ME Europa is one of more than sixty moons that orbit the planet Jupiter. Europa

Question

ME Europa is one of more than sixty moons that orbit the planet Jupiter. Europa is one of the ME = 4.8×1022 kg. r 6.71x10 m. M, = 1.90×1027 kg R,=7.15x107 m. b) For three extra credit points: calculate the average speed of Europa in its orbit of four large moons discovered by Galileo. Lately, there has been much speculation about whether there might be life on this Galilean moon. The mass of Europa is measured to be and, on average, its orbital radius is The mass of Jupiter is while its equatorial radius is Do the following: a) Calculate the magnitude of the average gravitational force exerted on Europa by Jupiter. Jupiter. For three extra credit points: calculate , the average orbital period of Europa.

Explanation / Answer

a)We know that the gravitational force is given by:

F = Gm1 m2/r^2

F = 6.67 x 10^-11 x 4.8 x 10^22 x 1.9 x 10^27 / (6.71 x 10^8)^2 = 1.35 x 10^25 N

Hence, F = 1.35 x 10^25 N

b)we know that in an orbit the gravitational force is balanced by the bentripital force,

Fc = Fg

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

v = sqrt (GM/R)

v = sqrt (6.67 x 10^-11 x 1.9 x 10^27/(6.71 x 10^8)) = 1.37 x 10^4 m/s

Hence, v = 1.37 x 10^4 m/s

c)we know that

speed = dist/time => time = dist/speed

dist = 2 pi R = 2 x 3.14 x 6.71 x 10^8 = 4.21 x 10^9 m

time = tau = 4.21 x 10^9/1.37 x 10^4 = 3.08 x 10^5 s

Hence, tau = 3.08 x 10^5 s = 15139 days.

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