Cosmology 20B S06 Homework 1-4

Cosmology 20B S06 Homework 1-4 - :/‘ a ll\ I...

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Unformatted text preview: :/‘ a ll\ I 11", IIn‘l.. LII fl _w\3“‘n Wm -‘ Homework 1 Due Date: Tue, Jan 18 2005. Turn in at lecture or to TA Kyle Stewart’s Mailbox by 4pm Tuesday Please use separate paper to write your answers on, and staple this page to the top w1th your name. Homework without this page attached will not be counted. All of the following (1-4) will be graded: . _ . 1. The closer a. planet, asteroid, or comet is to the Sun in its orbit, the faster 1t moves. This IS a consequence of A Kepler’s first law B the Law of Equal Areas C Kepler’s third law D Newton’s first law. 2. Not long after the death of Nicholas Copernicus, a. Danish nobleman used giant instruments called “quadrants” to make observations of the planet’s motions with unprecedented accuracy. Circle the name of this astronomer: A Galileo Galilei B Johannes Kepler C Isaac Newton D Tycho Brahe “ K . . 3. What was the name of Ptolemy’s major work? A. The Pdmagest, B. Primum Mobile, O. Revolutlombus, or E. Principia Mathematics. ‘ 4. A. Write 0000035 in Scientific notation: B. Write 134,000,000, 000 in Scientific notation: One of the following (5-8) will be graded: 5.. A. Write the answer in Scientific notation 1.5 x 10*8 X 300 =? B. (8x103)x(5x102)=? C.(8x103)+(5><102)=? 6. A. What is a light-year? B. If I wanted to write down the value of a light year in every—day units, would I use seconds or kilometers? C. Write down the value of a light-year in every—day units (either km or see, depending on which one is right). Use Scientific Notation: 7. The dinosaurs ruled the earth for roughly 190 Million years. If the age of the Universe were crunched down into one year, how long was the period of the dinosaurs? Show your work. (Hint: Answer is either 5 sec, 5 days, 5 weeks, or 5 months.) 8. Planet “X” is discovered orbiting around the Sun. It’s orbital period is 465 yr. A. Is planet “X” farther or closer to the Earth than Pluto? (Pluto’s period is given in the back of the book). B. What is the semi—major axis of planet X in A.U.? 17.! 3 M m» .. » \ 13 Pa" 2. D 3, A . 4- a) 3.5mm? b3 \.’3'4xmUL SQKSAS‘Z x 3 M01" 7- 45 xvié b ; )(Xstfi (Duo) = Ronny: LIMDL C) (Duos) «*Cs'xto") = ‘Booo «3'50 —-— Y.Sxtbj 6. 0L) A 'ntMTAGAR‘ Is 7»; msTANca LlLH-T Tuvns m on; Yam Hm \5’ \7. C) ‘46 K\O m = "ii-MK“) KM \AYMIJK 1 Send}, 3.; A- Lum'r Moves n A F-‘WTF SPEED] 5c. mm; 13 A We ML ’BE‘TUE‘EN award um? LS EMWED AMI) Ramveq ‘1: AN 013370 15 van PAH. Ms; we see :T #3 n I: H was" M7 (4am w “:3 . PB. 1. ’3. YES) Games; \SE 5-5;: Tm-EM A—S TL‘rE't 0.152313 C. MOT meat-Y. Mth Doe-s No‘r “nursz Mu: 76w»; US) Q.qu A4341“ PLO/A 0%, ALTA-0116..“ ]F W; OthER)? gm: comet) MD cLosip 11' ;«mn 135 PO:5\BLE: Kai/‘2 7% Q/ a —P —“' —-> \L \5 7' \ CENT MVE: AMA-1 TR ‘1 (—r <—-—- P k/ CURVED, gum-J) mam: fl't A)‘A5 on]? TMNELS 5mm»! r‘E‘t—o CNSTEwT/dfll AfPEAL cvm IMM " Du’fl—IHL A murmu— EcuPSE‘J ear-“n+2 sMpau F3 “54515 A CIfi-LLE QESHWS S/HL ANM' qvat Tm? malted} TM; gum. At..st WWW“ Pubs 7‘ m-Tm: my Is wwzmaT memws) » (W535 0? firms; "MM/~13 or» .jomEfL \Mu's- 1.- 5°L’45- 1M0 : 530th (4n = 500M = ‘Qgfim’ Rxor‘m ’ '-H‘r 3C5 LiK‘I-‘kbxfo‘Lw: 31““;35“ % x7, ’3 findsw 49“ q-xubr‘?