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AS 101 Final Exam Notes.docx

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Victor Arora

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AS 101 2012 Light & Matter Equations  An equation is a concise way to state the relationships between different quantities  An equation is also like a balancing scale-the quantities on one side of the equal sign must balance the quantities on the other side Equations: Universal Gravity  For example, the size of the gravitational force of attraction between two bodies (Let’s call it F1->2 can be summarized as: F1->2 Gm 1 2 2 d  M 1nd m a2e the masses of the two bodies  d is the distance separating the centres of the two bodies  G Newton’s Gravitational Constant (a fixed number)  You must keep the scale balanced! So: o If I increase1m , the1->2ust increase by the same factor o If I increase d, then Fmust decrease by the same factor squared 1->2 Spectrograph Spreads out Light  Light passing through a prism bends at different angles for every wavelength  A diffraction grating reflects (or transmits) light at different angles for different wavelengths also, but with greater dispersion (bending)  Three categories of spectral features can be present o The spectrum of an object gives clues about how the light was produced The Atom and Subatomic Particles  Massive, compact nucleus made up of: o Protons (positive charge); and o Neutrons (neutral)  Low mass, large electron cloud (negative charge)  Every element has a different number of protons. For a given element: o A different number of neutrons is an isotope of that element o If the number of electrons is equal to the number of protons, the atom is neutral; otherwise the atom is an ion Temperature, Heat  The particles that make up an object are constantly moving (e.g. electrons and atoms)  Averaging the random motion of these particles is one way to define the temperature of an object  This is why the Kelvin scale starts at absolute zero (-273 C), when there is absolutely no random particle motion How to Make Things Glow  The simplest way to produce EM radiation is to heat an object  Dense objects will product white light (a smooth mixture of colours)  A thin glass will produce light at specific colours o E.g. “neon” sign, fluorescent bulb, nebulae 1 AS 101 2012 Thermal Radiation  Imagine heating a nail-as its temperature rises, its colour changes from: o Red  Orange  Yellow-White  The object glows because a greater temperature corresponds to more particle motion, and more frequent collisions  Part of the energy of motion is converted to electromagnetic radiation  A hot opaque object emits thermal or blackbody radiation o Blackbody=perfect absorber AND perfect emitter Thermal/Blackbody Radiation  A continuous spectrum: radiates at all wavelengths  Wien’s Law: the wavelength of maximum emission for a glowing object decreases as its temperature increase o Λmaxis inversely proportional to temperature o Hotter  faster particles  stronger collisions  emit more energetic photons  The colour of a star tells us its relative temperature  Hotter objects also emit a greater overall flux than cooler objects o More frequent collisions  emit more energetic photons more frequently  Stefan-Boltzmann Law: as the temperature of a glowing object increases, the blackbody curve rises everywhere  A small increase in temperature causes a big increase in energy emitted Bohr Model  Negative electrons orbit the positive nucleus because of an attractive Coulomb force  To create an ion, the atom must be hit with an amount of energy greater than the binding energy for an electron in a particular orbit  Only certain very specific orbits are permitted-there is no in between  The pattern of specific orbits is unique for each element, isotope, and ion Excitation  Each orbit is an energy level  Electrons can move to another level if enough energy is supplied to make up the difference between levels Which Photons Excite Electrons?  Photons of the wrong wavelength are transmitted  If the wavelength corresponds to the exact amount of energy, the electron absorbs photon and becomes excited (excitation by collision is also possible)  The extra energy is released as new photons after a short while, and electron falls back to a lower level Chemical Fingerprints  Each neutral atom/isotope/ion has a different sets of levels  will emit or absorb at unique wavelengths  The characteristic wavelengths of light emitted or absorbed show up as lines in a spectrum and can be used to identify elements present o E.g. neon signs, sodium lamps  We can measure the Doppler Shift of individual lines 2 AS 101 2012 Recipe: Making a Real Spectrum 1. A hot, dense object emits a continuous spectrum a. All the wavelength are emitted, in all directions 2. A gas cloud absorbs some wavelengths, and transmits others 3. The wavelengths the cloud absorbs, are reradiated in random directions 4. What you see depends on the direction you are looking at (your line of sight) Summarizing Kirchoff’s Laws 1. Hot, dense object produces a continuous spectrum a. Light at all wavelengths 2. Low-density gas produces an emission line spectrum a. Bright lines at specific wavelengths 3. Low-density gas in front of a hotter thermal source produces an absorption line spectrum a. Dark lines on a continuous spectrum at the same wavelengths Refraction: The Bending of Light  Recall that light can change direction when interacting with matter  Refraction is the bending of a ray of light when it passes through a new medium  Observation of prisms show refraction depends on the wavelength of light: shorter wavelengths bend more Reflecting  A ray of light will reflect from a smooth surface at the same angle that it is incident with  Special property: for parabolic mirrors, rays of light that are parallel converge (come together) at the same point Refracting Telescopes  A primary or objective lens bends light and brings it to a focus o The lens must be flawless throughout o Different wavelengths of light are focused at different locations: chromatic aberration  An eyepiece is needed to magnify the inverted (upside-down) image Reflecting Telescopes  Light bounces from a convex (inwardly curved) primary mirror  A smaller secondary mirror can be used to redirect the light (it doesn’t “get in the way”)  An eyepiece is still required to magnify the inverted image Telescopes are Light Buckets  A larger bucket collects more rain…and its raining photons  A larger mirror will produce a brighter image  Light Gathering Power (LGP): is proportional to the area of the primary mirror or lens o A two metre mirror has four times the LGP of a one metre mirror Telescopes have Resolving Power  The ability to resolve fine details is like trying to separate two faraway points of light  The wave nature of light means that two faraway points of light viewed through a telescope blue together  The size of the diffraction fringes is inversely proportional to diameter of the primary mirror… o Doubling the size of the mirror means that I can resolve twice as well  …and is also proportional to wavelength o If I observe at longer wavelengths, I will have poorer resolution 3 AS 101 2012 Eyepieces Magnify Images  The magnification of an image is equal to the ratio of the focal lengths of the telescope and the eyepiece Magnification= Focal length of telescope Focal length of eyepiece  A smaller eyepiece gives a larger magnification o But the image will be dimmer (i.e. more spread out) o Seeing also limits the magnification (atmospheric turbulence causing stars to twinkle) o Rule of thumb: max 20x the aperture (cm), 300x max Professional Astronomers Rarely Observe at an Eyepiece  What are some of the disadvantages to scientific observing at an eyepiece? o No record of the image o Difficult to do a quantitative analysis o Cannot see the entire EM spectrum CCDs Record Images from a Telescope  A CCD (charge coupled device) is a semi-conductor chip made up of millions of pixels that can each detect light  When a photon strikes an individual pixel, the signal is detected via the photoelectric effect  The exact count in each pixel is read out and stored digitally  CCDs are more sensitive and can simultaneously image bright and faint sources  Already digitized  well suited for numerical analysis  Many science images are false-colour Light Pollution  Ligh9 that sprays horizontally/upwards into the sky  $10 lost annually in wasted light  One solution: shielded light fixtures Optical/Near IR Telescopes  In addition to being far from cities, telescopes are best built in: o Dry climates, often on mountains o Thinner air  more transparent o Airflow not so turbulent  better seeing Cutting-Edge Observatories  Mostly in Hawaii, Chile, and Canary islands  Most large mirrors are made up of smaller segments  Adaptive Optics- observes an “artificial” laser star to decide how to finely adjust telescope mirror in real-time to compensate for seeing  Future proposed telescopes will survey the entire sky every night using Gigapixel CCDs Radio Telescopes  Radio telescopes are placed to avoid interference from civilization  Why are they so large (GBT=100m)? o Degrades at longer wavelengths (radio waves are longest) o Improves with larger “mirrors” (radio telescopes are largest) o Interferometry can further improve resolution Our Atmospheric Window Into Space Gases in our atmosphere absorb most other forms of EM radiation-we must go higher! 