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Test 2: Overview The total energy radiated from entire surface every second is called the luminosity. Thus Luminosity = (energy radiated per cm2 per sec) x (area of surface in cm2) For a sphere, area of surface is 4pR2, where R is the sphere's radius. The "Inverse-Square" Law Applies to Radiation Each square gets 1/4 of the light Each square gets 1/9 of the light apparent brightness a 1 D2 D is the distance between source and observer. The frequency or wavelength of a wave depends on the relative motion of the source and the observer. Types of Spectra 1. "Continuous" spectrum - radiation over a broad range of wavelengths (light: bright at every color). 2. "Emission line" spectrum - bright at specific wavelengths only. 3. Continuous spectrum with "absorption lines": bright over a broad range of wavelengths with a few dark lines. Kirchhoff's Laws 1. A hot, opaque solid, liquid or dense gas produces a continuous spectrum. 2. A transparent hot gas produces an emission line spectrum. 3. A transparent, cool gas absorbs wavelengths from a continuous spectrum, producing an absorption line spectrum. The pattern of emission (or absorption) lines is a fingerprint of the element in the gas (such as hydrogen, neon, etc.) For a given element, emission and absorption lines occur at the same wavlengths. Sodium emission and absorption spectra Stellar Spectra Spectra of stars are different mainly due to temperature and composition differences. 'Atmosphere', atoms and ions absorb specific wavelengths of the blackbody spectrum Interior, hot and dense, fusion generates radiation with black-body spectrum Star The Nature of Atoms The Bohr model of the Hydrogen atom: electron _ _ + + proton "ground state" an "excited state" Ground state is the lowest energy state. Atom must gain energy to move to an excited state. It must absorb a photon or collide with another atom. But, only certain energies (or orbits) are allowed: _ _ _ + a few energy levels of H atom The atom can only absorb photons with exactly the right energy to boost the electron to one of its higher levels. (photon energy α frequency) When an atom absorbs a photon, it moves to a higher energy state briefly When it jumps back to lower energy state, it emits a photon in a random direction Ionization Hydrogen _ + Energetic UV Photon _ Helium + Energetic UV Photon + _ "Ion" Atom Two atoms colliding can also lead to ionization. Radio Window 13 Optical Telescopes - Refracting vs. Reflecting Refracting telescope Focuses light with a lens (like a camera). <-- object (point of light) image at focus Problems: - Lens can only be supported around edge. - "Chromatic aberration". - Some light absorbed in glass (especially UV, infrared). - Air bubbles and imperfections affect image quality. Chromatic Aberration Lens - different colors focus at different places. white light Mirror - reflection angle doesn't depend on color. Reflecting telescope Focuses light with a curved mirror. <-- object image - Can make bigger mirrors since they are supported from behind. - No chromatic aberration. - Reflects all radiation with little loss by absorption. Image of Andromeda galaxy with optical telescope. Image with telescope of twice the diameter, same exposure time. Resolving Power of a Mirror (how much detail can you see?) Andromeda Galaxy: (a) 10 arcminutes, (b) 1 arcminute, (c) 5 arcseconds, and (d) 1 arcsecond fuzziness you would see with your eye. detail you can see with a telescope. Seeing * Air density varies => bends light. No longer parallel Parallel rays enter atmosphere dome No blurring case. Rays brought to same focus. Blurring. Rays not parallel. Can't be brought into focus. CCD * Sharp image on CCD. Blurred image. Radio Telescopes Large metal dish acts as a mirror for radio waves. Radio receiver at focus. Surface accuracy not so important, so easy to make large one. But angular resolution is poor. Remember: Jodrell Bank 76-m (England) angular resolution α wavelength mirror diameter D larger than optical case, but wavelength much larger (cm's to m's), e.g. for wavelength = 1 cm, diameter = 100 m, resolution = 20". Interferometry A technique to get improved angular resolution using an array of telescopes. Most common in radio, but also limited optical interferometry. D Consider two dishes with separation D vs. one dish of diameter D. By combining the radio waves from the two dishes, the achieved angular resolution is the same as the large dish. Orbits of Planets All orbit in same direction. Most orbit in same plane. Elliptical orbits, but low eccentricity for most, so nearly circular. Two Kinds of “Classical” Planets "Terrestrial" "Jovian" Mercury, Venus, Earth, Mars Jupiter, Saturn, Uranus, Neptune Close to the Sun Small Mostly Rocky High Density (3.3 -5.3 g/cm3) reminder: liquid water is 1 g/cm3 Slow Rotation (1 - 243 days) Few Moons No Rings Main Elements Fe, Si, C, O, N: we learn