astro 100-02 midterm study guide
astro 100-02 midterm study guide astro100-02 Exploring the Universe
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This 23 page Study Guide was uploaded by Coco Chen on Tuesday March 10, 2015. The Study Guide belongs to astro100-02 Exploring the Universe at University of Massachusetts taught by Daniel Wang in Winter2015. Since its upload, it has received 270 views. For similar materials see Exploring the Universe in Astronomy at University of Massachusetts.
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Date Created: 03/10/15
Brief to Universe Course logistics and Primer Be familiar with the power of 10 and the exponents 1001 10A110 1002100 1003 1000 Scienti c Notation 1lt X gt10 times power of 10 ex 356000 356 X 1005 ex 000488 488 x 103 Be able to do the addition subtraction multiplication and division in scienti c notation form 250 x 56000 25 x 1002 x 56 x 1004 25 x 56 x 1006 14 x1007 xgtlt10a gtltampgtlt10b x ygtlt10ab XX 10 ygtlt 10 ampygtlt 10Aab know the difference between units in English and in Metric and be able to convert them Ex 100cm 1m 1 hour 60 minutes Trillion Tera T 10012 billion Giga G 1009 Million Mega M 1006 Thousand Kilo K 1003 thousandth milli m 103 millionth micro micro mu 10A6 billionth nano n 10A9 Speed of light lighttime distance C 3 x 1005 kms Earth lt 11008 years gt supernova 1 AU 150 million km 150 x 106 km 15 x 108 km 1AU is the distance from Sun to Earth 1yr315x 107 s 1 light year 3 X 105 kms X 315 X 107 s 945 X 1012 km Sun 13 million X Earth 400 times larger than Moon Angel diameter in radians diameterdistance 1 degree 60 arcminutes 60 1 60 arcseconds 60quot Horizon to zenith pont overhead 90 degree smallest detail Visible to naked eyes 1 60quot Sunset Midnight V lNoon North Earth39s Pole rotation Sunrise l quotl 39 Uth 1 OLIIquot PLaneTary NGIGHBOFHOOD Astronomy is the study of universe from Earth itself to the most distant galaxy from deciphering its nature at the beginning of time to predicting its eventual date in the remote future Galaxy is a slowly whirling system of billions of stars Through Astronomy we get to study places so remote that we can t never be able to visit and gain insights into alien environment unlike anything found on Earth mis our home planet with blue oceans white clouds and multihued continents o The size of Earth and features on it are useful reference points for appreciating the sizes of other objects 0 We also use Earth for defining the meter the fundamental unit of the metric system 0 meter used to be de ned as one 10 millionth of the distance from the equator to North Pole 0 measurement in 17003 was a bit off however Earth s circumference was roughly 40 000 kilometers 25 000 miles 0 Discover of another measurement one for interpreting the processes that shape other planets when geological processes occurred on Earth A volcano spews molten lava provided a hint that it is extremely hot underground and it caused the earthquakes this allows us to make hypotheses about the processes that create similars features on other planets We then use what we discover on another planet to help us think about our Earth in a new way The Moon it s the nearest neighbor from Earth our satellite and orbiting Earth nearly 400000km away A of Earth s size rocky place we see evidence of history of steady pounding by objects crashed into it and our planet the Earth must have experienced similar pounding since we are so close to the moon Moon does not have atmosphere and is not protected Moon keeps its scars while Earth s past has been erased therefore we study Earth s ancient history from observing the Moon There are seven other planet circulating the Sun like Earth and Moon do in order of increasing distance from Sun Mercury Venus Earth Mars Jupiter Saturn Uranus and Neptune dwarf planets plutoids Pluto amp Eris Jupiter is largest the 4 outer planets have vast atmospheres Jupiter has a storm system that s the same as of Earth s Uranus and Neptune are blue because of a deep layer of methane our nearest neighbors Venus amp Mars provide deeper insights of our own planet The Sun s immense gravity holds planets in the solar system in orbit it is a star is 100 times the diameter of Earth and 300000 times heavier generates energy in its core by nuclear reaction producing energy in furious rate heat goes from its coregtits surfacegtthe space lspreads the Sun would run out of fuel in another 56 billions years Solar system Sun the bodies orbiting it by its gravity filled