Section 6.2: Orbits. Gm r. v = v 2 = Gm r. m = rv2 G. Solution: m = rv2 G ( )( 7.5!10 5 m/s ) 2. = 5.34!1017 m m kg # # m2. kg 2

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1 Section 6.2: Obits Mini Inestigation: Exploing Gaity and Obits, page 298 A. When I incease the size of the Sun, Eath s obit changes: the obit is close to the Sun. B. he Moon is pulled out of Eath s obit and obits the Sun. When you incease the size of Eath, the Moon obits close and faste. C. he obital adius and obital peiod decease. D. Answes may ay. Students should descibe a system using the satellite and planet simulation that includes a gaity assist by haing the satellite use the planet s gaity to change diection. he scale is too small to notice changes in speed. utoial 1 Pactice, page Gien: m; m/s; G N m 2 /kg 2 Requied: m Analysis: Reaange the equation fo speed to sole fo mass: 2 m 2 G Solution: m 2 G 7.5!10 5 m/s !1017 m m kg # 6.67!10 "11 s 2 kg 2 # m2 m 4.5!10 39 kg Statement: he mass of the black hole is kg. 2. Gien: m; m kg; F g N; m Sun kg; G N m 2 /kg 2 Requied: ; Analysis: ; 2! Copyight 2012 Nelson Education Ltd. Chapte 6: Gaitational Fields 6.2-1

2 Solution: Detemine the obital speed of Mas: Sun 6.67!10 "11 s 2 #m2 kg !1030 kg 2.28!10 11 m !10 4 m/s two exta digits caied 2.41!10 4 m/s Detemine the peiod: 2! 2! 2.28 "1011 m m "10 4 s "10 7 s " 60 s " " 1 d 24 h " 1 y 365 d 1.90 y Statement: he speed of Mas is m/s, and its peiod is 1.90 Eath yeas. 3. Gien: d km m; E m; m E kg; G N m 2 /kg 2 Requied: ; Analysis: Detemine the obital adius, then use the alue fo to calculate the speed, hen use the equation fo peiod, 2!. d + E 6.000!10 5 m !10 6 m 6.98!10 6 m. Solution: 6.67!10"11 N #m 2 /kg !10 24 kg 6.98!10 6 m 7.559!10 3 m/s one exta digit caied Copyight 2012 Nelson Education Ltd. Chapte 6: Gaitational Fields 6.2-2

3 2! 2! 6.98 "106 m "10 3 m /s s " 60 s 97 min Statement: he speed of the satellite is m/s, and the peiod of the satellite is 97 min. 4. Gien: d 25 m; Moon m; m kg; G N m 2 /kg 2 Requied: Analysis: Solution: Detemine the obital adius: d + Moon 25 m +1.74!10 6 m 1.740!10 6 m Detemine the obital speed: 6.67!10 "11 s 2 #m2 kg !1022 kg 1.740!10 6 m 1.7!10 3 m/s Statement: he obital speed of the satellite is m/s. Reseach his: Space Junk, page 302 A. Ai esistance will slow a satellite and cause it to slip into a lowe obit. B. he satellite may hit othe satellites o bun up in the atmosphee. C. Sample answe: Yes. Diffeent styles of ockets and boostes ae being consideed fo space missions. Anothe way to educe space junk is to equip satellites with small boostes that would enable them to fall to Eath once they hae become obsolete. D. Sample answe: Space junk is egulaly falling to Eath. o speed up the emoal of space junk, specific missions to emoe space junk can be undetaken. A poposed technology that could help educe the amount of space junk is a lase boom. A lase boom is a gound-based lase beam that would heat space junk enough to cause it to beak apat into much smalle pieces o change diection and fall to Eath. Copyight 2012 Nelson Education Ltd. Chapte 6: Gaitational Fields 6.2-3

