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The Moon I_{o} orbits Jupiter once in 1.769 days. The orbital radius of the Moon I_{o} is 421700 km. Calculate the mass of Jupiter?

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#### Solution

Kepler’s third law is used to find the mass of the planet

`"T"^2 = (4π^2)/("GM") ("R" + "h")^2`

M = `(4π^2)/"GT"^2 ("R" + "h")^2`

= `(4(3.14)^2 xx (421700 xx 10^3)^2)/(6.67 xx 10^-11 xx (1.769 xx 86400)^2)`

= `(39.4384 xx 7.499128631 xx 10^25)/(6.67 xx 10^-11 xx 2.336055469 xx 10^10)`

= `(295.7536 xx 10^25)/(1.5581)`

= 189.8169 × 10^{25}

M = 1.898 × 10^{27} kg

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