with smaller bodies satellitemoons orbiting the planets sum of the mass of all lt 1 of Sun s disk shaped c Sun at center and outermost planet Neptune lies about 45 billion km from the Sun beyond enormous amount of small objects orbiting in the Kuiper Belt Astronomers had developed units for measurements And we use astronomical units to measure the scale of solar system or beyond Mercury 04 AU or 60 million km from Sun Neptune 30 AU from Sun however our technology has limited us to explore farther than the solar system VVVV A The Earth is one planet in the solar system which contains the Sun eight planets and a huge of smaller objects 2 The planets vary tremendously in size and appearance some much larger than the Earth and some smaller 3 The Sun is the largest body by far in the Solar system and the energy it radiates warms the surface of the planets 4 Astronomers generally use the metric system for measurements but they also use the size or mass of familiar objects like the Earth as a unit to describe other bodies 5 The spaces between bodies in the solar system are enormous compared to their sizes so astronomers use the distance between the Earth and Sun the astronomical unit to measure distances in the Solar System Motion of the Earth and Time 0 Sars rise and set just like Sun caused by Earth s rotation 0 there are 88 of cial constellations divide the sky into areas with clear boundaries 0 Names are in Latin most bright star names derived from Arabic 0 constellations aren t real 0 Big dipper asterismunof cial groupings of stars 0 North celestial pole above North Pole Where stars rotates around 0 Polaris is the brightest star near the North celestial pole 0 looking eastGemini and Orion 0 looking south canis major O northsouth position on Earth by distance from equator 0 north pole 90 degree north 0 south pole 90 degree south 0 eastwest position by angle relative to an arbitrary point Vivi E m HOW a 1939s prime quot meridian of a mum at imam Miami immune Lemma so 24 time zones 0 local moon roughly correspond to time when Sun is highest in sky 0 If it is noon in UK then it is midnight on the opposite side of world 0 the midnight line intemational date line 0 time for many astronomical events are given in Universal Time UT or the local time of Greenwich England GMT or Greenwich mean time 0 the location of constellations at certain time can be used to tell the longitude Positions on the Celestial Sphere are analogous to Longitude and Latitude 11 A star s longitude is called its Right Ascension n A star s latitude is called its Declination n Celestial poles like the poles on earth extended into sky 11 So is the celestial equator O the line that Sun traces across the CS in a year is called the ecliptic the 12 constellations along the ecliptic are called the zodiac animal circle roughly one per hour The scale of the universe relative scales of planets planet orbits the Sun and other stars galaxies and etc Radius of Earth 64 X103 km 1 AU 15 X108 km distance from Sun 1 ly 95 X 1012 km distance to the nearest star Size of the Milky Way 105 ly Most distant galaXies 1010 ly time and seasons day most fundamentally the solar synodic day month phases of the Moon Year seasonal changes related to the Sun Apparent solar day time from high noon to low noon average length of apparent solar day 24 hours sidereal day time for a star to the same position because Sun moves in respect to stars the sidereal day is different from the solar day Earth revolves about 360 degree 365 days 1 degree around Sun Earth rotates at a rate of 360 degree 24 x 60 025 degree minute so need an extra 1 degree 025 degree 4 minutes to complete a solar day there are 36525 solar clays and 36625 sidereal days in a year Sun shifts with respect to the stars by 1 degree each daytherefore we see different constellations in winter than in summer Longer clays stronger and more direct sunlights in summer than in winter angular size is inversely proportional to distance the farther the smaller we are 3 closer to Sun in Jan than in Jul 1 spring Equinox Ewing tagging in fine Northern l i h l 39 mu m llllg ll39 Southern Hemisphere Eng Summer Seleliee Summer Begins at the Herrera Hemisphere quotMme in the Seummn sphere Emmet barging m mag Hem53mm summit Southern Hermieth Fall Equine Fail m mil 35101 them Hem sphere spring m the Southern Hemisphere 0 Sun slips from west to east among stars about 10 per day or 300 per month Earth39s orbit around Sun as a result a constellation rises about two hours