ra upiter in newtons? In pounds? (1763 N, 396 Ib) 056 ular orbit ter\'s mt aroun

Question

ra upiter in newtons? In pounds? (1763 N, 396 Ib) 056 ular orbit ter's mt around Jupiter. (a) What is the gravitational force that Jupiter exerts on lo? (b) How fast ts lo moving? and (c) What is the 3 moon, lo, is a emoon, lo is a dry, large moon of Jupiter, that has an orbital radius ot 421,700,000 (4.22 x 10%) m and a mass of 8.93 x 10a io aroton hat is, how much time does it take lo to complete one orbit around Jupiter? (d) What is the orbital riod indays?(6.36 310 (c) What is the orbital period of lo s 153,000 sec, 1.77 days) . mi 4.22 XIO

Explanation / Answer

Part b)We know that the centripital force balances the gravitational force

m v^2/R = G M m /r^2

where m is the mass of io and M is that of Jupiter, m cancels both sides.

Solving for v we get

v = sqrt (G M/r)

M = 1.898 x 10^27 kg ; r = 4.22 x 10^8 ; G = 6.67 x 10^-11)

v = sqrt (6.67 x 10^-11 x 1.898 x 10^27/4.22 x 10^8) = 1.73 x 10^4 m/s

Hence, v = 1.73 x 10^4 m/s = 17300 m/s

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