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 x 1030 kg, mass of the earth = 6 x 1024 kg. Neglect the effect of other planets etc. (orbital radius = 1.5 x 1011 m).
Mass of the Sun, Ms=2×1030 kg Mass of the Earth, Me=6×1024 kg Orbital radius, r=1.5×1011 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)2GmMs=x2GmMe [x(r−x)]2=Ms/Me (r−x)/x=(60×10242×1030)1/2=577.35 1.5×1011−x=577.35x 578.35x=1.5×1011 x=1.5×1011/578.35=2.59×108m.