4 E. Answes may ay. Sample answe: Hi Amelia; I was eseaching the Intenet and found out that space junk is actually many types of debis. Accoding to the NASA Obital Debis Space Pogam Office space junk is abandoned spacecaft o spacecaft pats that no longe wok these items float aound in space cicling Eath until they fall back down o collide with othe space junk uppe stages of launch ehicles these ae pats of space shuttles that ae fied off o ejected in stages, usually the uppe pats of the ocket which get ejected last and ae tapped in Eath s obit solid ocket fuel some space shuttles use solid ocket fuel fo populsion and some can be left oe afte launch in the containe in which it was sent up tiny flecks of paint when spacecaft entes space, heat o collisions with small paticles chip paint fom the suface of the spacecaft I find it inteesting that paint flecks ae consideed space junk, and despite thei size they can actually do quite a bit of damage when they stike objects. Space junk can obit Eath at a speed of moe than 3.5! 10 4 km/h. If a speck of paint taelling at that speed hits a space station, it can ceate a 0.6 cm diamete hole in the window of the space station. Had to beliee something that small can cause a lot of damage! Section 6.2 Questions, page Natual satellites ae natual objects that eole aound anothe body due to gaitational attaction, such as the Moon in the Eath Moon system. Atificial satellites ae objects that hae been manufactued and intentionally placed in obit by humans, such as the Intenational Space Station. 2. Micogaity is a moe accuate tem than zeo gaity to descibe what astonauts expeience on the Intenational Space Station. Micogaity is one millionth the alue of g. 3. GPS satellites ae a netwok of 24 satellites that coodinate seeal of thei signals at once to locate objects on Eath s suface. 4. a A geosynchonous obit is an obit at a location aboe Eath s suface such that the speed of an object in a geosynchonous obit matches the ate of the Eath s otation. b A satellite in geosynchonous obit appeas to pass though the same position in the sky at the same time eey day to an obsee on Eath. c A satellite in a geostationay obit appeas to emain in the same position in the sky to an obsee on Eath. 5. Gien: 24 h; m E kg; G N m 2 /kg 2 Requied: Analysis: Use the equation fo peiod to isolate, 2! equation fo to isolate and sole fo,.. hen set the alue fo equal to the Copyight 2012 Nelson Education Ltd. Chapte 6: Gaitational Fields 6.2-4

5 But fist conet 24 h to seconds: 24 h 1 d s 2 2! 2!! 2! 4! 2 3 4! 2 2 2! 60 s Solution: 2 3 4! 2 m kg 6.67 "10 #11 s m 2 2 * kg 2 * 5.98 "1024 kg s 2 3 4! "10 7 m Statement: he obital adius of a satellite in geosynchonous obit is m. 6. a Gien: y; km m Requied: Analysis: Use the equation fo peiod to isolate and sole fo, 2!. But fist conet the peiod to seconds: y! 365 d 1 y! 24 h 1 d! 5.188!10 9 s two exta digits caied 2! 2!! 60 s Copyight 2012 Nelson Education Ltd. Chapte 6: Gaitational Fields 6.2-5

6 Solution: Detemine the obital speed of Neptune: 2! 2! 4.5"1012 m "10 9 s "10 3 m/s two exta digits caied 5.5"10 3 m/s Statement: he obital speed of Neptune is m/s. b Gien: km m; m/s; G N m 2 /kg 2 Requied: m Analysis: Use the equation fo speed to isolate and sole fo m, 2 m 2 G Solution: m 2 G 5.450!10 3 m/s 2 4.5!1012 m m kg # 6.67!10 "11 s 2 kg 2 # m2 m 2.0!10 30 kg Statement: he mass of the Sun is kg. 7. Gien: 29 y; 9.69 km/s m/s Requied: Analysis: 2! 29 y! 365 d 1 y! 24 h 1 d, but fist conet the peiod to seconds:!! 60 s 9.145!10 8 s two exta digits caied 9.1!10 8 s : Copyight 2012 Nelson Education Ltd. Chapte 6: Gaitational Fields 6.2-6

7 Solution: Detemine the obital adius of Satun: 2! 2! 9.69 "10 3 m/s 9.145"108 s 2! 1.4 "10 12 m Statement: he obital adius of Satun is m. 8. a Gien: m; m Sun kg; G N m 2 /kg 2 Requied: Analysis: Solution: 6.67!10 "11 s 2 #m2 kg !1030 kg 5.03!10 11 m !10 4 m/s two exta digits caied 1.62!10 4 m/s Statement: he speed of the asteoid is m/s. b Gien: m; m/s Requied: Analysis: 2! Solution: 2! 2! 5.03"1011 m m "10 4 s "10 8 s " 60 s " " 1 d 24 h " 1 y 365 d 6.17 y Statement: he peiod of the asteoid is 6.17 y. 9. Gien: m kg; m; G N m 2 /kg 2 Requied: Analysis: Copyight 2012 Nelson Education Ltd. Chapte 6: Gaitational Fields 6.2-7

