Io, one of Jupiter's moons, is about the size of Earth's moon. Io has a radius of about 1.85 x 106 m, and the mean distance between Io and Jupiter is 4.22 x 108 m. Jupiter has a mean radius of 7.15 x 107m, and a mass of 1.90 x 1027kg. If Io's orbit is circular, what is its orbital speed? a. 2.34 x 104 m/s c. 8.7 x 106 m/s b. 1.60 x 104 m/s d. 2.60 x 103 m/s

This subject is 100% physics.

You need to use Newton's Universal Law of Gravitation and the equation of centripetal accelerationt for the circular motion.

From Newton's Universal Law of Gravitation you can find the acceleration with which Jupiter attracts Io.

This is the formula: F = G*M*m / (r^2)

Where G is the universal constant of gravitation = 6.67 * 10^ - 11 N*m^2 / kg^2

M is the mass of JUpiter = 1.90*10^27 kg

r is the distance that separates the center of the two objects, i. e the radius of them both plus the distance between them

r = 4.22*10^8 m + 1.85*10^6 m + 7.15*10^7 m = 4.9535 * 10^8 m

The factor G*M / (r^2) is the gravitational acceleration, which we can calculate now:

6,67 * 10^ - 11 N*m^2 / kg^2 * 1.90*10^27 kg / (4.9535 * 10^8 m) ^2 = 0.51648 m/s^2

That is the centripetal acceleration. Call it Ac and use the equation of the circular motion for the centripetal acceleration:

Ac = v^2 / R

Here R = the radius of the orbit, which is the distance that separates the two objects plus the radius of the two objects, so you can solve for v:

v^2 = Ac*R = 0.51648 m/s^2 * (4.9535*10^8m) = 2.558 * 10^8 m^2/s^2

=> v = 1.599 * 10^4 m/s

And the answer is the option b. 1.60 * 10^4 m/s

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