earlier after a month Sun appears to move along ecliptic zodiac constellations north of celestial equator in our summer south of celestial equator in winter The seasons are caused by the tilt of the Earth relative to ecliptic Moon 0 The Moon is 14 of the Earth in diameter and l percent in mass 0 The moon s revolution around the Earth takes 27 days7 hours and 43 minutes explaining why the moon rises almost an hour later every night 0 The rotation of the Moon and its revolution are synchronized so that we only see one side of it E ltllrll llg I39ll ii tit t l Ali LI l Hr r l lit un v mintin Z tnttl ntgliL ii lisp 1T1 Eunl lg HE ff Why Rt 51 39e li m39ltit gil g 9gb quot9 7h lid i eai f rul 2ng M Few r E Eda513F111 LE L rm El UL E F U L H her i r39 EJEE JH IE 3 iii F O peorunce DE WE I39it i39 tl39 gm E rfh moon s phase cycle is 2953 0 12 lunar cycle is close to a year 0 Lunar and Solar Eclipses Alnnlula Eclime r r 391 Total Eralime Partial Eclipse 0 There is a total eclipse if the Moon directly passes in front of the Sun and blocking the light to Earth usually Moon s angular size is larger than Sun s There s a partial eclipse when it does not cover the Sun completely but if the angular size of the Moon is too small but still passes in front of Sun we called it an annular eclipse O the moon s orbit is tilted from the earth s orbit so there aren t any eclipses in each full moon see reading notes on unit 11 12 1416 for planets motion the imperfect heaven Newton s laws gravity tides and etc Unit 11 Planets The Wandering Stars Planetai from which the word planet come from means wanders 5 of the brightest stars that gradually shift from night to night instead of remaining in the same position on the celestial sphere Until telescope was invented planets were thought to be special stars and were free to roam in the sky And from their freedom to roam we can tell that they had special powers And as astronomers studied these motions and patterns of the motions they realized that Earth itself was also a planet A combination of the Earth s and the stars own orbital motions around the Sun causes planets to move against the background of stars Feature of this orbital motion planets always remain within a narrow band on either side of the ecliptic within the constellation of the zodiac all planets remain close to the ecliptic amp nearly all lie in the same plane see below planets usually move from west to east pass the stars but they don t always rise in the east and set in the west though seeing from Earth they rise in the east and set in the west because their movements on the celestial sphere were much slower than Earth s rotation NOTE Pluto Eris and a number of other small solar system bodies sometimes move outside the zodiac The motion of planets V quotW39le Retrograde background moving motions a planet will move west with respect to the stars When a planet is in this motion its path through the stars turns or loops backward for a month or more Planets still rise in the east and set in the west because this motion is slow compared to Earth s rotation All planets undergo this motion when they lie in the same direction as Earth from Sun Geocentric modelsGreek astronomer Eudoxus Earth is the center of the universe and planets and stars move around it at different speed because everything rise in the east and set in the west The bodies that are closest to the Earth seem to move at a fastest speed To explain the Retrograde motion Eudoxus requires that each planet s crystalline sphere should itself be attached to another crystalline sphere that rotated at a different angle By combining the steady rotation of both spheres a zigzag path has roughly resembled retrograde motion Over the next 5 centuries Claudius Ptolmey developed a model that could predict planets positions with good accuracy Ptolemy 0 each planet move in a small circle epicycle which in be carried along on a larger circle like a frisbee spinning on the rim of a bicycle wheel 0 the general eastward motions of planets relative to stars is caused by a slow rotation of the larger cycle relative to the celestial sphere o retrograde motion occurs when the epicycle carries the planet in a reverse direction relative to the celestial sphere 0 device to support the model the larger circle move around the Earth and not at a constant speed around Earth but instead around another point in space 0 but the model only lasts till 1500s because it is very complex and requires too much parameters that seemed arbitrary