One of the satellite of jupiter, has an orbital period of `1.769` days and the radius of the orbit is `4.22 xx 10^(8) m`. Show that mass of jupiter is about one thousandth times that of the mass of the sun. (Take `1` year `= 365.15` mean solar day).

Explanation

Mass of jupiter, `M_(1)` is given by `M_(1)=(4pi^(2)T_(1)^(3))/(GT_(1)^(2))=(4pi^(2)xx(4.22xx10^(8))^(3))/(Gxx(1.769xx24xx60xx60)^(2))` ……..(i)
We know that the orbital period of Earth around the sun,
T=1 year=365.25xx24xx60xx60s,
orbtial radius, `r=1A.U.=1.496xx10^(11)m`.
Mass of sun is given by `M=(4pi^(2)r^(3))/(GT^(2))=(4pi^(2)xx(1.496xx10^(11))^(3))/(Gxx(365.25xx24xx60xx60)^(2))` .....(ii)
Dividing eqn. (ii) by (i) we get
`(M)/(M_(1))=(4pi^(2)xx(1.496xx10^(11))^(3))/(Gxx(365.25xx24xx60xx60)^(2))xx(Gxx(1.769xx24xx60xx60)^(2))/(4pi^(2)xx(4.22xx10^(8))^(3))=1046`
or `(M_(1))/(M)=(1)/(1046)=(1)/(1000)rArrM_(1)=(1)/(1000)M` Proved.