Jupiter has many moons orbiting it. A. Find the mass of Jupiter, in kg, based on

Question

Jupiter has many moons orbiting it.

A. Find the mass of Jupiter, in kg, based on data for the orbit of one of its moons.

(50%) Problem 2: Jupiter has many moons orbiting it. Average rtitall PerodTyTkm'l Parent Satellite Average orbital radius r(km) 1.01x1018 3.35x1024 3.35x10 Earth |Moon | 3.84x105 0.07481 |Earth Jupiter 7.783x10 11.86 |1.496× 10.11.000 Sun 1496x101.000 Jupiter lo 22x10 0.00485 (1.77d 3.19x1021 1671x105 10.00972 (3,55 d)|320x1021 Europa Ganymede 1.07x10 0.0196(7.16d) 3.19x102 Callsto 1.88x10 0045716.19d3.20021 Otheexpertta.com Find the mass of Jupiter, in kg, based on data for the orbit of one of its moons

Explanation / Answer

Considering Io,we have

r = 4.22 x 10^5 km = 4.22 x 10^5 m ; T = 0.00485 Y = 1.77 d = 1.15 x 10^5 s ;

We know that,

T = 2 pi r / v => v = 2 pi r / T

Also v = sqrt ( G M / r)

From above two we get,

2 pi r / T = Sqrt(G M / r)

Squaring both sides and solving for M we get

M = (2 pi r / T)2 x (r / G)

M = 4 x 9.86 x (4.22 x 108)3 / (1.52 x 105)2 x 6.67 x 10-11

M = 2964 x 1024 / 1.541 = 1923.4 x 1024 Kg

Hence Mass of the Jupiter = M = 1.923 x 1027 kg

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