Detailed Study Guide for Exam 1
Detailed Study Guide for Exam 1
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Date Created: 01/29/15
Astronomy Section 1 1615 103 PM Course Overview Science has two simple beliefs An objective reality exists 39 Humans can gain knowledge about the nature of this reality 39 ie we believe that the universe is comprehensible all other thoughts are tested against evidence The Scienti c Method use multifaceted observations to pursue consistent evidence when trying to answer questions about the natural world 1 Observation every natural phenomena begins here 2 Hypothesis educated guess testable idea tries to explain that observation 3 Experiment test hypothesis 4 Conclusions i In disagreement with initial hypothesis discard and create new one ii In agreement with initial hypothesis run more experiments 5 Theory arises from several hypotheses veri ed to be correct in agreement w hypothesis i Much work behind it Explore physical world using observation logic and skepticism 0 Test explanations against experiment 0 Discard explanations that don t work 0 Self correction is its key strength 39 Theory description of nature based on data explains what we see 0 Good theories stands the test of time predictions and experiments 0 Hypothesis is predata while a theory is postdata 0 Good theories explain reality and can be applied to explain new observations Astronomy the science of studying the universe Why is Pluto no longer a planet 39 Pluto was determined to no longer be a planet because of its size and location in space It s smaller than any other planet including Earth s moon It s orbit is erratic unlike the planets in our solar system 39 It doesn t meet the criteria of a planet because its orbit crosses Neptune s orbit 39 It is now a dwarf planet or a plutoid dwarf planet that s farther in space than Neptune 17 Why is Astronomymportant Drives technological innovation 0 Pro table in the long run 39 Perpetuation of our species Answers fundamental questions Eye opener and enriches our culture One light year is the distance light travels in one year 39 Speed of light 300000 kms speed distancetime The Milky Way Galaxy 39 Our solar system is located here 39 Galaxy collection of stars 39 Planetary nebula sunlike star late in life 0 M27 The Dumbbell Nebula 39 M1 The Crab Nebula a supernova remnant closer to us than the Andromeda Galaxy 39 Eta Carinae a star that has ejected its outer atmosphere 0 It s the most massive star known at 150 times the mass of the sun M3 a globular cluster The Milky Way s satellites M3 a globular cluster The Milky Way s satellites o The Large Magellanic Cloud 0 The Small Magellanic Cloud The Milky Way s Neighbors o The Adromeda Galaxy M31 PARSEC pc 1 pc 326 ly 39 M33 a spiral galaxy in the Local Group M101 the Pinwheel Galaxy M51 the Whirlpool Galaxy 39 The Coma Cluster of Galaxies 39 Other galaxies of which we do not know could be many light years away ChapteLlBLedicjingthem9tinnsQfthestarssunandann The night sky constellations 0 3000 stars are visible at one time Stars are distributed randomly Human brain picks up patterns Constellations one of 88 sections of the sky Asterisms recognizable dottodot patterns most useful in navigating the sky Stars are different distances from us stars that appear close on the sky may not actually be close in space Nebulae huge clouds of interstellar gas from which stars are born 0 Supernova detonation that blows a star apart ending its life and forming a new nebulae 0 Black hole almost inconceivable dense object with powerful gravity that ends stars lives 00000 O 39 Seasons 39 Phases of the moon 39 Solar and lunar eclipses Other interesting solar system objects Daily Motion and the Earth s Rotation Half of the earth is always lit by the sun The earth spins changing which part is lit by the sun Yearly Motion and Earth s Orbit The Earth orbits the Sun in an almostperfect circle 39 The side turned toward the Sun sees its light 39 The side turned away from the Sun sees a changing pattern of stars Different constellations are seen from the night side of earth at different times of the year 39 Changes over the year the Sun appears to move through a xed set of constellations over a year the apparent path of the Sun is called the ecliptic 39 The Zodiac constellations along the ecliptic 39 Celestial sphere immense hollow sphere with Earth at its center and all the stars at the same distance from Earth 0 Imaginary object 0 Project the equator and poles into space 39 Celestial equator divides the sky into northern and southern hemispheres 0 North celestial pole and south celestial pole where Earth s axis of rotation intersects the celestial sphere 39 Zenith the point in the sky directly overhead an observer anywhere on earth if the celestial sphere is tilted 39 Circumpolar stars suf ciently near the north celestial pole that revolve around the pole never rising or setting