Class 11

Physics

Modern Physics

Gravitation

A rocket is fired from the earth towards the sun. At what distance from the earths centre is the gravitational force on the rocket zero? Mass of the sun = $2×10_{30}kg$, mass of the earth = $6×10_{24}kg$. Neglect the effect of other planets etc. (orbital radius = $1.5×10_{11}m$).

Mass of the Sun, $M_{s}=2×10_{30}kg$

Mass of the Earth, $M_{e}=6×10_{24}kg$

Orbital radius, $r=1.5×10_{11}m$

Mass of the rocket $=m$

Let $x$ be the distance from the centre of the Earth where the gravitational force acting on satellite P becomes zero.

From Newton’s law of gravitation, we can equate gravitational forces acting on satellite P under the influence of the Sun and the Earth as:

$(r−x)_{2}GmM_{s} =x_{2}GmM_{e} $

$[x(r−x) ]_{2} =M_{s}/M_{e}$

$(r−x)/x =(60×10_{24}2×10_{30} )_{1/2} =577.35$

$1.5×10_{11}−x=577.35x$

$578.35x=1.5×10_{11}$

$x=1.5×10_{11}/578.35=2.59×10_{8}m$.