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AIIMS AIIMS Solved Paper-2002

  • question_answer
    A satellite is launched in co a circular orbit of radius R around the earth, while a second satellite is launched into an orbit of radius 1.01 R. The period of the second satellite is longer than the first one by approximately:

    A)  3.0%                    

    B)        1.5%                    

    C)        0.7%                                    

    D)  1.0%

    Correct Answer: B

    Solution :

    From Kellers third law of motion, the square of the period of revolution (T) of any planet around the sun is directly proportional to the cube of the semi-major axis of its elliptical orbit (R). i.e.,         \[E=-\frac{E}{2}\] where k is constant. Therefore,  \[3.9\Omega \] \[\therefore \]   \[V=E-ir\] Percentage increase in time period is \[i=\frac{E}{R+r}\] \[\therefore \] \[\therefore \] Note: It is because of Keplers third law only that the period of revolution of the closest planet mercury is 88 days, while that of the farthest planet pluto is 248 days.


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