Precession of the Equinox ll vulllr vlnl 39 UVWAU UWAAAVAVAAVAJ AAVWA VAAV ALVA VAL VVAVUVAWA IJVAV 41va AV 1 VA 1 v WAVVIAA VAAV pole never rising or setting Precession of the Equinox 39 The earth s axis precesses it is caused by the gravitational pull of the sun and moon 39 Precession the earth makes a circle in space 39 Takes 26000 years for earth to make a full circle in the sky 39 Today earth s axis is pointed towards Polaris Measuring Angles in the Sky Moon is 12 degree Width of nger is 1 degree hand is 10 degrees 39 Pole to equator is 90 degrees Motions of the Celestial Sphere 39 Objects near the north celestial pole seem to move in a circle never setting circumpolar 39 Your latitude impacts how the stars appear to move Seasons 39 We have seasons because the earth is tilted on its side 39 The earth s north pole is always tilted toward the north star this won t change in our lifetime 39 Earth doesn t change its tilt toward or away from the sun 39 The tilt of the earth causes sunlight to hit the earth more directly and for a longer period of time during summer 39 The sun is higher in the sky in the summer and not as high in the winter 115Lquin0xesandsolstices 39 Longer days in the northern hemisphere 39 Winter solstice December 21 larger ground area covered from sunlight 39 Vernal equinox March 21 39 Summer solstice June 21 smaller ground area covered from sunlight o Longest day of the year 39 Autumnal equinox September 21 39 Equinox when the ecliptic and celestial equator intersect day and night are each 12 hours long 39 Solstice when the sun reaches its most northern and southern points in the sky Arctic circle circle around Earth at 665 degrees North latitude 39 Antarctic circle bounds corresponding region around the South pole at 666 South latitude 39 During winter days are shorter but the sun is less effective at heating the ground because the sunlight is spread The earth s orbit is very nearly circular the distance from the sun doesn t cause seasons the inclination of the earth s axis with respect to its orbit does 39 In fact the earth is slightly closer to the sun in January Phases of the Moon The Moon s Synchronous Rotation 39 The moon makes one orbit around earth and spins one time on its axis in the exact same amount of time 39 We always see the same side of the moon but we don t see the far side this isn t the same as the moon s dark side 39 As the moon makes its way around earth it changes phases 28 day cycle 39 Lunar phases different appearances of the moon 0 New moon moon is barely not visible in the same direction of the sky as the sun rises at sunrise sets at sunset 0 Waxing crescent more of moon s illuminated half becomes exposed 4 days old 0 First quarter we see moon s illuminated hemisphere and half of dark hemisphere 7 days old rises at noon sets at midnight U1 0 First quarter we see moon s illuminated hemisphere and half of dark hemisphere 7 days old rises at noon sets at midnight Waxing gibbous moon is even more illuminated 10 days old Full moon 14 days old Waning gibbous less of moon is illuminated decreasing 18 days old Third quarter last quarter 22 days old rises at midnight sets at noon 0 Waning crescent 26 days old getting smaller 39 Sidereal month time it takes the moon to complete one full orbit of earth as measured 0000 with respect to the stars Synodic month lunar month time it takes the moon to complete one cycle of phases from new moon to new moon or full moon to full moon and is measured with respect to the Sun 0 Longer than sidereal because Earth is orbiting the Sun while the Moon goes through its phases Solar and Lunar Eclipses 39 Eclipses occur when the sun moon and earth are perfectly aligned o The Earth s shadow can fall on the moon or the moon s shadow can fall on Earth 0 The moon s orbital plane is just a little off of the ecliptic The sun moon and earth rarely line up 0 When they do we say the moon is on the line of nodes Lunar Eclipses 39 When the moon is opposite the sun it can travel through the earth s shadow occurs when Sun Earth and Moon are in a straight line 39 The earth s shadow is complete in the center and partial on the edge 39 Every place on earth that can see the moon will see the eclipse The moon appears reddish during an eclipse 39 It depends on how well the moon earth and sun are aligned 39 Umbra where the earth s shadow is the darkest no part of Moon s surface can be seen 39 Penumbra where the earth s shadow is not as dark Total lunar eclipse moon is completely in the umbra shadow o Occurs in full moon phase Partial eclipse moon is partially in umbra and penumbra Penumbra eclipse moon is in just penumbra 0 Earth blocks only part of Sun s light and none of lunar surface is completely shaded 39 Totality the period when the Moon is completely within Earth s umbra 39 As Earth rotates the tip of the umbra traces an eclipse path across Earth s surface only those within the eclipse path