‘ ta 6 3 : 3.1—%x\0 CM :— 3.1YK\DM = 3"” “0“” Ml: object, "-"""‘ "a: HomeworkWZAL: Gfiwkl (to Due Date: Tue Jan 24 2005. Turn in at lecture or to TA Kyle Stewart’s mailbox by 4pm Tue Please use separate paper to write your answers on, and staple this page to the top with your name. Homework without this page attached will not be counted. _ A l- - r ' 1 a 9% All of the following (1—4) will be graded: _’ 1. All other things being equal, and ignoring atmospheric efiects, a reflecting telescope with a large objective mirror will have, compared with a telescope with a smaller mirrorJ ' A better light—gathering power only. M fl 6 7‘ G)" fl B better resolution only. I better light—gathering power and better resolution v m oficamn a \D/btt 11 ht th ' b t It ' V n“? ' ms“ e er g —ga ermg power u poorer resou ion Ma“ r * 1N" o 61 WM Wfié mad: 0? pas-3min? 2. A radlo telescope is 100 meters across. How many times bigger is it than th ypical wavEW’ measures, if it typically measures lD—centimeter waves? (i.e., how many wavelengths across is it?) \ i A 1000000 wavelengths across. H O M 1; ——% ION/o \AOOO wavelengths across. g1) 9K {Idaaf/ C 100 wavelengths across. 3. An object is moving through space. If all forces are removed, the object will: 1C Continue in a straight line, and eventually (after a very long time) slow down, and stop. 1 “ -nter a circular orbit, much like the moon. J Continue in a straight line at constant speed. 9.! Become a black hole. 4. True or False: Kepler’s laws a ply only to lanets orbiting the sun. His laws must be modified for satellites orbiting the earth. One of the following (5-9) will be graded: 5. Earth’s atmosphere shields us from most kind of electromagnetic radiation. Name one kind of electro- magnetic radiation that is prevented from reaching the earh’s surface Warmers, x—rays, etc.). i Y S 6. What year was Newton born. If you were to ask a random person in his town what the term “gravity” . .f. , meant, what would they have said. LP L ‘ golmfi: Moocfl (\o‘r GK 7. A. Why do astronomers put telescopes in space? M l“? flWQ‘SQVW/RL 92:14 - pe a K t S B. Are we more likely to want to put a gamma—ray telescope into space or radio telesco 0 space? Why? wife. C. Discuss the limits of space probes compared to telescopes in terms 0 learning about the distant un1~ verse. 8. What is the doppler effect? How is it related to the property of light known as “redshift”? 9. Why is it hot in the Summer and cool in the Winter? é. mm was lawn Gm What/z bear-"1 ad: Solewml' Moocl no‘\ a gr"le 7. 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SrAca FMfiES 9w 12.53904 onV TH»; ENE 0F We Saul-1L s-rgTEM M A FEASdHMLF TIME. TELESCOPE"; vw swan-r #mum-a M0945 PISTANT 033665.. ‘5’. Th: DOPFLEJC EFFECT :5 1w; ” smarmwa“ m“- A GAVEvEflkTH csF' dep mdsau Br 4,1 OESECT- MonNL W AT Prth SPEED LILLYI’ SEEN PrzaM AN og'SEa' 79.45;? \s rume A—o/‘r!’ NT mm 5W5 D 13 SPn'F'YE‘D want-pg asylum maxi-ELEM MW am: my, "JV-h; \s *fizpsH‘PTfl WINK 7, $ow'rwu5 ; {93- ‘t. $ME¢ km! 9- fl av U‘NTErL ,’ :somm 7%; THE OF THE E'EPI’W'I'H [Ang P—Esya err 7:: as 17—07%de Ans (Asia-rs Twi— sewsogs, ANNE!) Tower—1;; sans % 1,-9.9 ATm5/Hytus <5 mm; 11431715“. gas—fl x o_ ‘ A, DE’cfi-EA'SE WY“ Prudka Popps TouMbs G. 'fl’r‘g Subs ( c. A D. X FMRT Stou‘es'r Wm: 2. saws. M: (Q Pr. 0 DUTAl-ilct? A—flnwub = INK , W“ _,. ‘ZSKR Rpm: *— “mm: H ‘13“ 4 1/? T3 xv _. 71‘1": KK\..5‘xw“M A r i t v 7n. vi, a- . P - Homework 3 4,, - 1,, r143 i will' Due Date: Fri, Feb 17 2006. Turn in at discussion or in TA Kyle Stewart mailbox by 11am Fri. Please use separate paper to write your answers and staple this page to the top with your name. Homework without this page attached will not be counted. MULTIPLE CHOICE: All problems (1-8) will be graded. 