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?

Explanation

`{:("Time period of"),("the moon T"):}}=1.769"days"`
`{:("Orbital radius"),("of the Moon"):}}=4217xx10^(2)km`
Time period `T^(2)=(4pi^2)/(GM_J)(R_(M)+h)^(3)`
`M_(J)` = Mass of Jupiter
`GM_(J)=(4pi^(2)R_(M)^(3))/(T^2)[hltltR_(E)]`
`{:("Mean radius of"),("the moon" R_(M)):}}=1.737.1xx10^(3)m`
`M_(J)=(4pi^(2)R_(M)^(3))/(GT^2)`
Mass Jupiter `M_(J)=(4xx(3x14)^(2)xx(1737xx10^3)^(3))/(6.67xx10^(-11)xx(1.769)^(2))`
`=(20668xx10^(27))/(20872xx10^(-11))`
`=0.99022xx10^(27+11)`
`=990226xx10^(38-5)`
`=990226xx10^(33)`
`=0.990226xx10^(27)`
`~=1xx10^(27)kg`