The radius of the satellite’s orbit around the center of the Earth is r = 17 2 R , where R is the radius of the Earth. Hint: You may find it

Question

The radius of the satellite’s orbit around the center of the Earth is r = 17 2 R , where R is the radius of the Earth. Hint: You may find it useful to take into account that the gravitational force is a conservative force. Hint: The universal gravitational force law is F~ = G M m r 2 ˆr . Earth R Satellite 17 2 R Caution: Neglect the rotational kinetic energy due to the Earth’s rotation. Find the energy required to launch a satellite from Earth into the circular orbit at the specified radius r = 17 2 R.

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Acacia 5 years 2021-08-06T02:24:06+00:00 1 Answers 80 views 0

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  1. minhkhang
    -1
    2021-08-06T02:25:54+00:00
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    Answer:

    E = \frac{15GMm}{17R}

    Explanation:

    The potential energy of the satellite at the surface of the Earth is:

    U_i = -\frac{GMm}{R}

    The potential energy of the satellite in the circular orbit is:

    U_f=-\frac{GMm}{17/2 R}

    The energy required to put the satellite in the orbit is the difference between the two potential energies:

    E=U_f-U_i =-\frac{GMm}{R}(\frac{2}{17}-1)\\E = \frac{15GMm}{17R}

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