1© Manhattan Press (H.K.) Ltd. 6.4 Escape speed 2 © Manhattan Press (H.K.) Ltd. Escape speed 6.4 Escape speed (SB p. 224) Go to More to Know 18 More.

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1© Manhattan Press (H.K.) Ltd. 6.4 Escape speed

2 © Manhattan Press (H.K.) Ltd. Escape speed 6.4 Escape speed (SB p. 224) Go to More to Know 18 More to Know 18 Launch rocket from earth’s surface to infinity (rocket escapes completely from gravitational attraction of earth) escape speed

3 © Manhattan Press (H.K.) Ltd. Escape speed 6.4 Escape speed (SB p. 224) Go to More to Know 19 More to Know 19 Escape speed of earth’s surface Note: ×10 3 m s −1 is the minimum escape speed. When v > 11.2 ×10 3 m s −1, the rocket can also escape.

4 © Manhattan Press (H.K.) Ltd. Escape speed 6.4 Escape speed (SB p. 224) 2. The average velocity of air molecules is much less than 11.2 ×10 3 m s −1. So that the gravitational force can keep the atmosphere around the earth. 3. Gravitational force of the moon is much less than that of the earth and the air molecules can escape from it. This accounts for the lack of atmosphere around the moon. Go to Example 8 Example 8

5 © Manhattan Press (H.K.) Ltd. End

6 © Manhattan Press (H.K.) Ltd. Kinetic energy of a body The initial kinetic energy of a body which escapes from the earth or other planets, must be great so that the body is still in motion at infinity. Return to Text 6.4 Escape speed (SB p. 224)

7 © Manhattan Press (H.K.) Ltd. Escape speed and mass of object From the equation about the escape speed, the escape speed is independent of the mass of objects. Thus, all objects on a planet's surface has the same escape speed. Return to Text 6.4 Escape speed (SB p. 224)

8 © Manhattan Press (H.K.) Ltd. Q: Q: (a) Assume the escape speed of a body at the earth’s surface is 11.2 × 10 3 m s −1. What is the value at an altitude of 0.1R E ? (b) The root-mean-square speed of helium atoms at 290 K, the temperature of the lower atmosphere, is 1.3 × 10 3 m s −1. (i) Calculate their root-mean-square speed at K, the temperature of the atmosphere at an altitude of 0.1R E. (ii) Some radioactive substances decay to produce helium, which eventually passes into the earth’s atmosphere. However, the total quantity of helium which has been released in this way is very much greater than the amount actually present in the atmosphere. Explain briefly. Solution 6.4 Escape speed (SB p. 225)

9 © Manhattan Press (H.K.) Ltd. Solution : Return to Text 6.4 Escape speed (SB p. 225) (ii) The amount of helium left in the atmosphere is much less than the amount produced because helium atoms, which have speeds greater than the escape speed, will escape from the gravitational force of the earth and not to return.