A spacecraft S is orbiting Jupiter in a circular path 1650 km above the surface with a constant speed. Using the gravitational law, calculate the magnitude v of its orbital velocity with respect to Jupiter. Use Table D/2 of Appendix D as needed. 1650 km Answer: v = i km/h

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Chapter1: Units, Trigonometry. And Vectors
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Table D/2 Solar System Constants
6.673(10 1") m³/(kg · s²)
3.439(10 8) ft* /(lb - sec*)
5.976(1024) kg
4.095(1023) lb- sec² / ft
Universal gravitational constant
G
Mass of Earth
me
Period of Earth's rotation (1 sidereal day)
23 h 56 min 4 s
23.9344 h
0.7292(10 4) rad /s
0.1991(10 °) rad /s
Angular velocity of Earth
Mean angular velocity of Earth-Sun line
w =
Mean velocity of Earth's center about Sun
107 200 km /h
66,610 mi / hr
Body
Surface Gravitational Acceleration m/s²
(ft/sec?)
Mean Distance to Sun km
Eccentricity of Orbit Period of Orbit solar
Mean Diameter km
Mass Relative to
Escape Velocity km/s
(mi/sec)
(mi)
days
(mi)
Earth
Sun
1392 000
333 000
274
616
(865 000)
(898)
(383)
Мoon
384 3984
0.055
27.32
3 476
0.0123
1.62
2.37
(238 854)
(2 160)
(5.32)
(1.47)
Mercury
57-3 x 106
87.97
0.054
0.206
5 000
3.47
4.17
(35.6 x 106)
(3 100)
(11.4)
(2.59)
Venus
108 x 106
0.0068
224.70
12 400
0.815
8.44
10.24
(67.2 x 106)
(7 700)
(27.7)
(6.36)
Earth
149.6 x 106
0.0167
365.26
12 7422
9.8213
11.18
1.000
(92.96 x 106)
(7 918)2
(32.22)3
(6.95)
Mars
227.9 x 106
0.093
686.98
6 788
0.107
3-73
5.03
(141.6 x 106)
(4 218)
(12.3)
(3.13)
Jupiter4
778 x 106
0.0489
4333
139 822
317.8
24.79
59.5
(483 x 106)
(86 884)
(81.3)
(36.8)
1 Mean distance to Earth (center-to-center)
2 Diameter of sphere of equal volume, based on a spheroidal Earth with a polar diameter of 12 714 km (7900 mi) and an equatorial diameter of 12 756 km (7926 mi)
3 For nonrotating spherical Earth, equivalent to absolute value at sea level and latitude 37.5°
4 Note that Jupiter is not a solid body.
Transcribed Image Text:Table D/2 Solar System Constants 6.673(10 1") m³/(kg · s²) 3.439(10 8) ft* /(lb - sec*) 5.976(1024) kg 4.095(1023) lb- sec² / ft Universal gravitational constant G Mass of Earth me Period of Earth's rotation (1 sidereal day) 23 h 56 min 4 s 23.9344 h 0.7292(10 4) rad /s 0.1991(10 °) rad /s Angular velocity of Earth Mean angular velocity of Earth-Sun line w = Mean velocity of Earth's center about Sun 107 200 km /h 66,610 mi / hr Body Surface Gravitational Acceleration m/s² (ft/sec?) Mean Distance to Sun km Eccentricity of Orbit Period of Orbit solar Mean Diameter km Mass Relative to Escape Velocity km/s (mi/sec) (mi) days (mi) Earth Sun 1392 000 333 000 274 616 (865 000) (898) (383) Мoon 384 3984 0.055 27.32 3 476 0.0123 1.62 2.37 (238 854) (2 160) (5.32) (1.47) Mercury 57-3 x 106 87.97 0.054 0.206 5 000 3.47 4.17 (35.6 x 106) (3 100) (11.4) (2.59) Venus 108 x 106 0.0068 224.70 12 400 0.815 8.44 10.24 (67.2 x 106) (7 700) (27.7) (6.36) Earth 149.6 x 106 0.0167 365.26 12 7422 9.8213 11.18 1.000 (92.96 x 106) (7 918)2 (32.22)3 (6.95) Mars 227.9 x 106 0.093 686.98 6 788 0.107 3-73 5.03 (141.6 x 106) (4 218) (12.3) (3.13) Jupiter4 778 x 106 0.0489 4333 139 822 317.8 24.79 59.5 (483 x 106) (86 884) (81.3) (36.8) 1 Mean distance to Earth (center-to-center) 2 Diameter of sphere of equal volume, based on a spheroidal Earth with a polar diameter of 12 714 km (7900 mi) and an equatorial diameter of 12 756 km (7926 mi) 3 For nonrotating spherical Earth, equivalent to absolute value at sea level and latitude 37.5° 4 Note that Jupiter is not a solid body.
A spacecraft Sis orbiting Jupiter in a circular path 1650 km above the surface with a constant speed. Using the gravitational law,
calculate the magnitude v of its orbital velocity with respect to Jupiter. Use Table D/2 of Appendix D as needed.
1650 km
Answer: v =
i
km/h
Transcribed Image Text:A spacecraft Sis orbiting Jupiter in a circular path 1650 km above the surface with a constant speed. Using the gravitational law, calculate the magnitude v of its orbital velocity with respect to Jupiter. Use Table D/2 of Appendix D as needed. 1650 km Answer: v = i km/h
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