4 AS 101 2012 Space/Airborne Telescopes  Perfect seeing (i.e. Hubble)  Observe regions of the EM spectrum not visible from Earth o SOPHIA-a far-infrared space telescope o Spitzer, Herschel-far-infrared space telescope o WMAP, Planck- microwave space telescope  Observe high-energy phenomena o Chandra X-Ray Observatory o Compton Gamma Ray Observatory, SWIFT The Hubble Space Telescope  2.9 m telescope launched in 1990  Orbits 500 km above the Earth’s surface The Scale and Contents of the Solar System  The solar system is made up of: o 1 Sun o 8 planets o At least 5 dwarf planets o >100 natural satellites o 1000s of asteroids and comets  The sizes of the planets are tiny compared to the vast distances between them  All the planets revolve around the Sun more or less in the ecliptic plane in the same direction  The sun and most planets also rotate in this direction The Sun  Radius: 109x Earth  Mass: 333,000x Earth  Composition: 98% hydrogen and helium, 2% other gases  Age: 5 x 10 years  Surface Temperature: 5800 K  On average, just slightly denser than water o Density is mass divided by volume Mercury  Distance from Sun: 0.04 AU  Radius: 0.38x Earth  Mass: 0.05x Earth  Composition: metal and rock with large iron core; almost no atmosphere o o  Temperature: +450 C (day); -170 C (night) Venus  Distance from Sun: 0.72 AU  Size: 0.95x Earth  Mass: 0.82x Earth  Composition: rocky surface, atmosphere is 97% carbon dioxide; permanently cloudly  Temperature: 464 C  Rotates “backwards” 5 AS 101 2012 Earth  Distance from Sun: 1 AU  Composition: surface is liquid water/rocky; core is molten metal atmosphere is 78% nitrogen, 21% oxygen  Avg. Temperature: 15 C  Has one of the largest moons in the solar system Mars  Distance from Sun: 1.52 AU  Size: 0.53x Earth  Mass: 0.11x Earth  Composition: rocky, iron rich soil; thin carbon dioxide atmosphere  Temperature: -87 to -5 C  Two very small moons Jupiter  Distance from Sun: 5.2 AU  Size: 11x Earth  Mass: 318x Earth  Composition: hydrogen and helium atmosphere; large liquid metallic hydrogen interior; small heavy element core  67 moons and small ring system The Galilean Satellites of Jupiter  Lo: extreme tides, highly volcanic  Europa: iced over, possible subsurface water ocean  Ganymede: largest moon in solar system  Callisto: large, heavily-cratered iceball Saturn  Distance from Sun: 9.6 AU; Size: 9.4x Earth; Mass: 95x Earth  Composition: hydrogen and helium atmosphere; liquid metallic hydrogen interior; heavy element core; least dense  62 moons including Titan, with a dense nitrogen atmosphere…like Earth?  Ring system of ice chunks with an overall extent of 8x Saturn’s own radius, yet just 30m thick Uranus  Distance from Sun: 19 AU  Size: 4x Earth  Mass: 15x Earth  Composition: hydrogen, helium, and methane atmosphere; slushy interior (rocks, water, methane); heavy element core  27 moons and ring system  Axis of rotation is tilted by 98 (rotates backwards) Neptune  Distance from Sun: 30 AU  Size: 3.8x Earth; Mass: 17x Earth  Composition: hydrogen, helium, and methane atmosphere; slushy interior (rocks, water, methane); heavy element core  13 moons and ring system 6 AS 101 2012 Terrestrial vs. Jovian Planets Terrestrial Jovian Membership Mercury, Venus, Earth, Mars Jupiter, Saturn, Uranus, Neptune Size Small Large Distance from Sun Close Far Mass Light (less massive) Heavy (more massive) Composition, Density Rocky; more dense Hydrogen, helium, slushy; less dense Moons Less to no moons More moons Rings No rings rings Space Debris  The total mass of all the other objects is less than that of the Earth’s moon  Includes: o Asteroids (over 500 000 known)  Found throughout Solar System, but mostly between Mars and Jupiter  Average separation in asteroid belt is 1-3 million km  Rocky/metallic composition  Size: few hundred km to less than km (many more smaller ones than larger ones) 8 12 o Comets (estimated 10 to 10 )  Mostly unchanged since the time the planets were forming Asteroids have had a rough life…  Irregularly shaped (non spherical) o Forces holding the material together are greater than the force of gravity o Some are just “rubble piles”  Heavily cratered: Evidence of impacts  Some even with moons: evidence of past collisions Comets are dirty snowballs  Icy nucleus 10s of km across  Composition rock+ices: o Ices: water ice, dry ice, carbon monoxide, methane. Ammonia  If its orbit carries it toward the Sun, the warmth will cause gas and dust to be released from the nucleus  Comet tails can stretch about 10 km, always pointing away from Sun Comets can come from 2 places  Short period comets that orbit in the ecliptic come from the Kuiper Belt (beyond Neptune)  Long period comets approaching the Sun from random directions come from the Oort Cloud (about one light-year from the Sun) Shooting Stars are Really Meteors  A momentary trail of light across the sky  Source: sand and pebble-sized particles of rock, dust, or metal (i.e. from asteroids or comet tails) entering the atmosphere  Travelling at a high speed  ionize and excite atoms roughly 80 to 120 km above Earth  Easy to see, but be patient (2-100 per hour) 7 AS 101 2012 Meteorites  If a meteoroid survives the plunge, it is called a meteorite  Although meteorites are rare, about 40,000 tons a year is added to the Earth’s mass this way  Carbonaceous chondrites, are a type of meteorite that contain many low melting point compounds  Since heat would vaporize these compounds, these meteorites are likely unchanged since they formed Ages in the Solar System  