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Question
The Moon Io orbits Jupiter once in 1.769 days. The orbital radius of the Moon Io is 421700 km. Calculate the mass of Jupiter?
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 × 1025
M = 1.898 × 1027 kg
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