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The Moon Io orbits jupiter once in 1.769...

The Moon Io orbits jupiter once in 1.769 days. The orbital radius of the Moon Io is 421700 Km. Caculate the mass of jupiter?

Text Solution

Verified by Experts

Kepler.s third law is used to find the mass of the planet
`T^(2) = (4pi^(2))/(GM) (R+h)^(2)`
` M = (4pi^(2))/(GT^(2)) (R+h)^(2)(4(3.14)^(2) xx (421700 xx10^(3))^(2))/(6.67 xx10^(11) xx (1.769xx86400)^(2))`
` = (39.4384 xx 7.499128631xx10^(25))/(6.67xx10^(-11) xx 2.336055469 xx10^(10))`
` = (295.7536 xx10^(25))/(1.5581 ) = 189.8169 xx10^(25)`
`M = 1.898 xx10^(27)` kg
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