# Physics #8Jupiter's four large moons -- Io, Europa, Ganymede, and Callisto -- were discovered by Galileo in 1610. Jupiter also has dozens ?

Jupiter's four large moons -- Io, Europa, Ganymede, and Callisto -- were discovered by Galileo in 1610. Jupiter also has dozens of smaller moons. Io has a radius of about 1.82 106 m, and the mean distance between Io and Jupiter is 4.22 108 m.

(a) If Io's orbit were circular, how many days would it take Io to complete one full revolution around Jupiter?

days

(b) If Io's orbit were circular, what would its orbital speed be?

M/s

### 4 Answers

- daniel gLv 78 months ago
Such measurement are from the centers of mass of each. An ellipse has a mean circle. Solve that first then solve for the differences in mass and you can find Io's orbital velocity. Knowing that, solve for the time of one orbit.

Piece of cake.

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- 8 months ago
So, you didn't give us the mass of Jupiter... I assume it's in your book.

a) use the equation for orbital period (T): T = sqrt( (4 x r^3 x pi^2) / G x M))

where r is the radius of Io's orbit from the center of Jupiter, G is the gravitational constant, and M is Jupiter's Mass.

b) Now that you know the period for Io, you can divide distance by time to get speed:

Distance to complete 1 orbit = 2 x pi x 1.82 x 10^6 m.

Take the period from a) and divide the orbital distance by this.

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