1. What physical process allows for the technique of “carbon dating” to work? A. Energy level transitions B. Nuclear Fusion C. The scattering of red light preferentially over blue light D. Radioactive Decay E. Both a. and d. 2. The stellar luminosity—temperature relation A. Holds only for very hot stars B. Applies only to white dwarfs C. Applies to main Sequence Stars D. Can be used to determine distances to stars E. Both 0. and d. 3. Einstein’s impact on science included i A. Laying the foundation for modern cosmology B. Reformulating our notions of fixed space and time C. Introducing the concept of “light quanta” D. All of the above. E. Both a. and b. 4. If, after a supernova, the stellar core retains more than 2 or 3 solar masses, the result will be a: A. black dwarf B. black hole. C. neutron star. D. supermassive star E. white dwarf. 5. Stars in the galactic halo are generally A. very old. B. very young. 0. very massive. D. accompanied by clouds of gas and dust. E. Both b. and c. 6. At the event horizon of a black hole, what is equal to the speed of light? ‘ A. The rotation velocity B. The escape velocity C. The terminal velocity D. The pressure gradient E. The apparent velocity of a distant observer 7. The largest elliptical galaxies A. tend to have older stars than spiral galaxies B. tend to have a lot of recent star formation 0. have a disk-like configuration D. can contain more than 100 billion stars both a. and d. 8. True or False: The first supernova ever recorded by humans occured in 1997. TWO OF THE FOLLOWING (9-15) WILL BE GRADED. 9. A. What two things did Einstein assume in order to prove his famous formula E = 11162? B. According to this equation, how many Joules of energy are contained in 5 grams of sugar? C. According to Einstein’s equation, how many Joules of energy are contained in 5 grams of fat? D. Assume that a Food Calorie is equal to 4, 200 Joules. Our bodies can extract about 9 Food Calories from each gram of fat. How many Joules of caloric energy can our bodies extract from 5 grams of fat? 10. A. What is Nuclear Fusion? B. What are the physical conditions in the Sun that make nuclear fusion happen? C. What is Nuclear Fission? D. Name one example where Nuclear Fission occurs 11. What two forces are competing when a star is in “hydrostatic equilibrium”? 8. 15am- M. H - - WW3 V€(D(J1-A( 7. W. M03325 B. 25m 6 SOMLQ %. fl? 0? . 9'93 garm Uni—MI) )‘a gal/051,33 Cami?!" p3. Yul/5c; ’3? 3h,“ 2:: 5. O Hbvg bf“ BOX/0831 um»... I 31:”???wa C. M 5 W? gm :50 mu 5 ‘. 12?; ea?“ V 5; 2‘ 12?) . , mic (3+8 .Ho W. , _ C :: lag/Seg‘qflfl . 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Qwhtmu, amok nun-{3 dazsz , 3%]:va media mafi- .V‘vae mm @smbk +1»th flow. CH“ S‘l-LCL'IO\ max-77$. Emu 06 W pmdufi-cc/ K91 um . 30 mi\\-¥m .L- {'5 }6 H63” ken? enough QM M mve‘bfiivh&£/\:§E .O "HA-L 0/1?“ it’lfl '1. «bur- no}: "70 Mbmh‘v~._ {R‘V'fifi ‘gokar S _ 33mm, bah; 30f? f’Vh-Hllim Ligars seems “we M (:9? MW PmL-es<r($, such («S {(05% k occur. ‘ \50, thwa Kdvm was; mw‘nwc? as h» ‘Fh‘lfi COWSSC 69 N Cit/18‘.“ L \QCWN 'ZL--L-rh- be C m-<$--< .lflg 0046» M ()Wwefiluxmbwsflég .flM SLm geouéa W. guano" “Warn 1mm. EV Ct“- é-ébf‘f’k wake- 12 /_50 \xi‘ L. _ - Cosmology 203 Homework 4 . as = bue Date: Tue Mar 7 2006. Turn in at lecture or to TA Kyle Stewart’s mailbox by 4pm Tue Please use separate paper to write your answers on, and staple this page to the top with your name. Homework without this page attached will not be counted. All of the following (1-4) will be graded: 1. What settled the “age crisis” in cosmology in the late 1990‘s? (that the Universe seemed to be younger than the oldest stars)? A Evidence that radio carbon dates were off by a small factor B Evidence that the Univese was expanding @FEvidence that the Universe was accelerating D Evidence that the Universe was slowing down in. its expansion 2. How did Hubble determine the recessional velocities to distant galaxies? —TLL.