Please show all work and explain, thank you! Background/Hints: In this equation,

Question

Please show all work and explain, thank you!

Background/Hints:

In this equation, T is the orbital period of a given moon and R is the mean distance of the moon from the center of Jupiter. For moons executing elliptical orbits, it can be shown that the mean distance equals the semi-major axis of ellipse.

The Wikipedia website http://en.wikipedia.org/wiki/Moons of Jupiter tabulates all of the physical data for
the moons of Jupiter, including the orbital period in (earth) days and the semi-major axis in km.

Problem:

For each of the six moons numbered 5 through 10 (Io through Leda), calculate the ratio R3/T 2 in m3/s2 . Then, from the average value of these six ratios, calculate the mass of Jupiter.

Explanation / Answer

Using the values from the Wikipedia website, for the ratio R^3/T^2 I get: Io 3.20967 x 10^15 Europa 3.20967 x 10^15 Ganymede 3.20967 x 10^15 Callisto 3.20967 x 10^15 Thermisto 3.20963 x 10^15 Leda 3.20975 x 10^15 Average 3.20968 x 10^15 Then... using the given equation, avg ratio = GM / 4pi^2 so... M = 4pi^2 * ratio / G = 4pi^2 * 3.20968x10^15 / 6.67 x 10^-11 = = 1.90 x 10^27 kg is the mass of Jupiter

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