Key, Homework #6, AST 3018, Fall 2011

Key, Homework #6, AST 3018, Fall 2011 - £5 393.8...

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Unformatted text preview: £5? 393.8 HGMEWORK #6 QUE 11f3lli ALL 0? THESE PRGBLEMS ARfi FROM THE TEX? 2.3) The apparent magnitude of the Sun is —26.8. How much brighter does the Sun appear than the brightest star, which has m = ~l? {mawmfi/af ,mg 3: -~ at“? J M; -:». ‘t ,. .- N‘Ba my 53-, met/2,5; fa 3m ,19 $3}? 2/ E‘E "(-2Lré’fl/QMF‘M 2. 5} Show that our definittnn of magnitudes has the feiiowing property: If we have three stars with eaergy fimesnc 1} f2 and ‘3 am? we define m2 — m1— — 2 S logmm/E) and 113— mi: 2.5 iogmfizlfg), then m3 _ {111:2 5 §0g1{)(f1/f3} Mbwmfi 35333551452.) f .r mfivwwz; 2,5“ Eciigiygdgsk} (4 99 me: eewewe Mbwm M2»)::L% W9 >+f6§637fgj W“ ”i; .3. w w W23 W13 2.17) How does the absolute magnitude of a star vary with the size of the star (assuming the temperature stays constant)? fill/f” fifilgrylfiflfififfilfitfl ‘laf‘eei A; om WW \éifi has: as“; R QWM m m M? Mr G :2 53056:; bl 3 all a, by: lag, Er [£1 _. rash! .1, a?” Ff.“ Gd l? sé’ElE fk T‘fiT’Zfl P "La l We 1% 3 a»? “i e eta/13 “5 W‘ L 1.." I 2%“ SGMTAJI“? by l will 61_/2~7‘ " _,., 3. f wit l? flfl L Mi ~42» {it}? be” by H Q‘s-Tgag‘ WET/LE? 2’ XL, 2. WWW” r“ (”a fix M WWWW “30:3 «— e eat; 2.26) (a) if we can measure parallaxes as small as 0.1 arc sec, what is the greatest distance that can be measured using the method of trigonometric parallaxes? (b) By what factor will the volume of space over which we can measure parallax change if we can measure to 0.001 arc sec? (c) Why is the volume of space important? ‘9’) {330A Oll'w’l" :1 “L, x {(3 53¢. 55 {A :o,eo; alga-A" M “M 3; {mafia 3 1 W M W l/lw p—EEWR fl/i dly Ravage)?" 23 E 3? 5 a t; teemffia if; £35.53; __ ; Cla\ agiflézfet gigw} s, ””1 W” ”i?” ”W9; Vi fivfihfitd \lef \ §' ‘ ' ee- giz-a a; 3;: Wise”? a) fisgmmswrfie ”“ am T%EE stale. ggwgny as ,W j e: W; assets-.1 Wm: Nee/WEEK are: areas way daemmm “5? Eifififlffit ffiérflafisTréfiefi “fa The: Uocuxngt ‘ WW “lessee-gees c351“ swam T’B mama we» cm; w t :«r F Mamauwm Ta “em l6 Vera magma 2.27) If we lived on Mars instead ofthe Earth, how large would the parsec be? A Pager-ac, re T'Hfiflf‘ emmwme Fara mews-E {fie}; 4}” w a?" 4 as? .m “rte; fififieimffifilfi‘iflflfi; «use smerewa sea! mm {E at" l flfififififi P: a”; PE” :3 6&1: fgxfl‘im . M: m “a,“ me 'Nh w“ W27 52.“; 45%,?” r3 ... g; —<: ' w fies ' l . ”frag ash-rifle, metres me a? — tPQ 1% the augefiew ex 5', El (”We Mews Pfifgfigg}; 7; L52... E’filfiTl’l l>fififig¥fifi {NA 2.29) Derive an expression for the distance to a star in terms of its distance modulus. 1J5"? (jlr‘fl jéis'lflanJCfi Wirfielmlug -; {MM/Vl- Wfiflfi%§lfl%&fig WwMfi\dMfifl9§Q;L; ”3 {£le 3 fl 3L “3:: refill/f" Oi :; moral fl 4.7) The focal length of the objective on your telescope is 0.5 m. (a) What focal length eyepiece would you have to use to have the image ofthe full Moon (whose actual size is 30 arc min) subtend an angle of 2 degrees? (b) If you then took a photograph with a 500 mm focal length camera lens, how large would the image be on the film? A) [44 3&0 .3. a {$2, I: 2;” ’““ {3; (E). "““ {9 i) 4.13) Suppose you have a Cassegrain telescope at home, with a 0.25 m diameter primary mirror and a secondary mirror with a diameter of 5 cm. What fraction of the primary is blocked by the secondary? 3f Camus” ”it 4.29) If a radio source emits a solar luminosity (4x1033 erg/s) in radio waves, (a) What would be the power per surface area reaching us if we ‘were (i) 1 AU away, (ii) 1 pc away? (b) Ifthat power is uniformly spread out over a frequency range of 1011 Hz, what is the flux density (power/surface area/Hz) in each case? (c) How does this compare with the power you receive from a 50 kW radio station 10 km from you? :53 IQ: Li'XI’DE: :ezg/ggg a) {a} ,2: flgggie 213‘, mu. ~29 ,5; a. a: ”is, M m ‘33gsw a. - . w»W%br-iw 9%, WWWQ «an {$.33 =33 m W575 “ ‘fx/pggems/sse fi-‘cl “We. 3-3 3 O” in} W“ (a) 3: ‘ G % s u" . . a «s :2. ' L mew wwwmmwwss'“? it; “Film 3&3“ ‘3" M “,2“ i l \at “64» - i ‘22 32W) flflmfieffi“ 3“ ‘v , $€¥Mxfi Mia»? hi; ‘ M L“) ,cgwg éfiwfikflfi (:9 ilefiu @1er “ g” a 31:53:: 5‘ K g z: “fig/sic WWW I???” fig! if am g; _ Wgwgmm W 360 CQ‘ {$ég 63- gas Kefl’fi m am. “age ‘ Wit»; 2? We m £3 w 4.32) What is the total collecting area of- (a) the VLA (b) the ALMA with 75 10 m diameter telescopes? (c) For ALMA, how many 12 m diameter telescopes would you need to have the same collecting area as 75 10 m diameter telescopes? a) WA: 4'? " Team? :5: fififamaf ZJQWJM 53347 i L 2.3” I 2”? :cé‘flm #5} :3 M‘TLE) : “2'7 WEE“); :il31330 W a V1?” M a L W m: u A :1 75W 5 ”9 lWfiw {,Efi?‘ {Q fink“ Err, $53 {WSW 0) flJ‘N‘m/M "’ Q/filb ...
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