‘.:EEW‘ r x -- rat... ~" @He measured the periods of Cepheid variable stars I @He measured the shift in wavelengths of “lines” in their spectra C He measured the parallax angles to each galaxy using the 100 inch Hooker telescope D He measured each galaxy’s black body temperature .3. Among the fundamental expectations of the Big Bang theory is that The Universe was much smaller and more complicated in the past. . he Universe was much smaller, denser, and colder in the past. he Universe was much denser and hotter in the past. . The Universe itself is a black hole. 4. The earliest time we can directly “see” using light waves is a . About 3 million years after the big bang ' About 300,000 years after the big bang . About 3 years after the big bang D. About 3 minutes after the big bang Two of the following (5-9) will be graded: & 11/“th ‘ 5'. Name the four “pillars” of the big bang. Walsh“ 3 WW“? ' I. A. If H0 is Hubble’s constantI in what sgns‘epvi‘s 9the value of l/Ho a “limiting case” for the age of the Universe? B. If H0 : 50km s‘l Mpc‘1, what is the value of 1 / H0 in years? I 5' + l : mu L,,\‘I\,‘f .1; .( Lx'yrfid .' r' t)? r Vin lg. . .A - -' ' : .-“l~< , -'..r a!“ j _: A 7 In." ‘15.. 3'0 what. ,rkj‘f- :r w l =' I . 7'. Suppose an astronomer measures a galaxly redshift to be 2 = 0.08. What is the approximate recession velocity of this galaxy? 15‘ C r ,__,:,,Lf__._.__._ it: "5‘ " - - a if 1 1]. 32-390 79c C: 8. Why can’t we “see” what the Universe was like before the epoch of the cosmic microwave background radiation? f,“ 9. Explain the connection between the geometry of the Universe and its overall density. (Hint: What density of the universe gives “flat space”?.) For 10. choose either “less math” (V1) or the “more math” (V2) version. Please make clear which of the versions (V1 or V2) you are answering. # 10 Will be graded. V1: Less Math 10. A. What was the primary plan for determining H0 via the Hubble Space Telescope? Be sure to mention what the two types of “standard candles” were and what the term “standard candle” means. How were velocities determined? B. What was the main evidence for “Dark Energy” and how was this evidence obtained? C. What is the percentage “composition of the cosmos” in terms of dark matter, dark energy, heavy elements, etc.? V2: More Math 10. A. The current “best guess” range of H9 is Ho = 65 m 85km s—l Mpc_1. What range of “Hubble times” (1 / 1%) does this correspond to? B. Suppose that the radiation left over from the big bang were actually at a temperature of 10K rather than 3K. At what wavelength would the radiation be most intense? (Hint: use the black body law). Man“ :9 z ,‘i am“ I1 K 11. (This question will be graded.) Long answer (1 paragraph) What is the Cosmic Microwave Background radiation? Who discovered it? Why was its discovery important in our acceptance of the big bang theory? Oalw‘aflvfl HI? «may f/Z-HIM __ - .1, Km ((73be yfifi-mefim flgfltfl, fifth/‘09 TE: pr: W‘ W‘Afifiag 1L4 Irma: f m h c)? W)” S 1445-7» {rad/g, SWIM/M 'LM\W'S‘E .. 6' A: E a Iwzaqic 1} 5:» ¢-.{<fflc:s?'§ 41%.} M {jg-icwgrfi fix (Mud! fink wok anal 5150:2531 kW 43;” 41M {Effidfi'lré‘éi 3‘“ ‘fpé-tflc i, 510 {g m JELMS $bvwflxé éwémjf . SON/Ea. .sac, l'jI: 3.\Smi()1m km YD . {-DS‘L-x’1:"LwMY‘Mmm ‘ [Ba-W'Vd W'M‘AL’“ .13 m u \C’ Q‘sfiwhp “ham Elk git if Wk W ha «1 m am MA 0m m Hack. wax/it; fin}? £53; {LE-.41: :3: . Ip-é.-rfic?-.fz~$ Md Dada Li 7 0N9? 505; 3%"??? C(EBCm‘fu" 4141; f” M‘nhhl‘h JIM“ 9%19 ‘ 10‘." aficmnw £003 Mim‘oafl M “a” ‘1 W313“ ‘ *0 hi -HVHUM.’ GK E’m‘fi (an-x; C-émgk how. M. {Jr} W21 gals W‘n “47%” $1 4-K M 63431-1 {Law IMTM .: i LL16} Ci!” “3 $513". :3 if?” r - > My w’t‘i (“‘10P : '“ w a.