o simplicity is important in scientific theory Nicolaus Copernicus began the demolition of the geocentric model and started a revolution in astronomical thinking Heliocentric model Sun is the center of a system of planets and Earth is just one of them he showed that such model offer a far more simple explanation of retrograde motion a simple consequence of one planet on a smaller faster orbit overtaking and passing another on a larger and slower orbit retrograde motion occurs to Earth around time of opposition of Mars conjunction when a planet lies in the same direction as the Sun on the far side of the Sun Superior conjunction Venus and Mars undergo retrograde motion when they pass Earth in inferior conjunction between Earth and Sun largest angular separation from the Sungreatest elongation is determined by the sizes of the planets orbits relative to the Earth s orbit quadrature900 from the Sun he could also use Heliocentric model to calculate the relative size of all of the planets orbits and derive the distance of the planets by using geometry Unit 12 The Beginnings of Modern Astronomy Tycho Brahe born into the Danish nobility designed built and used instruments that permitted the most accurate spectroscopic measurements ever made he could uses his measurements to measure positions in the sky with high precision to 1 arc minute he saw supernova exploded and reminded in a fixed position in the celestial sphere he realized that comet is far away beyond the moon Brache s model all planets except Earth went around Sun while Sun as in earlier model circled the Earth last astronomer to say Sun circled Earth Johannes Kepler Brahe s younger assistant he described Brahe s planet orbiting the Sun which orbits the Earth as a pretzel When Brahe died he passed on his observational datas to Kepler Mars did not move along a circular path but rather along an ellipse The shape of an ellipse is described by its long and short dimensions its major axis and minor axis And for most calculation the most important value is half the major axis length or Semimajor axis Sun located in the ellipse offcentered at one of the focus eccentricity e describes how round or stretchout the ellipse is e indicates how far Sun is from the center of ellipse as a fraction of the semimajor axis if the ellipse is a circle e0 and the two focus will be on top of each other Kepler s discoveries of the nature of planetary motions are expressed as Kepler s 3 laws 0 l planets move in elliptical orbits with the Sun at one Focus of the ellipse 0 II the orbital speed of a planet varies so that the a line joining the Sun and the planet will sweep over equal areas in equal time intervals 0 III the amount of time a planet takes to orbit the Sun P is related to its orbit s size p2 a3 p in years and a in astronomical units this allow us to predict the period of any body if its semimajor axis is known And possible to find the semimajor axis of a body orbiting the Sun from its orbital period Galileo Galilei was trying to understand the heaven he found out Moon is like a rock There are black spots on Earth the sun sportson its surface he notice the positions of those black spots change everyday the Sun had not only blemishes but also not a perfect celestial orb moon and sun have irregular surfaces more like Earth bodies than heavenly matter Galilean satellites proves that some bodies in heaven do not orbit Earth Saturn has saturn ringssatellite around it Jupiter has satellites around it much as Earth has its own Moon Venus passes through a full set of phases including crescent and gibbous indicating that it must orbit the Sun Unit 14 Astronomical Motion Inertia Mass and Force Since Aristotle it was believed that without some continuing application of power all objects would come to rest Galileo G demonstrated weight dropped from Leaning Tower of Pisa allows him to recognize several properties of motion 1st law of motion was deduced by Galileo from the experiment on the manner in which bodies move and fall A complete understanding was achieved by Isaac Newton 16421727 He did not only reduced Gravity but he also invented Calculus Inertia central to laws of motions the tendency of a body at rest to remain at rest and of a body in motion to keep moving in a straight line at a constant speed ex We are exposed to inertia everyday in life as When we apply brake of our car suddenly sitting standing in a bustrain we measure an inertia by an object s mass l Newton s First Law of Motion The Law of Inertia