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Energy needed to move a satellite into a different orbit

This type of question, asked 2 times: 9 Apr 2024, 21 Jan 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    9 Apr 2024

    12
    An astronaut takes a ball of mass mm from earth to space. He throws the ball into a circular orbit about earth at an altitude of 318.5 km318.5\text{ }km. From earth's surface to the orbit, the change in total mechanical energy of the ball is xGMem21Rex\frac{GM_{e}m}{21R_{e}}. The value of xx is (take Re=6370 kmR_{e}= 6370\text{ }km ):

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  2. Question 2

    9 Apr 2024

    101
    A satellite of 103 kg10^{3}\text{ }kg mass is revolving in circular orbit of radius 2R2R. If 104R6J\frac{10^{4}R}{6}J energy is supplied to the satellite, it would revolve in a new circular orbit of radius: (use g=10 m/s2,R=g = 10\text{ }m/s^{2},R = radius of earth)

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  3. Question 3

    21 Jan 2026 S1

    19
    Initially a satellite of 100 kg is in a circular orbit of radius 1.5RE1.5R_{E}. This satellite can be moved to a circular orbit of radius 3RE3R_{E} by supplying α×106 J\alpha \times10^{6}\text{ }J of energy. The value of α\alpha is ____\_\_\_\_ . (Take Radius of Earth RE=6×106 mR_{E}= 6 \times10^{6}\text{ }m and g=10m/s2g = 10m/s^{2} )

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