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 = `2 xx 10^(30) `kg. Mass of the earth = `6xx10^(24)`kg. Neglect the effect of other planets etc. (orbittal radtus = `1.5 xx 10^(11)` m ).

Explanation

`implies`  Suppose, forces of gravitation by sun and earth exerted on a rocket of mass m at a distance x from the centre of earth are becomes same.
Here, `M_E = 6 xx 10^(24) kg.`
`M_s = 2 xx 10^(30)kg`
`r = 1.5 xx 10^(11) m`

Now `F_E = F_s`
`:. (GM_Em)/(x^2)=(GM_sm)/((r-x)^2)`
`:. ((r-x)/x)^2=M_s/M_E`
`=(2 xx 10^(30))/(6xx10^(24))`
`=10^6/3`
`(r-x)/x = 100/sqrt3` " " ( `:.` Taking square root) 
`:. sqrt3 r = 1000 x `
[ `sqrt3` x is neglected relative to 1000 x ]
`:. (1.73 xx 1.5 xx10^(11))/1000 = x`
` :. 2.595xx 10^8 =x`
`:. x ~~ 2.6 xx 10^(5)km`