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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

Time period of moon Io = 1.769 days
`=1.769 xx 24 xx 60 xx 60s`
Orbital radius of the moon `(r) = 4.217 xx 10^(8)m`
`M = (4pi^2r^3)/(GT^2) = (4xx3.14xx3.14 xx (4.217 xx 10^8)^(3))/(6/67 xx 10^(-11) xx (1.769 xx 24 xx 60 xx 60)^(2))`
`M = 1.898 xx 10^(27) kg`.
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