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

Let `x` be the distance of body of mass `m` from Earth, where the resultant gravitational pull on the body due to Earth and sun is zero. Then
`(GM_(E)m)/(x^(2)) = (GM_(S)m)/((r - x)^(2))` or `((r - x)^(2))/(x^(2)) = (M_(S))/(M_(E)) = 3.25 xx 10^(5)`
or `(r - x)/(x) = sqrt(3.25 xx 10^(5)) = 570`
or `x = (r)/(570 + 1) = (1.5 xx 10^(8))/(570) = 2.63 xx 10^(5) km`