   Chapter 7, Problem 47AP

Chapter
Section
Textbook Problem

(a) One of the moons of Jupiter, named Io, has an orbital radius of 4.22 × 108 m and a period of 1.77 days. Assuming the orbit is circular, calculate the mass of Jupiter, (b) The largest moon of Jupiter, named Ganymede, has an orbital radius of 1.07 × 109 m and a period of 7.16 days. Calculate the mass of Jupiter from this data, (c) Are your results to parts (a) and (b) consistent? Explain.

(a)

To determine
The mass of the Jupiter.

Explanation

Given Info:

Orbital radius of the Io moon is 4.22×108m .

Period of the Io moon is 1.77days .

Explanation:

According to Kepler’s third law,

T2=(4π2GM)r3

• G is the gravitational constant
• M is the mass Jupiter

On re-arranging,

Formula to calculate the mass of the Jupiter is,

M=(4π2GT2)r3

Substitute 6.67×1011Nm2kg2 for G, 1.77days for T and 4.22×108m for r to find the mass of the Jupiter,

M=4π2(4

(b)

To determine
The mass of the Jupiter.

(c)

To determine
The results to (a) and (b) is consistent or not.

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