The four largest of Jupiter\'s 63 moons are listed in the table below (a) Comple
ID: 1784003 • Letter: T
Question
The four largest of Jupiter's 63 moons are listed in the table below (a) Complete the table Moon Semimajor Axis (km) Orbital Period (days) 0 421,700 1.769 2.815 We are given a table of the semimajor axes and orbital periods of Jupiter's four largest moons. Since all of the moons are orbiting the same planet, we can set up ratios betweern the semimajor axis and period of Io and the semimajor axis and period of the moon we are interested in to solve for the missing information Europa 671,034 1705632X We are given a table of the semimajor axes and orbital periods of Jupiter's four largest moons. Since all of the moons Ganymede are orbiting the same planet, we can set up ratios between 7.155 the semimajor axis and period of Io and the semimajor axis and period of the moon we are interested in to solve for the missing information 3978378X We are given a table of the semimajor axes and orbital periods of Jupiter's four largest moons. Since all of the moons are orbiting the same planet, we can set up ratios between the semimajor axis and period of Io and the semimajor axis and period of the moon we are interested in to solve for the missing information Callisto 16.689 (b) Determine the mass of JupiterExplanation / Answer
Given
r -- semimajor axis , T = orbital period , day = 86400 s
for I0 given r = 421700000 m , T = 1.769 days
we know the formula for orbital peiod is T = 2pi sqrt(r^3/GM)
G = 6.67*10^-11 Nm2/kg^2, M = mass of Jupiter
substituting the values we get mass of JUpiter is
T = 2pi sqrt(r^3/GM)
1.769*86400 = 2pi sqrt(421700000^3/(6.67*10^-11*M))
M = 1.90*10^27 kg
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Europe
r = 671,034,000 m , T =?
T = 2pi sqrt(r^3/GM)
T = 2pi (sqrt(671,034,000^3/(6.67*10^-11*1.9*10^27)))s
T = 306801.11901558435 s
T = 3.5509 days
Ganymede
r = ? , T = 7.155 days
T = 2pi sqrt(r^3/GM)
7.155*86400 = 2pi sqrt(r^3/(6.67*10^-11*1.9*10^27))
r = 1070505294 .99 m
r = 1070505.29499 km
Callisto
r = ? , T = 16.689 days
T = 2pi sqrt(r^3/GM)
16.689*86400 = 2pi sqrt(r^3/(6.67*10^-11*1.9*10^27))
r = 1882793126.423 m
r = 1882793.126423 km
b) mass of the jupiter is M = 1.9*10^27 kg
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