A body continues in a state of rest or in uniform motion in a straight line at a constant speed unless made to change that state by forces acting on it Inertia cause an object to resist changes in either soeed or direction A body maintains a constant velocity unless forces act on it A soacecraft a planet or an entire galaxy will continue to move through soace along a straight line at a constant speed unless some force anything that can cause a body to change velocity acts upon it There are also times times that there s not net force when the combination of all forces cancel out An example would be a book resting on a table gravity pulls the book down so the book applies force on the table but the reaction force equal but opposite force cancel it out Mass a property of matter Weight a force on an object key points 0 bodies resist change to their state of motion because of their inertia o the amount of inertia of an object is given by its mass which is measured in kg 0 the term velocity is used to specify a speed in a particular direction 0 Newton s 1st law a body maintains a constant velocity unless forces act on it law of inertia o anything that causes an object to change speed or direction is a force a planet on a curved orbit must be experiencing a force mass is a property indicating the amount of matter in an object weight depends on both the mass of an object and the forces that are acting upon it Unit 15 Force Acceleration and Interaction Acceleration changes in motion motion of an object is a change in its position which we characterize both by the direction of the object and by its speed Vector expressed in arrows a quantity that has both a size and a direction lfthe soeed and direction of an object remain the same we would say it has a constant velocity But if it has a change in either direction or speed we say it has a change in velocity And a change during a period of time or defined as Acceleration Basically any change in speed is acceleration Acceleration m secquot2 change in velocity change in time Example suppose a car was going 15m sec southward along a straight road If the car increases its speed 30 msec over 3 sec we could say that the change of velocity 30 msec 15msec 15msec and the change in time 3 sec acceleration 15msec 5 m secquot2 3 sec NewTon39s Second Law of MoTion F m x a The force F acTing on an objecT equals The producT of iTs acceleraTion a and mass m a F m The amounT of acceleraTion a ThaT a body will experience is equal To The force F applied divided by The body39s mass m acceleration grows proportionally to the force applied m Fa Newton s Third Law of Motion law of actionreaction III when Two bodies interact They create equal and opposite forces on each other However when one body has a smaller mass than the other the one with smaller mass moves faster according to second law Unit 16 The Universal Law of Gravity Newton saw apple falling from a tree he realizes there s gravity Law of gravity Every mass exerts a force of attraction on every other mass The strength of the force is directly proportional to the product of the masses divided by the square of the distance between them FG G M x m G is a constant factor M and m in kg d in meter FG in newton dquot2 G 667 x 10quot11 newtons metersquot2 kgquot2 1 newton 1 kg x msecquot2 If either mass of the two increases and other factors remain constant the force increases by the same amount If the distance between the 2 masses is 2x the gravitational force is decreased by a factor of 4 Inverse square proportionality Gravity accelerates on objects similar as they were being dropped on Earth or Moon even though they have different mass Galileo Earth does pull with a larger force than larger mass we can use Newton s second law to calculate the acceleration due to the Earth s gravity gFGGme GM m m X Rquot2 Rquot2 key points an object is falling but it has a large enough sideways velocity to never hit the surface of the object it is orbiting gravity is a pull felt between all objects with mass the force of gravity between 2 bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them objects near the surface of the Earth all accelerate downward at the same rate one g about 98 msecquot2 the surface gravity felt on other bodies such as the Moon differs from that on the Eanh the force of gravity grows weaker with distance but it never drops to zero LIGHT electromagnetic waves light is energy and informations light as wave electromagnetic waves It is electricity and magnetism