8 Solution: 6.67!10 "11 s 2 #m2 kg !1030 kg m s! 60 s 4.05!10 12 m!! 1 km 1000 m 2.06!10 4 km/h Statement: he obital speed of the exoplanet is km/h. 10. Gien: m; 1100 d; G N m 2 /kg 2 Requied: m Analysis: Use the equation fo to isolate and then sole fo, 2!. hen use the equation fo speed to isolate and sole fo m, 1100 d! 24 h 1 d!! 60 s 9.504!10 7 s two exta digits caied 2! 2! 2 m 2 G Solution: Detemine the obital speed of the exoplanet: 2! 2! 4.03"1011 m "10 7 s "10 4 m/s two exta digits caied. But fist, conet the peiod to seconds: Copyight 2012 Nelson Education Ltd. Chapte 6: Gaitational Fields 6.2-8

9 Detemine the mass of the sta: m 2 G 2 " m 4.03!10 11 m 2.664!10 4 # s m kg 6.67!10 11 s 2 m2 kg 2 m 4.3!10 30 kg Statement: he mass of the sta is kg. 11. Gien: m; m kg; G N m 2 /kg 2 Requied: Analysis: Use the equation fo peiod, 2! 2! 2! 2! 3 Solution: 2! 3 2! 9.38 "10 6 m 3 kg m 6.67 "10 #11 s 2 m2 * * kg "1023 kg s " 60 s " " 1 d 24 h. Fo in the equation fo peiod, use d Statement: he peiod of Phobos is days. 12. Gien: 24 h; m E kg; G N m 2 /kg 2 Requied: Analysis: Using the equations fo peiod and speed, isolate in each: 2!,. hen set the two equations equal to each othe and sole fo.. Copyight 2012 Nelson Education Ltd. Chapte 6: Gaitational Fields 6.2-9

10 But fist conet 24 h to seconds: 24 h 1 d s 2! 2! 2! 2 3 2! Solution: 2! 2!! 60 s ! kg m 2! 6.67 "10 #11 s 2 m2 * * kg "1024 kg s 3073 m s " 60 s " " 1 km 1000 m 1.11"10 4 km/h Statement: he obital speed of a satellite in geosynchonous obit is km/h. 13. a Gien: m Sun kg; Mecuy m; Venus m; Eath m; Mas m; G N m 2 /kg 2 Requied: Mecuy ; Venus ; Eath ; Mas Analysis: Copyight 2012 Nelson Education Ltd. Chapte 6: Gaitational Fields

11 Solution: Mecuy Sun Mecuy 6.67!10 "11 s 2 #m2 kg !1030 kg Mecuy 4.79!10 4 m/s 5.79!10 10 m Venus Sun Venus 6.67!10 "11 s 2 #m2 kg !1030 kg Venus 3.51!10 4 m/s 1.08!10 11 m Eath Sun Eath 6.67!10 "11 s 2 #m2 kg !1030 kg Eath 2.98!10 4 m/s 1.49!10 11 m Mas Sun Mas 6.67!10 "11 s 2 #m2 kg !1030 kg Mas 2.41!10 4 m/s 2.28!10 11 m Statement: he obital speed of Mecuy is m/s. he obital speed of Venus is m/s. he obital speed of Eath is m/s. he obital speed of Mas is m/s. b he fathe a planet is fom the Sun, the slowe its obital speed. Copyight 2012 Nelson Education Ltd. Chapte 6: Gaitational Fields

12 14. Gien: d 410 km m; Moon m; m kg; G N m 2 /kg 2 Requied: ; Analysis: d + Moon ; 2! 4.1!10 5 m +1.74!10 6 m 2.15!10 6 m one exta digit caied Solution:. Fist, calculate the obital adius: 6.67!10 "11 s 2 #m2 kg !1022 kg 2.15!10 6 m 1.511!10 3 m/s two exta digit caied 1.5!10 3 m/s Detemine the peiod: 2! 2! 2.15"106 m 1.511"10 3 m s 8.9 "10 3 s Statement: he speed of the satellite is m/s, and its peiod is s. Copyight 2012 Nelson Education Ltd. Chapte 6: Gaitational Fields