A rocket is fired from the Earth towards the Sun. At what distance from the Earth's centre the gravitational force on the rockets is zero? Mass of the Sun = 2 × 10 30 kg and mass of the earth = 6 × 10 24 kg . Distance between earth and sun = 15 × 10 10 m

Question

A rocket is fired from the Earth towards the Sun. At what distance from the Earth's centre the gravitational force on the rockets is zero? Mass of the Sun = 2 × 10 30 kg and mass of the earth = 6 × 10 24 kg . Distance between earth and sun = 15 × 10 10 m, 2 .6 × 10 8 m, 3 .2 × 10 8 m, 3 .9 × 10 9 m, 2 .3 × 10 9 m

MARKS App · Accepted Answer

Let P be a point at a distance r from the Earth's centre, where gravitational force due to Sun and Earth are equal and opposite and hence, the gravitational force on the rocket is zero. G M S m x - r 2 = G M e m r 2 ⇒ G M S x - r 2 = G M e r 2 2 × 10 30 x - r 2 = 6 × 10 24 r 2 x - r 2 r 2 = 2 × 10 30 6 × 10 24 = 1 3 × 10 6 ⇒ x - r r = 10 3 3 ⇒ r = 3 1735 x ⇒ r = 3 1375 × 1.5 × 10 11 = 3 × 15 × 100 × 10 8 1735 r = 2.594 × 10 8 m r = 2.6 × 10 8 m from Earth

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