can see the solar eclipse Total Solar Eclipses When the moon is directly between sun and earth 0 When the Earth passes through the Moon s shadow the Moon moves in front of the Sun as seen from Earth 39 The moon totally covers the face of the sun from inside the darkest part of the moon s shadow 39 Those inside the moon s partial shadow see a partial eclipse 39 You see a very bright corona Line of nodes a line on which the planes of Earth s orbit and Moon s orbit intersect passes through Earth and is pointed in a certain direction in space 0 Eclipses can only occur if the line of nodes is pointed toward the sun and if at the same time the Moon lies on or very near the line of nodes Annual Solar Eclipses 39 When the moon is at its farthest position the cone of its shadow doesn t reach earth 39T LA AAA Ruu a LA LA LAA ut11 LA AAHH LLA A A 412 Sum ADLLA nu 2 AAA A A J Annual Solar Eclipses 39 When the moon is at its farthest position the cone of its shadow doesn t reach earth 39 The moon appears to be too small to cover the sun a thin ring of the sun is seen around the edge of the moon Types of Solar System Objects Inner planets solid rocky bodies 39 Outer planets giant gaseous bodies 0 Rings are common 0 Natural satellites moons are common Dwarf planets Asteroids 39 Comets dirty snow balls meteoroids meteors meteorites The Terrestrial Planets 39 Mercury Venus earth and mars are the rocky worlds of our inner solar system 0 The other large bodies in the solar system are all moons of the outer gas giant planets 39 Outer planets have no solid surface and are much larger than earth Primary gases are hydrogen and helium Uranus and Neptune have substantial rock ice cores 39 Moons of Jupiter lo Europa Ganymede Callisto 39 Asteroids Gaspra Idea and Dactyl Parts of a Comet 39 The actual nucleus is tiny compared to the tails and always point away from the sun due to radiation from the sun pushing on the gas and dust in the comet s tail 39 Meteor showers the remnants of comets o A comet leaves a trail of debris 0 Some parts can be thicker than others some passages make meteor storms Larger meteors can strike the earth 39 Some meteors are large enough to survive passage through the atmosphere and strike the ground with enough force to be vaporized and release large amounts of energy 0 They hit at 50 kms so a rock the size of a building can make a hole a mile across 39 Too large an impactor gt 50 mi would replace our entire atmosphere with rock vapor for a few centuries only life in the deepest oceans would survive mpter 2 Decoding the Hidden Messages in Starligm How do astronomers study the universe 39 Astronomy is a science built from light 39 No earthbound labs Astronomers observe Light takes time to travel 39 When earth is near Jupiter we observe eclipses of Jupiter s moons earlier than expected 39 When earth is far from Jupiter we observe eclipses of Jupiter s moons later than expected Light takes time to travel the extra distance 39 c 300000 kms 7 times around the earth in 1 second What is light Light acts both like a 0 Wave a moving pattern that carries energy 0 Particle something that comes in xed pieces Waves 39 Any disturbance that carries energy without the motion of material from one place to another The disturbance is often in the form of a repeating pattern the pattern is what moves and carries energv WLLU Lllvl The disturbance is often in the form of a repeating pattern the pattern is what moves and carries energy Ex water wave 0 Water just moves up and down 0 Wave travels and can transmit energy 39 Wave properties 0 Wavelength distance bt successive peaks troughs if we freeze the wave at one moment in time Period a related idea the amount of time it takes for the pattern to repeat if you stay in the same place Period 1 frequency inversely related 0 Frequency the number of times the wave pattern will repeat per second if you stay at a xed place or how many cycles pass by per second Measured in cycles per second Hertz o Amplitude height maximum departure of the disturbance from an undisturbed state it will always be related to the amount of energy the wave carries 0 Speed how fast the wave travels must travel one wavelength in one period one wavelength distance in one period of time Speed wavelength period wavelength X frequency The Speed of Light 39 Wave speed of electromagnetic waves c 30 X 10A8 ms All forms of light electromagnetic radiation travel at this same speed in a vacuum 39 This speed is very large but nite it can take light millions or billions of years to traverse astronomical distances 39 We se things as they were when the light left them not as they are now 39 Ex sunlight takes 8 minutes amp 20 seconds to get to Earth so the sun is about 8 light minutes from Earth Water Waves 39 Water waves show diffraction addition and canceling Light travels in waves 39 Water waves show diffraction addition and canceling and so does light