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Chrome File Edit History Bookmarks People Window Help Mon 1128 PM aega Study I Guided solutio x Chrome Far Edit View History C O wwwwebassign Responses last?dep 16215998 s, o points sercP10 Posa. The average distance My Notes Earth and the Moon separating Earth and the Moon (center to center) is 3s4000 km. use the data in the table to find the nee gravieaeional force exerted by on a 300x10 kg spaceship located halfway between them. Body Mass (kg) Mean Radus (m) Period Distance from Sun (m) Mercury 318 102 2.43x 10s 60 x 10s Venus 488 1024 6 og 10s 1.94 x 107 Earth 10 10° 3.16 10 150 10 297 10-1 Mars 642 x 102a 3.37 x 10% |s94 x 107 Saturn s68 102s 102 93s 108 1.43 1012 2.99 x 10-13 Neptune 1.03 102 221 10' s 22 109 4.50 x 1012 Need Help?Explanation / Answer
The average distance separating Earth and the Moon is,
r = 384000 km = 384 x 106 m
The net gravitational force exerted by Earth and the Moon on a 3 x 104 kg spaceship located halfway between them is
F = F - Fo .............. (1)
where F = force on ship due to earth = GMm / (r/2)2
G = Gravitational constant = 6.67 x 10-11 Nm^ 2/ kg^ 2
M = mass of earth = 5.98 x 1024 kg
m = mass of ship = 3 x 104 kg
Fo = force on ship due to Moon = GMm / (r/2)2
Mo = mass of Moon = 7.36 × 1022 kg
On putting the values in equation (1), we get
F = [Gm /(r/2)2 ] [ M - Mo ]
= [4Gm / r2 ] [ M - Mo]
F = 0.3206 x 103 N (Ans)
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