Example 1.23.2 According to the law of universal gravitation, there should be an

Question

Example 1.23.2 According to the law of universal gravitation, there should be an attractive force between any two say between a piece of chalk and a duster. Why don't we observe these objects attracting to objects, Example 1.23.3 (a) The mass of the Earth is 5.98×1024 kg. The radius of the earths 6371 km. Calculate the acceleration due to gravity on the Earth's surface. (b) Mount Everest is 8848 m high. Calculate the acceleration due to gravity at the top of the mountain. (c) The Moon has a mass of 7.35 × 1022 kg and a radius of 1.74 × 106 m. Calculate the acceleration due to gravity on the Moon. Suppose a satellite moves in a circular orbit around the earth. In addition, assume the gravitational force between the earth and the satellite is the only force acting on the satellite

Explanation / Answer

1.23.3

a) GMm/R2 = mg

where G is the universal gravitaional constant, M is the mass of earth, m is the mass of the object, R is the radius of the earth

g= GM/R2 = 6.67*10-11*5.98*1024 / (6.371*106)2

g=9.826 m/s2

b) g= GM/(R+h)2 where h is the hieght of Everest

g= 6.67*10-11*5.98*1024 / (6.371*106 + 8848)2

g=9.799 m/s2

c) GMm/R2 = mg

where G is the universal gravitaional constant, M is the mass of moon, m is the mass of the object, R is the radius of the moon

g=g= GM/(R)2 = 6.67*10-11*7.35*1022 / (1.74*106)2

g=1.619 m/s2

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