What do we mean by electromagnetic 39 One of the fundamental forces of nature is gravity another is the electromagnetic force This sometimes acts like 2 different forces 0 1 The electric force most particles have a positive or negative charge to them Like charges repel opposites attract This force holds together atoms molecules and people 0 2 The magnetic force magnets have North and South poles like poles repel opposites attract Electric and Magnetic Fields 39 We can draw imaginary arrows describing how strong electric or magnetic forces are and in what direction they point we call these the electric eld or the magnetic eld Creating Electric and Magnetic Fields 39 When electric charges move in a periodic way the electric eld will move in a period way too there will be a wave in the eld 39 A changing electric eld creates a magnetic eld and in turn a changing magnetic eld creates an electric eld 39 The result is an electromagnetic wave a wave occurring in the electric and magnetic elds Light is generated by moving charges Electromagnetic Waves in Astronomy 39 The charged constituents of stars move around producing electromagnetic waves m1 1 Electromagnetic Waves in Astronomy 39 The charged constituents of stars move around producing electromagnetic waves 39 These waves travel through space to Earth 39 Our instruments telescopes or eyes contain charged particles that vibrate in response to the vibrating electric and magnetic elds 39 In this way we see or detect the light and get information from it 39 Radiation refers to any physical process in which energy passes from one place through some intervening region to another place so we sometime refer to light as electromagnetic radiation Electromagnetic Spectrum Types of Light 39 Most sources of light emit at many frequencies or wavelengths 39 Newton white light or sunlight is made up of all colors of the rainbow The range of all wavelengths of light is known as the electromagnetic spectrum 39 When we split light into its components we call it a spectrum Visible light ROYGBIV human eye can see 39 Each color is a different wavelength Infrared light invisible energy wavelengths longer than those of visible light 39 Radio waves light with even longer wavelengths than infrared 39 Gamma rays light waves that have the shortest wavelength 39 Ultraviolet light wavelengths just short of visible light 39 Microwaves wavelengths from 1mm to 10 cm Sunlight is a Mixture of all Colors 39 Prisms don t add colors to the sunlight 39 Each color light bends a different amount as it passes through the material The Electromagnetic Spectrum Different ranges of wavelength or frequency have difference names 39 No limit on wavelengths Higher frequency implies lower wavelength and higher energy 39 Earth s atmosphere doesn t let all light through 39 Shows how much light is blocked at a wavelength opacity of the atmosphere Wavelengthxsliequencylsamggy 39 c wavelength X frequency 0 is always the same 0 So wavelength is inversely proportional to frequency 0 Larger longer wavelength smaller frequency always 39 Energy is proportional to frequency 0 Higher frequency higher energy 39 Gamma rays are created by the universe s hottest and most cataclysmic events 39 Xrays are emitted by highly energetic phenomena where gas is heated to millions of degrees Groundbased Visible and Infrared Astronomy Infrared light can pass through interstellar clouds that visible light cannot 39 If our eyes can only see some parts of the spectrum there must be things we can t see Infrared light can pass through clouds of dust and gas Opacity of Earth s Atmosphere Only a small fraction of the radiation produced by astronomical objects actually reaches our eyes in part because of the opacity of Earth s atmosphere 39 Opacity extent to which radiation is blocked by the material through which it s passing air 39 The more opaque an object is the less radiation gets through it 127 Thermal Radiation 39 When you heat an object it glows it gives off light 39 All objects emit radiation all the time bc the electricallycharged particles everything is made of randomly jostle around 0 Temperature measures how much iostling there is All chcts cum radiation an we umc we we electricallycumch pal uv1uo everything is made of randomly jostle around 0 Temperature measures how much jostling there is 39 When charged particles move light is emitted Higher temperature more jostling more light gets emitted 39 At typical Earth temperatures we mostly radiate in the infrared which our eyes can t see The Kelvin Temperature Scale All motion stops at 0 K absolute zero 39 Water freezes at 273 K and boils at 373 K 39 We will refer to temperature in terms of degrees Kelvin or K 39 Celsius water boils at 100 degrees C and freezes at 0 degrees C Fahrenheit water boils at 212 degrees F and freezes at 32 degrees F Blackbody Radiation Thermal radiation emitted by an opaque object 39 A perfect