Study notes for midterm no.2

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Astronomy & Astrophysics
Marija Stankovic

Study notes for midterm (no.2) Lectures 5-7, and ch. 5-6 & 14 Chapter 5 5.4 Learning from Light Matter leaves its fingerprints whenever it interacts with light Examining the color of an object is a crude way of studying the clues left by the matter it con- tains If we take light and disperse it into a spectrum we can see the spectral fingerprints more clearly The process of obtaining a spectrum and reading the information it contains is called spec- troscopy Radiation = intensity The intensity at a given wavelength is proportional to the number of photons observed at that wavelength times the energy of those photons How does light tell us the temperatures of planets and stars? In a cloud of gas that produces a simple emission or absorption line spectrum, the indi- vidual atoms or molecules are essentially independent of one another Most photons pass easily through such gas, except those that cause energy level transi- tions in the atoms or molecules of the gas Atoms and molecules within everyday objects like rocks and light bulb filaments and people can- not be considered independent and therefore have much more complex sets of energy levels These objects tend to absorb light across a broad range of wavelengths, which means light cannot easily pass through them and light emitted inside them cannot easily escape. The same is true of almost any large or dense object, including planets and stars Idealized case where an object absorbs all photons that strike it and does not allow photons in- side it to escape easily: Photons trying to escape are quickly absorbed by an atom or molecule, which quickly reemits the photon - but often with a slightly different wavelength and in a different di- rection The emitted photons bounce randomly around inside the object, constantly exchanging ener- gy with the objects atoms or molecules By the time the photons finally escape the object, the radiative energies have become randomized so that they are spread over a wide range of wavelengths The wide wavelength range of photons explains why the spectrum of light from such an ob- ject is continuous Spectrum from such an object depends on only one thing: the objects temperature Temperature represents the average kinetic energy of the atoms or molecules in an object The randomly bouncing photons interact so many times with those atoms or molecules, they end up with energies that match the kinetic energies of the objects atoms or molecules - which means the photon energies depend only on the objects temperature, regardless of what the object is made of The temperature dependence of this light explains why we call it thermal radiation and why its spectrum is called a thermal radiation spectrum Thermal radiation spectra are the most common type of continuos spectra No real object emits a perfect thermal radiation spectrum but almost all familiar objects emit light that approximates thermal radiation Sun, planets, rocks - even you Two laws of thermal radiation Midterm 2 Law 1: each square meter of a hotter objects surface emits more light at all wavelengths Law 2 (Wiens Law): hotter objects emit photons with a higher average energy, which means a shorter average wavelength Poker in fireplace example: While the poker is stiller relatively cool it emits only infrared, which we cannot see.As it gets hot it begins to glow with visible light and it glows more brightly as it gets hotter (law1). At first it glows red hotbecause red light has the longest wavelengths of visible light As it gets even hotter the average wavelengths of the emitted photons moves toward the blue end of the visible spectrum The mix of colors emitted at this higher temp makes the poker look white to ours eyes = White hot Because thermal radiation spectra depends only on temperature, we can use them to measure the temperatures of distant objects In many cases we can estimate temperatures simply from the objects color While hotter object emit more light at all wavelengths, the biggest difference appears at the shortest wavelengths At human body temperature of about 310K people emit mostly in the infrared and emit no vis- ible light at all (which is why we dont glow in the dark) Arelatively cool star, with a 3000K surface temperature emits mostly red light Ex Betelgeuse The Suns 5800K surface emits most strongly in green light but the sun looks yellow or white to our eyes because it also emits other colours throughout the visible spectrum Hotter stars emit mostly in the ultraviolet but appear blue-white in color because our eyes can- not see their ultraviolet light If an object were heated to temp of millions of degrees it would radiate mostly xrays Ex disks of gas encircling exotic objects like neutron stars and black holes How do we interpret an actual spectrum? The spectra of real astronomical objects are usually combinations of the three idealized types of spectra: continuous or thermal, absorption line, and emission line They may also show features produced by reflection or scattering An object that reflects light will have the spectrum of the light shining on it, minus the light it absorbs (reflect light spectra) Different atmospheric gases reflect and absorb light at different wavelengths The surface materials of a planet determine how much light of different colors is reflect- ed or absorbed 5.5 The Doppler Effect The Doppler effect causes shifts in the wavelengths of light If an object is moving toward us, the light waves bunch up between us and the object, so that its entire spectrum is shifter to shorter wavelengths Because shorter wavelengths of visible light are bluer, the Doppler shift of an object coming to- ward us is called a blueshift If an object is moving away from us, its light is shifter to longer wavelengths. We call this a redshift because longer wavelengths of visible light are redder Astronomers use these terms even they they arent talking about visible light Spectral lines provide the reference points we use to identify and measure Doppler shifts Rest wavelengths = wavelengths in stationary clouds of gas Study notes for midterm (no.2) Lectures 5-7, and ch. 5-6 & 14 The Doppler shift tells us only the part of an objects full motion that is directed toward or away from us (the objects radial component of motion) Consider three stars: one moving erectly away from us, one moving across our line of sight and one moving diagonally away from us The doppler shift will tell us the full speed of only the first star (directly away) It will not indicate any speed for the second star (across line of sight) The doppler shift will use only the part of the stars velocity that is directed away from us for third star (diagonally) To measure how fast an object is moving across our line of sight we must observe it long enough to notice how its position gradually shifts across our sky Lectures Five and Six Nearly all large or dense objects emit thermal radiation, including stars, planets and you! Type of heated material does not affect the radiation - > all produce the same continuos spectrum An objects thermal radiation spectrum depends on only one property: its temperature Continuos radiation = thermal radiation (also called blackbody radiation) Properties of thermal radiation 1. Hotter objects emit more light at all wavelengths per each square meter The amount of emission increases rapidly with increasing temperature 2. Hotter objects emit photons with a higher average energy The peak emission shifts to shorter wavelengths as the temperature increases (Wiens law) Objects color is a way of determining temperature The spectrum of a hot sold does not tell you what it is made of Ablue star is hotter than a red star Why dont we glow in the dark? People only emit light that is invisible to our eyes How does light tell us the speed of a distant object? Motion changes the wavelengths we detect - the Doppler Effect When a light source moves away from us it appears redder and has longer wavelength (redshift) When a light source is moving toward us it appears bluer and has shorter wavelength (blueshift) We generally measure the Doppler effect from shifts in the wavelengths of spectral lines Doppler shift tells us ONLY about the part of an objects motion toward or away from us - radi- al velocity With a star moving directly away from us the doppler shit tells us its full speed With a star moving across our line of sight, but not toward or away from us, the doppler shift indicates no speed at all With a star moving diagonally away from us the doppler shift tells us the part of the stars speed away from us, but not the part of the speed across our line of sight The amount of blue or red shift tells us an objects speed toward or away from us Telescopes are critical for studying light Have been around for 400 years and importance continues today Light-collecting area - telescopes collect more light than our eyes
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