that from the spectra Far from the Sun Large Mostly Gaseous Low Density (0.7 -1.6 g/cm3) Fast Rotation (0.41 - 0.72 days) Many Moons Rings Main Elements H, He Dwarf Planets compared to Terrestrial Planets "Terrestrial" Dwarf Planets Mercury, Venus, Earth, Mars Pluto, Eris, many others Close to the Sun Small Mostly Rocky High Density (3.3 -5.3 g/cm3) Slow Rotation (1 - 243 days) Few Moons No Rings Main Elements Fe, Si, C, O, N Far from the Sun Very small Rock and Ice Moderate Density (2 - 3 g/cm3) Rotation? Few Moons No Rings Main Elements Fe, Si, C, O, N And an icy surface Early Ideas René Descartes (1596 -1650) nebular theory: Solar system formed out of a "whirlpool" in a "universal fluid". Planets formed out of eddies in the fluid. Sun formed at center. Planets in cooler regions. Cloud called "Solar Nebula". This is pre-Newton and modern science. But basic idea correct, and the theory evolved as science advanced, as we'll see. A cloud of interstellar gas a few light-years, or about 1000 times bigger than Solar System The associated dust blocks starlight. Composition mostly H, He. Too cold for optical emission but some radio spectral lines from molecules. Doppler shifts of lines indicate clouds rotate at a few km/s. Clumps within such clouds collapse to form stars or clusters of stars. They are spinning at about 1 km/s. Now to make the planets . . . Solar Nebula: 98% of mass is gas (H, He) 2% in dust grains (Fe, C, Si . . .) Condensation theory: 3 steps: 1) Dust grains act as "condensation nuclei": gas atoms stick to them => growth of first clumps of matter. 2) Accretion: Clumps collide and stick => larger clumps. Eventually, small-moon sized objects: "planetesimals". 3) Gravity-enhanced accretion: objects now have significant gravity. Mutual attraction accelerates accretion. Bigger objects grow faster => a few planet-sized objects. Result from computer simulation of planet growth Shows growth of terrestrial planets. If Jupiter's gravity not included, fifth terrestrial planet forms in Asteroid Belt. If Jupiter's gravity included, orbits of planetesimals there are disrupted. Almost all ejected from Solar System. Simulations also suggest that a few Mars-size objects formed in Asteroid Belt. Their gravity modified orbits of other planetesimals, before they too were ejected by Jupiter's gravity. Asteroid Ida The Structure of the Solar System L3 L5 L4 ~ 5 AU ~ 45 AU Interplanetary Matter: Asteroids Asteroids and meteoroids have rocky composition; asteroids are bigger. (below) Asteroid Gaspra (above) Asteroid Ida with its moon, Dactyl (above) Asteroid Mathilde Interplanetary Matter: Comets Comets are icy, with some rocky parts. The basic components of a comet Oort Cloud The size, shape, and orientation of cometary orbits depend on their location. Oort cloud comets rarely enter the inner solar system. Meteor Showers Meteor showers are associated with comets – they are the debris left over when a comet breaks up. Earth's Internal Structure How do we know? Earthquakes. See later Crust: thin. Much Si and Al (lots of granite). Two-thirds covered by oceans. Mantle is mostly solid, mostly basalt (Fe, Mg, Si). Cracks in mantle allow molten material to rise => volcanoes. Core temperature is 6000 K. Metallic - mostly nickel and iron. Outer core molten, inner core solid. Atmosphere very thin Earthquakes They are vibrations in the solid Earth, or seismic waves. Two kinds go through Earth, P-waves ("primary") and S-waves ("secondary"): Like all waves, seismic waves bend when they encounter changes in density. If density change is gradual, wave path is curved. S-waves are unable to travel in liquid. Thus, measurement of seismic wave gives info on density of Earth's interior and which layers are solid/molten. Zone with no S waves: must be a liquid core that stops them But faint P waves seen in shadow zone, refracting off dense inner core No P waves too: they must bend sharply at core boundary Curved paths of P and S waves: density must slowly increase with depth Earthquakes and volcanoes are related, and also don't occur at random places. They outline plates. Plates moving at a few cm/year. "Continental drift" or "plate tectonics" What causes the drift? Convection! Mantle slightly fluid and can support convection. Plates ride on top of convective cells. Lava flows through cell boundaries. Earth loses internal heat this way. Cycles take ~108 years. Plates form lithosphere (crust and solid upper mantle). Partially melted, circulating part of mantle is asthenosphere. When plates meet... 1) Head-on collision (Himalayas) side view 2) "Subduction zone" (one slides under the other) (Andes) 3) "Rift zone" (two plates moving apart) (Mid-Atlantic Ridge) 4) They may just slide past each other (San Andreas Fault) top view => mountain ranges, trenches, earthquakes, volcanoes The Greenhouse Effect Main greenhouse gases are H2O and CO2 . If no greenhouse effect, surface would be 40 oC cooler!