blackbody absorbs all light hitting it 5800K 39 Blackbody spectrum The Planck curve 39 A blackbody spectrum is determined only by its temperature 0 Spectrum because it changes based on its wavelength Higher the temperature more intense the radiation emitted is 39 Objects emit speci c amounts of light revealing their temperatures The sun is a nearlyperfect blackbody 39 The higher the temperature of a blackbody the shorter the wavelength of maXimum emission and the more light is emitted at all wavelengths Radiation Laws 39 Wien s Law the higher the temperature the more intense the light and shorter the wavelength 0 The hotter the object the bluer it looks 39 StefanBoltzmann Law total energy emitted is proportional to fourth power of temperature 0 Larger stars of the same temperature are more luminous a cool star can be very luminous if it s very large The inef ciency of an incandescent light bulb 39 An incandescent light bulb burns at 3000K most of the radiated energy is in the infrared as heat we use energy in the form of electricity to heat it for light 39 A compact uorescent bulb is not a blackbody it radiates most of its energy in the visible part of the spectrum between 400 and 700 nm Kirchoff s Laws 39 Law 1 a hot opaque body or a hot dense gas produces a continuous spectrum a complete rainbow of colors without any spectral lines 39 Law 2 a hot transparent gas produces an emission line spectrum a series of bright spectral lines against a dark background 0 Emission spectra can be used to identify elements 39 Law 3 a cool transparent gas in front of a source of a continuous spectrum produces an absorption line Spectrum a series of dark Spectral lines among the colors of the continuous spectrum 39 The wavelengths absorbed by the gas exactly match the wavelengths emitted by the gas 39 An absorption spectrum can also be used to identify elements Electrons Occupy Speci c Orbits Within Atoms Each orbit is a speci c energy state Electrons leap between orbits 39 Electrons leap when they absorb the perfect amount of energy 39 Electrons fall and emit that same specific amount of energy Atoms and Radiation 39 The Bohr Model based on Bohr s assumption that the electron in a hydrogen atom can Liwuws it um um same specific WNW or energy Atoms and Radiation 39 The Bohr Model based on Bohr s assumption that the electron in a hydrogen atom can orbit the nucleus only in certain speci c orbits o The electrons in an atom don t actually move in precisely circular orbits but thinking of it this way is handy Emission energies correspond to energy differences between allowed levels 39 Modern model has electron cloud rather than orbit 39 Energy levels of the hydrogen atom showing two series of emission lines o The emission lines correspond to the energy differences Light behaves like packets of energy called photons o It can only have a discrete amount of energy that s precisely equal to the difference in the emitting atom s energy levels Light particles each have energy E that is proportional to the frequency of the radiation E hf h Planck s constant 663 X 10A34 joule seconds Molecules 39 Molecules can vibrate and rotate besides having energy levels 39 Electron transitions produce visible and ultraviolet lines 39 Vibrational transitions produce infrared lines 39 Rotational transitions produce radiowave lines 39 Molecular spectra are much more complex than atomic spectra even for hydrogen Light Scattering 39 The atmosphere scatters blue light more effectively than red light hence mostly blue light reaches your eye when you look at the sky 0 Additionally because of this mostly red light reaches your eye when you look through a thick slice of atmosphere at the setting sun The Doppler Effect 39 If one is moving toward a source of radiation the wavelengths seem shorter if moving away they seem longer The amount of shift in wavelength is proportional to the speed of the object 39 Depends only on the relative motion of source and observer Spectra also reveal motion 39 An object s motion through space is revealed by the precise wavelength positions of its spectrum of light The Doppler Effect the change in wavelength is proportional to the speed of the moving object o The faster the object moves the more changes in wavelength the wave will be 39 change in wavelength true wavelength speed of object speed of wave Blueshift when all lines in the spectrum of an approaching source are shifted toward the shortwavelength blue end of the spectrum 0 This occurs when a wave crest is being emitted from a position slightly closer to the observer on the left so they see a shorter wavelength distance from one crest to the next than they would if the source were stationary Redshift all the lines in the spectrum of a receding source are shifted toward the longerwavelength red end of the spectrum Information from Spectra 39 Spectral lines a pattern of thin bright lines against a dark