Radioactive elements are atoms that have unstable nuclei; over time, they decay into more stable, lighter elements  Rocks are formed with a known proportion of radioactive elements  The proportion that remains in a rock at the present time can be used to tell us its age Radioactive Dating  The half-life of an element is the time it takes for one-half of the radioactive atoms in a sample to decay More ages in the Solar System  Another way of figuring out the age of bodies is by examining the number of craters on an object (more craters suggests an older body) The Big Bang Theory  Our whole universe was in a hot dense state  Then nearly 14 billion (13.7 billion to be more exact) years ago, expansion started, wait… o Making hydrogen and helium (15 min) o The Universe to become transparent (400,000 years) o First stars to form (400 million years) o First galaxies to form (1 billion years) o First and second generations of stars to enrich the Universe with the other elements (9 billion years) Star Formation  Observation: the visible surface of the Sun and molecular clouds have the same composition  Hypothesis: the Sun formed within a large, cool rotating molecular cloud o Temperature: 10K, radius: 4000-40,000 AU  If the gas in the cloud is compressed and becomes clumpy  the force of gravity on other gas particles increases  more gas is attracted  This core of gas continually grows hotter and denser until a star is born The Solar Nebula Theory  Observation: o The Sun and all the contents of the Solar System have a common age o Solar System bodies share common rotation and revolution in the same plane  Hypothesis: the planets formed in a rotating disk of gas and dust around a newly formed star How does a cloud make a disk?  Gravity from the forming star pulls the particles inward  The rotation of the particles increases as they fall inwards because of conservation of angular momentum  Particles rotating faster  can orbit the star, and not fall directly inward  Particles “above” and “below” the star collide in the middle; this ends up making a flattened disk  Prediction: if all stars form like this, there should be disks (and planets) around most other stars 8 AS 101 2012 Different Materials at Different Distances  Observation: two types of planets o i.e. higher densities closer to the Sun  the Solar Nebula was mostly homogeneous, but was warmer closer to the forming Sun  the gas must condense, or solidify, to provide a starting point for objects to grow  since different compounds have different melting points, different materials condense out of the Solar Nebula at different distances from the Sun Accretion-Just think snow  solid grains stick to each other and grow into larger particles  lots of planetesimals (size about 1 km) form, but larger objects grow faster o larger surface area for collisions o greater massstronger gravitational attraction Terrestrial Planet Formation  formed via accretion over 30 million years  Differentation: radioactive decay “melts” the planet o Denser elements (heavy metals) sink inward, less dense element float to form the crust (silicates)  Accretion of icy planetesimals may be the source of Earth’s water Jovian Planet Formation  Ices are also present in the outer solar systemJovian planets can accrete more mass  Since these planetesimals are more massive, they can use their larger force of gravitational attraction to pull gas rapidly out of the nebula Jovian Problem  Observation: most stars form in clusters  Prediction: disks may be evaporated by light from other stars before Jovian planets can grow large enough  Possible Refinement: if the disk is thick enough, Jovian planets could skip accretion, and grow gravitationally Heavy Bombardment  the early Solar System was filled with thousands of moon-sized planetesimals, and many more smaller objects  off-centre collisions probably caused: o Venus’ retrograde rotation and Uranus’ tilt/rotation o Formation of Earth’s moon  A collision with a smaller object caused: o The end of the Cretaceous period on the Earth 65 million years ago Leftover Construction Material  Observation: two types of space debris  Asteroids: remnants of rocky planetesimals that were disrupted by Jupiter’s gravitational influence  Comets: icy planetesimals that were either o Scattered into the outer solar system (Oort Cloud) by the Jovian planets o formed in situ (Kuiper Belt), but never grew into a planet (includes Eris and Pluto-they even have similar compositions to comets) 9 AS 101 2012 Other Planetary Systems  observations show debris disks (collisions among remnant planetesimals) around other stars also  there are over 60 confirmed extrasolar planets Terrestrial Planet Evolution  recall that terrestrial planet formation begins with condensation and accretion  each planet (and the Moon) experiences the next three steps to a different degree: 1. Differentiation 2. Heavy Bombardment 3. Slow-Surface Evolution *the Earth will be our
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