How much energy would be required to move the earth into a circular orbit with a radius 2.0 kmkm larger than its current radius

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How much energy would be required to move the earth into a circular orbit with a radius 2.0 kmkm larger than its current radius

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Thiên Ân 4 years 2021-09-05T02:42:20+00:00 1 Answers 17 views 0

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  1. Sigrid
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    2021-09-05T02:44:13+00:00
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    Answer:

    3.52\times 10^{25}\ \text{J}

    Explanation:

    G = Gravitational constant = 6.674\times 10^{-11}\ \text{Nm}^2/\text{kg}^2

    M = Mass of Sun = 1.989\times 10^{30}\ \text{kg}

    m = Mass of Earth = 5.972\times 10^{24}\ \text{kg}

    r_i = Initial radius of orbit = 1.5\times 10^{11}\ \text{m}

    r_f = Final radius of orbit = ((1.5\times 10^{11})+2\times 10^3)\ \text{m}

    Energy required is given by

    E=\dfrac{1}{2}\Delta U\\\Rightarrow E=\dfrac{GMm}{2}(\dfrac{1}{r_i}-\dfrac{1}{r_f})\\\Rightarrow E=\dfrac{6.674\times 10^{-11}\times 1.989\times 10^{30}\times 5.972\times 10^{24}}{2}(\dfrac{1}{1.5\times 10^{11}}-\dfrac{1}{(1.5\times 10^{11})+2\times 10^3})\\\Rightarrow E=3.52\times 10^{25}\ \text{J}

    The energy required would be 3.52\times 10^{25}\ \text{J}.

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