‘ l M 6 1"“ ' '1 ’ “7/5/30 Cosmology 20B Homework 4 Due Date: The Mar 7 2006. Turn in at lecture or to TA Kyle Stewart’s mailbox by 4pm Tue Please use separate paper to write your answers on, and staple this page to the top with your name. Homework without this page attached will not be counted. All of the following (1-4) will be graded: 1. What settled the “age crisis” in cosmology in the late 1990’s? (that the Universe seemed to be younger than the oldest stars)? A Evidence that radio carbon dates were off by a small factor B Evidence that the Univese was expanding @Evidence that the Universe was accelerating D Evidence that the Universe was slowing down in its expansion 2. How did Hubble determine the recessional velocities to distant galaxies? He measured the periods of Cepheid variable stars B He measured the shift in wavelengths of “lines” in their spectra C He measured the parallax angles to each galaxy using the 100 inch Hooker telescope D He measured each galaxy’s black body temperature 3. Among the fundamental expectations of the Big Bang theory is that A. The Universe was much smaller and more complicated in the past. B. The Universe was much smaller, denser, and colder in the past. @ The Universe was much denser and hotter in the past. D. The Universe itself is a black hole. 4. The earliest time we can directly “see” using light waves is A. About 3 million years after the big bang ®About 300,000 years after the big bang C. About 3 years after the big bang 2. About 3 minutes after the big bang (HQ, “(ck 59W kw Two of the following (5—9) will be graded: 5. Name the four “pillars” of the big bang. 6. A. If H0 is Hubble’s constant, in what sense is the value of 1 /H0 a “limiting case” for the age of the Universe? B. If H0 = 50kms‘1 Mpc_1, what is the value of l/Ho in years? 7. Suppose an astronomer measures a galaxy redshift to be 2‘: 0.08. What is the approximate recession velocity of this galaxy? _,_ \J/ t 7);?! H 7’ (We; Marc ' ‘ \“f 1H1 \U 8. Why can’t we “see” what the Universe was like before the epoch of the cosmic microwave background radiation? ,; 9. Explain the connection between the geometry of the Universe and its overall density. (Hint: What density of the universe gives “flat space”?.) For 10. choose either “less math” (V1) or the “more math” (V2) version. Please make clear which of the versions (V1 or V2) you are answering. # 10 Will be graded. V1: Less Math 10. A. What was the primary plan for determining Ho via the Hubble Space Telescope? Be sure to mention what the two types of “standard candles” were and what the term “standard candle” means. How were velocities determined? B. What was the main evidence for “Dark Energy” and how was this evidence obtained? C. What is the percentage “composition of the cosmos” in terms of dark matter, dark energy, heavy elements, etc.? @re Math 10. A. The current “best guess” range of H0 is Ho = 65 — 85km s‘1 Mpc_1. What range of “Hubble times” (1 [110) does this correspond to? B. Suppose that the radiation left over from the big bang were actually at a temperature of 10K rather than 3K. At what wavelength would the radiation be most intense? (Hint: use the black body law). 11. (This question will be graded.) Long answer (1 paragraph) What is the Cosmic Microwave Background radiation? Who discovered it? Why was its discovery important in our acceptance of the big bang theory? . EVIL "‘-’< '3“: ‘4' iQ—C. ‘ . “. ‘5 . __ A . . . ,Ad- 9“! ?\'\‘HS 09’ TV“; ngmngficfl as} W \JJMU‘J-‘H-C r :7 1 1. 1w, Lox-mt; Mwnw‘wt LDKQVL/Cflfndr g thibrdficdrMucrleufijfl’rkas\ ‘N f . . , ._., Ll- 1"— évou’f‘“ “5 (Sdont‘ ac“ V154 Soda .2. ‘ gawmwew o3? kw... 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Cosmology 20B S06 Homework 1-4 - :/‘ a ll\ I...

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