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).

A rocket is fired from the earth towards the sun. At what distance fro

1.	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).
Answer» Solution :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`.