswarmer near the Sun, e.g. no solidwater ice inside about 4 AU.Origin of the Solar System• Asteroids– Remaining rocky planetesimals inthe inner solar system– Failed to become protoplanets dueto gravity of Jupiter• Comets– Remaining icy planetesimals inouter solar system -> Kuiper belt– Gravitational interactions withJovians flung planetesimals• Into inner solar system (deliveringsome water to Terrestrial planets)• To outer solar system – Oort cloudRecall: The Importance of Light• We can not hope to visit objects outside the solarsystem in our lifetime.• The easiest way we can learn about distant objectsis by studying the light they emit.• Using information in their light, we can measurecompositions, temperatures, distances, masses andages of astronomical objects.• As light travels at a finite speed, by lookingfurther and further away we look back further andfurther into the past.

The Wave Nature of Electro-Magnetic Radiation• Visible light is justone form of electromagneticradiation• Light often behaveslike a wave– Diffraction: wavesbend around obstacles– Interference: wavesadd their amplitudestogetherRecall: Properties of Waves• A wave is described by four properties– The wavelength (") - units of length– The amplitude of the wave– The speed of the wave (c) - units of speed length/time– The frequency of the wave (f) - units of 1/time• Three of these properties are interrelated: c = f x "Recall: Wave Nature of Electro-Magnetic RadiationAll EM radiation is composed of two waves that move together– An electric field and a magnetic field– The fields are at 90 degrees to each other– It needs no medium to be transmitted through, i.e. it can travel through avacuum– Energy is carried by the waveRecall:•EM spectrumextends fromradio to gammarays•The Earth’satmosphere onlytransmits certainfrequencies

Light Also Behaves Like A Particle!• When light interacts with matter, itoften behaves like a particle• A particle of light is called a Photon• First suggested by Max Planck (1899)– The energy of a particle of light (photon)depends only on its frequency– h is a constant known as Planck’s constant• Photoelectric effect - Einstein (1905)– Certain metals emit electrons when exposed tolight• basis of exposure meters, night vision gogglesetc...– This only happens when a high enough frequency(i.e. short enough wavelength) light is used,because a certain amount of energy is needed tofree each electron from the metal and that energymust come from a single photon of high enoughenergy. Lots of low energy photons don’t work.E = h x fWave-Particle Duality VideoWave-Particle Duality• Light sometimes behaves like aparticle, sometimes like a wave.• Traditional “particles”, e.g.electrons, protons, bullets, whenmoving also sometimes behavelike waves, but the effects are onlynoticeable on scales of thewavelength, which are typicallyminiscule and too small to see ineveryday life.• Quantum mechanics describes thebehavior of these “waveparticles”.All objects have thisbehavior, but in everyday life wedon’t notice it.particle-likewave-likeThe Interaction of Light with Matter• Matter is composed of atoms– Atoms have nuclei composed ofProtons (+ve electric charge)Neutrons (neutral)– The nuclei are surrounded by a cloud ofElectrons (-ve electric charge)– The number of protons determines whatelement it is. To be electrically neutral thenumber of electrons must equal thenumber of protons• Light typically interacts with matter byinteracting with the electrons around atoms

The Interaction of Light with Matter• The possible energies whichan electron can have arequantized: only certainparticular energies areallowed.• Electrons and photons canexchange energy– An atom can absorb aphoton by moving anelectron to a higher energystate– An atom can emit a photonby an electron moving to alower energy state– The change in the energyof the electron mustexactly equal the energy ofthe photonFinger Printing the Elements• Each type of atom (i.e. different elements likeHydrogen, Helium, Carbon, Oxygen, etc) has aunique configuration of electrons• Each type of atom has a unique set of possible energylevels• Each type of atom emits and absorbs photons with aunique pattern of energiesThe Stair Case AnalogySpectra of Atoms• You can think of the levels of anatom as being like a flight ofstairs• To step up to a higher levelrequires enough energy to lift youone or more stairs• When you come back down thestairs you give up the energy yougot by going up the stairsf

Kirchhoff’s Laws• Gustav Kirchoff derived three lawsto explain how matter and lightinteract• He noted that three types of spectraarise under different conditions– Continuous spectra– Emission line spectra– Absorption line spectraWien’s Law• Wien’s law tells you at whatwavelength (or frequency) theblackbody spectrum peaks(has the maximum value)– Hotter objects emit light thatpeaks at shorter wavelengths(higher frequencies & higherenergy photons)– Colder objects emit a spectrumthat peaks at longer wavelengths(lower frequencies & lowerenergy photons)" max = 0.29cmT (K)The Generation of Light• All dense matter with a temperature above absolute zero emits light becauseof vibrating electric charges (electrons)• The spectrum is the amount (intensity) of light at different frequencies (orwavelengths)• The peak of the spectrum dependson the temperature:hotter temperature leads to peak athigher frequencies (shorter wavelengths)• This is calledBlackbody Radiationwhich is an example of acontinuous spectrumUse of Wien’s LawWe can use Wien’s law to find the temperatures ofdistant bodies we can never visit, by measuring thewavelength (or the frequency) at which the spectrumpeaks.

• A hot and opaquemedium emits acontinuous spectrum,because the atoms arevery close to eachother which smearsout the energy levels.• This is the blackbodyspectrumKirchhoff’s 1 st Law• If a continuous spectrumpasses through a transparentgas at a lower temperature,the cooler gas will cause theappearance of darkabsorption lines, whosecolors and number willdepend on the elementspresent in the gas• This is because particularenergies are absorbed by thecool gas (electrons are raisedto higher energy levels). Thenwhen the electrons fall downand new photons emitted,these photons can go in anydirection: most do not gothrough the slit.Kirchhoff’s 3 rd LawAn absorption spectrumis produced when lightpasses through a cold gas• A hot, transparent, lowdensitygas produces aspectrum of bright emissionlines. The number and colorsof the lines depend on whichelements are present. Becausethe atoms are quite far apartthe energies of the photonsare not smeared out.• The emission lines are due toelectrons moving from higherto lower energy statesKirchhoff’s 2 nd LawSummary of Kirchoff’s Laws