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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. Calnah «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 Suntiter, ‘For 219ml #thl 1.,
+1“, lev mass wfuﬁmcs the. cladtr Meekerthen beetutu.
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
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2. 121 122 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. ‘fT’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: gaffL2. 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. astronautl1 can be "MarshHen
+ is Sam 'h: w. maskHm rFflis in Hammad orbs“, H “f “n", Chﬁ‘MCC hcﬁnx wt ob?“ $0!" 'H’W. arth‘hzﬁOnJ
who ‘32.. maﬁdlnHe 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; Wintersn2 WI ‘H‘L gpactchf“ Ndulo‘. LINK D‘f}. olz‘zgzgg
3 r‘ 2' (11" ‘ Newton’s Theory ofGravity  CHAPTER 12 123 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“: beenasi— 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. Porer.
0930411116 ultradine, Tb; Two masses wt.“ an} Kmdu.
ﬁner037' an.) +9431 approach end1 O'HAlr‘ 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. «orlai'i‘al fcrfo‘l {5 inAQng. 5F w mass 0? Hub
(gtloam“Q load? ‘ Prometpol warm “st—hat) war; was
is Muck leis ‘HMm 'HNG. mass: 03 N bade1 befmbor—b.+el. 124 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'le 17:3 mass is nai‘ Peters«Ti, ha? «1‘ Twice—v Molishcn, H3
Orbi'i'kl flrioal is archW57 ¢~ 5‘11““ 0'? JGL)?‘ 3 25. ‘Bu't ’r‘kc. Africa“ "d mms‘l‘ had tint:33 £0.61 pedal is Alina tarect” . . 1 . .L
'01 «Halor of 2. Thus, rt: tipzeal ks {FL its; o ﬁles; V5 3 6101“,}; 7: 1,071 5f; 9:. “hue5..“— 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. oleﬁn19, HS Wag gnuuses asli’ Lose; Meshkl
“er.31 M 3665 kind“. “0:31, ...
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