background 0 Important because they provide reliable evidence about the chemical composition of distant objects 39 Every chemical substance has its own speci c color spectrum wen burned and passed through a prism showing these spectral lines 39 Spectroscopy the identi cation of chemical substances by the unique patterns of lines in their spectrum 0 A core aspect of astronomy Telescnnes 1n tnelr spectrum 0 A core aspect of astronomy Telescopes 39 Telescopes gather light They aren t primarily used to magnify stars 39 Lightgathering power is directly related to the size of its objective lens the gathering area Refracting Telescopes 39 Use a lens to concentrate incoming light at a focal point Magni es near objects 39 Focal length distance from lens to the special point where all light converges 39 Objective lens largediameter longfocallength lens at the front of the telescope that forms the image Eyepiece lens smaller shorterfocallength lens at the rear of the telescope that magni es the image for the observer Optical Telescopes Refracting lens 39 Images can be formed through re ection or refraction 39 Re ecting telescopes use a curved mirror to concentrate incoming light at a focal point 0 More durable and can be made bigger and less expensive 0 Primary mirror the mirror that forms the image objective mirror Modern telescopes are all re ectors because Light traveling through lens is refracted differently depending on wavelength Some light traveling through lens is absorbed Large lens can be very heavy and only be supported at edge 39 A lens needs 2 optically acceptable surfaces mirror only needs one Since prisms separate light into its component colors using lenses for telescopes causes chromatic aberration Telescope Size Lightgathering power can see fainter objects 39 Amount of light collected is proportional to square of radius of mirror area 39 Resolving power ability to distinguish objects that are closer together 0 Want resolution to be small this is the angle between two objects you can tell apart 0 Resolution is proportional to wavelength and inversely proportional to telescope size 0 Larger telescopes are better better resolution and can see fainter objects Atmospheric blurring is due to air movements 0 Solutions put telescopes on mountaintops especially in deserts 0 Put telescopes in space Adaptive optics 39 Track atmospheric changes with laser adjust mirrors in real time 39 Computers compensate for turbulence in the atmosphere Active optics control mirrors in real time to adjust for change in focus of mirror due to minute changes in temperature and orientation of mirror Chargecoupled devices record very ne image details Looking toward the center of the Milky Way using the best of Earthbased and space telescopes ChargeCoupled Device CCD 39 The most sensitive light detector currently available to astronomers 39 In a CCD there s a semiconductor wafer divided into an array of small lightsensitive squares called picture elements or pixels 39 When an image from a telescope is focused on the CCD an electric charge builds up in each pixel in proportion to the number of photons falling on that pixel 39 When an image from a telescope is focused on the CCD an electric charge builds up in each pixel in proportion to the number of photons falling on that pixel 39 35 times more sensitive to light can record much ner details and respond more uniformly to light of different colors compared to photographic film 39 Useful for measuring brightness of stars Radio Astronomy 39 Subfleld of astronomy that studies celestial objects at radio frequencies 39 Came about when an initial detection of radio waves from an astronomical object was made by Karl J ansky 39 Conducted using radio telescopes 39 Radio telescopes usually need to be extremely large to receive signals with high signal tonoise ratio Infrared Astronomy 39 Branch of astronomy that studies astronomical objects visible in infrared radiation 39 Wavelength of infrared light ranges from 075 to 300 micrometers XRay Astronomy and Telescopes 39 Observational branch of astronomy that deals with the study of Xray observation and detection from astronomical objects 39 Xradiation is absorbed through Earth s atmosphere so instruments to detect Xrays must be taken to high altitude by balloons sounding rockets and satellites 39 It s the space science related to a type of space telescope that can see farther than standard lightabsorption telescopes 39 Xray telescopes have varying imaging ability based on glancing angle re ection rather than refraction which limits them to much narrower fields of view than visible or UV telescopes Gamma Ray Astronomy 39 Astronomical observation of gamma rays Their observation is more problematic than Xrays or visible light because gamma rays are rare and difficult to focus resulting in very low resolution 1615 103 PM 1615 103 PM
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