Two stars of masses 3 × 10 31   kg each, and at distance 2 × 10 11   m rotate in a plane about their common centre of mass O . A meteorite passes through O moving perpendicular to the stars,s rotation plane. In order to escape from the gravitational field of this double star,…

Question

Two stars of masses 3 &#215; 10 31 &#160; kg each, and at distance 2 &#215; 10 11 &#160; m rotate in a plane about their common centre of mass O . A meteorite passes through O moving perpendicular to the stars,s rotation plane. In order to escape from the gravitational field of this double star, the minimum speed that meteorite should have at O is ( Take Gravitational constant G = 6.67 &#215; 10 - 11 &#160; N &#160; m 2 &#160; kg - 2 &#160; )

Aicharya · Accepted Answer

To escape, the total energy of small particle must be zero. T E = K E + U 0 = 1 2 m V 2 + - G M m d 2 × 2 ⇒ V = 8 G M d = 8 × 6.67 × 10 - 11 × 3 × 10 31 2 × 10 11 = 2.8 × 10 5 m s - 1

Two stars of masses 3 × 10 31   kg each, and at distance 2 × 10 11   m rotate in a plane…

Solution

Two stars of masses 3 &#215; 10 31 &#160; kg each, and at distance 2 &#215; 10 11 &#160; m rotate in a plane…

Solution

Two stars of masses 3 × 10 31 kg each, and at distance 2 × 10 11 m rotate in a plane…