The mean orbital radius of the earth around the sun is `1.5xx10^8 km`. Calculate the mass of the sun if `G=6.67xx10^(-11)N*m^2*kg^(-2)`.

Explanation

Here `r=1.5xx10^8km =1.5xx10^(11)m`
T=365 days =`365xx24xx3600 s`
Since, centripetal force required = gravitational force between the earth and the sun.
`therefore (mv^2)/r =(GMm)/(r^2) or, m/r((2pir)/T)^2=(GMm)/(r^2)`
or, `M=(4pi^2r^3)/(GT^2)=(4xx9.87xx(1.5xx10^(11))^3)/(6.67xx10^(-11)xx(365xx24xx3600)^2)`
`therefore M=2.01xx10^(30)kg`