A rocket is fired from the earth towards the sun. At what distance from the earth's centre is the gravitational force on the rocket zero? Mass of the sun`=2xx10^(30)kg`, mass of the earth`=6xx10^(24)kg`. Neglect the effect of other planets etc. (orbital radius=`1.5xx10^(11)m`).

Explanation

Given `M_(s)=2xx10^(30)kg`.
`M_e= 6xx10^(24)kg, r=1.5xx10^(11)m`
Let m be the mass of the rocket. Let at distance x from the earth, the gravitational force on the rocket be zero.
Then at this distance, Gravitational pull of the earth on the rocket = gravitational pull of the sun on the rocket.
`(GM_e m)/(x^2)= (GM_e m)/((r-x)^2)" or "((r-x)^2)/(x^2)= (M_s)/(M_e)`
or `(R-x)/(x)= sqrt((M_s)/(M_e))= sqrt((2xx10^(30))/(6xx10^(24)))= (10^3)/(sqrt(3))=577.35`
or `r-x=577.35x`
or `578.35x=r=1.5xx10^(11)`
or `x=(1.5xx10^(11))/(578.35)=2.59xx10^(8)m`.