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WB_Solution_Ch12 - 1 2 Newton’s Theory of Gravity 12.1 A...

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Unformatted text preview: 1 2 Newton’s Theory of Gravity 12.1 A Little History 12.2 Isaac Newton 12.3 Newton's Law of Gravity 1. Is the earth’s gravitational force on the sun larger than, smaller than, or equal to the sun’s gravitational force on the earth? Explain. The. carnit'i'h‘fihfil 'i'DI'CQs are. Cal-nah «AOL OPPOS‘V'LC. ’nu‘Y Owe. om «chen- reaction acne, 2. Star A is twice as massive as star B. a. Draw gravitational force vectors on both stars. The length of each vector should be proportional to the m :2," unit File-‘3 size of the force. m b. Is the acceleration of star A larger than, smaller than, or equal to the acceleration of star B? Explain. “Tl"- m‘lmhm o‘i‘ )i'kr- “is Sun-titer, ‘For 219ml #thl 1., +1“, lev mass wfufimcs the. clad-tr Meeker-then bee-tutu. 9': F7!“ 3. The gravitational force of a star on orbiting planet 1 is F1. Planet 2, which is twice as massive as planet 1 and orbits at twice the distance from the star, experiences gravitational force F2. What is the ratio F [F ? . __ 2 1 Fl 3 G~::’ So F2 :- 6 math 3 (11". ‘GM (ii-MI) E/fi '3 (any: 6"" M. 3 [at—1”, )— 2. 12-1 12-2 CH AFTER 12 - Newton‘s Theory of Gravity 4. Comets orbit the sun in highly elliptical orbits. A new comet is sighted at time :1. a. Later, at time :2, the comet’s acceleration a2 is twice as large as the acceleration a1 it had at I]. What is the ratio r; in of the comet’s distance from the sun at 12 to its distance at I]? _ _ 71 , r} , . For 6113'- 101..; F1. #26 . Fz/F‘ - [3/41 EL - 2.. 50 V: J. ‘f-T’fi. b. Still later, at time :3, the comet has rounded the sun and is headed back out to the farthest reaches of the solar system. The size of the force F3 on the comet at I3 is the same as the size of force F; at :2, but the comet’s distance from the sun :3 is only 90% of distance r;,_. Astronomers recognize that the comet has lost mass. Part of it was “boiled away” by the heat of the sun during the time of closest approach, thus forming the comet‘s tail. What percent of its initial mass did the comet lose? F3 0‘ m9 -~ E—é- . r, 3 . q rt. 50 (‘31: gaff-L2. 1" 1 9‘1”:- l“ ' r3 1 Titanium. W13 3. ?lmz,. Comet's orbit 5 7. 12.4 Little 9 and Big G 5. How far away from the earth does an orbiting spacecraft have to be in order for the astronauts inside to be “weightless”? TLa. astronaut-l1 can be "Marsh-Hen + is Sam 'h: w. mask-Hm rFf-l-is in Hammad orbs“, H “f “n", Chfi‘MC-C hcfinx wt ob?“ $0!" 'H’W. arth-‘hzfiOn-J who ‘32.. mafidlnH-e OLiS‘itncc radar. 6. The acceleration due to gravity at the surface of planet 1 is 20 mfsz. The radius and the mass of planet 2 are twice those of planet 1. What is g on planet 2? gored; Winters-n2 WI ‘H‘L gpactchf“ Ndulo‘. LIN-K- D‘f}. ol-z‘zgzgg 3 r‘ 2' (11" ‘- Newton’s Theory ofGravity - CHAPTER 12 12-3 12.5 Gravitational Potential Energy 7. Explain why the gravitational potential energy of two masses is negative. Note that saying “because that’s what the formula gives” is not an explanation. An explanation makes use of the basic ideas of force and potential energy. 11’“ fimfih‘ho‘nsl Pokn'hkl .2“ng is “£34113“: been-asi— we. Clause.- +19 place t'ke zero Point? 0; pohafl'ial cor—1'37 0r!- “and?! (“at”). '3- 0). gram ‘l‘kis (Janice; m -fil‘0\\lfl‘i2\‘i;0‘\ot fi>ofimfikl emu-{yr is «1.284113% locus-«ss— ‘l'lm consem‘lt'u. Pore-r. 0930411116 ultra-dine, Tb; Two masses wt.“ an} Kmdu. finer-037' an.) +9431 approach end-1 O'HAl-r‘ 12.6 Satellite Orbits and Energies 8. Planet X orbits the star Omega with a “year" that is 200 earth days long. Planet Y circles Omega at four times the distance of planet X. How long is a year on planet Y? RUM Klgf’lCr'S ‘flmn‘ lam)! HAL orbr'l‘i Penal 51“ is i’t‘ofor‘fimusl +9 +1“. aPBfihl Mid-.5 cutback Tat" F3: 2 Wasted“ 1} = m) T?“ (a :33 = 5qu: “(311) TY :- STX . A’Yfifl'fln rlfinc'l' Y is 1500 ewtkdqrslma_ 9. The mass of Jupiter is M Jupiter = 300114531111. Jupiter orbits around the sun with TJupim = l 1.9 years in an orbit with rjupim = 5.2rcanh. Suppose the earth could be moved to the distance of Jupiter and placed in a circular orbit around the sun. The new period of the earth’s orbit would be a. 1 year. .119 years. c. Between 1 year and 11.9 years. d. More than 11.9 years. c. It could be anything, depending on f. It is impossible for a planet of earth’s mass the Speed the earth is given. to orbit at the distance of Jupiter. Circle the letter of the true statement. Then explain your choice. We. «or-lai'i‘al fcrfo‘l {5 inAQng. 5F w mass 0-? Hub (gt-loam“Q load? ‘ Prometpol warm “st—hat) war; was is Muck leis ‘HM-m 'HNG. mass: 03 N bade-1 befmbor—b.+el. 12-4 C H A PTER 12 - Newton‘s Theory of Gravity 10. Satellite A orbits a planet with a speed of 10,000 mfs. Satellite B is twice as massive as satellite A and orbits at twice the distance from the center of the planet. What is the speed of satellite B? Saddll'l-e 17:3 mass is nai‘ Peters-«Ti, ha? «1‘ Twice—v Molishcn, H3 Orbi'i'kl flrioal is arch-W57 ¢~ 5‘11““ 0'? JGL)?‘ 3 2-5.- ‘Bu't- ’r‘kc. Africa“ "d- mms‘l‘ had tint-:33 £0.61 pedal is Alina tare-ct” . . 1 .- .L '01 «Hal-or of- 2. Thus, rt: tip-zeal ks {FL its; o files; V5 3 6101“,}; 7: 1,071 5f; 9:. “hue-5..“— 11. a. A crew of a spacecraft in a clockwise circular orbit around the moon wants to change to a new orbit that will take them down to the surface. In which direction should they fire the rocket engine? 0n the figure, show the exhaust gases coming out of the spacecraft. 15,", m rad“: Mona $0M . b. 0n the figure, show the spacecraft‘s orbit after firing its rocket engine. 0. The moon has no atmosphere, so the spacecraft will continue unimpeded along its new orbit until either firing its rocket again or (ouch!) intersecting the surface. As it descends, does its speed increase, decrease, or stay the same? Explain. As a. olefin-19, HS Wag gnu-uses asli’ Lose; Meshkl “er-.31 M 3665 kind“. “0:31, ...
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