Q.

A satellite S is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Which of the following statements is correct?

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a

The total mechanical energy of S is not constant.

b

The linear momentum of S remains constant in magnitude.

c

The angular momentum of S about the centre of the earth changes in direction, but its magnitude remains constant. 

d

The acceleration of S is always directed towards the centre of the earth. 

answer is A.

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Detailed Solution

For elliptical orbit, the earth is at one focus of the ellipse. For spherical bodies, the gravitational force is central ( or radial). Hence statement ( a) is correct. The gravitational force exerts no torque on the satellite. Hence the angular momentum of S remains constant in magnitude as well as direction. Hence choice (b) is incorrect. For elliptical orbit, the distance of the satellite from the earth varies periodically. Hence potential energy, kinetic energy and linear momentum vary periodically. Hence choices ( c) and ( d) are also incorrect.

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