moving through the space can be dispersed into its component colors and does not require a physical medium to propagate Visible light is only a small part of the entire electromagnetic spectrum Wavelength the distance between crests or troughs of a wave Frequency the number of crests or troughs that pass by each second Speed the rate at which a crest or trough moves 9L V C length X frequency speed C 3 X lO 8 m J quot I 7 y I l X 1 my quot Winn 7 i I r 1 ad t l 7 vquot W 7 hr 39 H l l 1 39 i l i i i i 39 V g HE39ETE39EEEHE39E Emma Elquot light comes in quanta of energy called photonSirreducible quantity of electromagnetic radiations photon has energy and reacts to gravitational eld All types of electromagnetic radiation act as both waves and particles Wavelike properties interference and diffraction Particlelike properties the minimal chunks of radiation of a given frequency Ehv h is the Planck39s constant All light travels with a VGLOCITH 3 X 105 KmS frequency how much energy spectrum of light shows how an object emits absorbs transmits radiation at different wavelengths we can see visible lights 4 z F E e E F E E E I BE E Shert Wavelength E Lang Wavelength err Ia high frequency uw frequency l l IhIgh energy A A e e W EIIEI39QIIJ we 3 E73 E 3quotquot In I fa we E a m z m ET e I v Ee e pq I e 44 e H I e I E e L3 39 39 i E 1 I I a V i I I A 3 I I II I W I III I l I I II I quotI I I I Hi 7 V 39I 7 II I I I I I I II I I I I I I I I I I I I V I I E E E I E E I I E E E E E E E E E E E g E I g E E E 5 E u u E g a a I a I I I E I r n n rI quot393 I I 2 I I I E B E g I a Intensity of Light More photons coming from it more intense light is composed of photons and spread out over larger and larger area as they travel through space brightness decreases as distance increases another inversesquare law Brightness 06 1 d2 Molecules clusters of atoms held together by covalent bond gt atomsgt nucleusgt protons and neutrons mass of atom protons neutrons Heat or thermal energy refers to the amount of energy stored in a body as agitation among its particles and depends on density as well as temperature Temperature refers to the average speed of the particles atom molecule all atoms are vibrating unless at absolute zero 0 Degree kelvin Wiggling electrons give off electromagnetic radiationlight 3 Cool or i J CDWPTESS s w Heater 3 reduce pressure p s j Gas Liquid Crystalline solid 0 Black bodyperfect absorber and perfect emitter O spectrum of blackbody depends on its temperature 0 hotter objects emits photons with a higher average energy max TKelvin o the harder atoms wiggle the more light is produced Wien s law tells the peak wavelength of a blackbody spectrum hottergtbluer coldergtredder StefanBoltzmann Law hottergtbrighter coldergtf21inter emitted power per squaremeter 6 T4 LA GT4 Brightness is different from Luminosity A star s brightness depends on its distance from us the closer the brighter B 4n distance2 o Luminosity total amount of power given off by a star in watts Luminosity of Sun o 1 watts l joulessec L B 439Td2 Bwatts received by each square meter L 1300 wattsm2 X 4n X 15 X 10quot11m2 13 X 10A3Wm2 X 26 X 1023 mA2 L SllIl4 X 10A26 watts generated and being radiated on Sun s surface 0 amount of sunlight striking the Earth is 5 X 1024 joulesyear 0 lO 9 of Sun actually hits Earth 0 consists of nuclei protons amp neutrons and electrons electrons and nuclei bond by the EM force While nuclei bond by strong nuclear force of protons in atom determines its chemical properties of protons and neutrons determines its mass can be in different phases depending on temperature or pressure on it Atom Structure and Spectral Lines 0 electrons orbit nuclei in discrete energy level 0 if electrons absorb photons at the right energy can jump to higher energy level absorption line in spectrum 0 electrons may later emit some color protons and energy transition caused by collision with another atom or electron collisional excitation or ionization energy of photons depend on intensity Interacts in 4 ways 0 emissionphotons are created in matter 0 absorption energy in the photon is absorbed and turned into thermal energy 0 re ection doppler effect 0 moving light sound source emits a different frequency in the forward direction than in the reverse direction O the nature frequency at which an object is emitting is called the rest frequency 0 you ll seehear higher frequency as it gets closer and lower frequency as it gets farther
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