How far from Earth must a body be along a line joining the sun to the earth so that resultage gravitational pull on the body due to Earth and sun is zero ? Distance between sun and the Earth is `1.5 xx 10^(8) km`. Mass of sun `= 3.25 xx 10^(5)` times mass of Earth.

Explanation

Refer to Fig. Here,
`M_(e) = 6 xx 10^(24) kg, M_(s) = 2 xx 10^(30) kg`.
`r = 1.5 xx 10^(11) m`
Let `m` be the mass of rocket.

Let `P` be a location at a distance `x` from earth where the resultant gravitaional force on the rocket is zero.
So at `P`, the gravitational force on rocket due to earth= gravitational force on rocket due to sun.
`:. (GM_(e)m)/(x^(2)) = (GM_(s)m)/((r - x)^(2))`
or `(M_(e))/(x^(2)) = (M_(s))/((r - x)^(2))` or `(r - x)/(x) = sqrt((M_(s))/(M_(e)))`
or `(r )/(x) = sqrt((M_(s))/(M_(e))) + 1 = sqrt((2 xx 10^(30))/(6 xx 10^(24))) + 1 = 577 + 1 = 578`
`:. x = (r)/(578) = (1.5 xx 10^(11))/(578) = 2.6 xx 10^(8)m`