From the gravitational law, calculate the weight W (gravitational force with respect to the earth) of a 70 kg spacecraft traveling in a circ

Question

From the gravitational law, calculate the weight W (gravitational force with respect to the earth) of a 70 kg spacecraft traveling in a circular orbit 275 km above the earth’s surface. Express W in Newtons and pounds.

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Kiệt Gia 2 years 2021-07-29T20:08:11+00:00 1 Answers 76 views 0

Answers ( )

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    2021-07-29T20:09:50+00:00

    Answer:

    The  value in Newton is [tex]W =  631.92 \  N[/tex]

    The  value in pounds is    [tex]W  = 142 \ lb[/tex]

    Explanation:

    From the question we are told that

      The  mass of the spacecraft is  [tex]m =  70 \  kg[/tex]

       The distance above  the earth is  [tex]d =  275 \  km  =  275000 \  m[/tex]

    Generally the gravitational force with respect to the earth is mathematically represented as

           [tex]W =  \frac{G * m *  m_e}{ (d + r_e)^2}[/tex]

    Here [tex]m_e[/tex] is the mass of earth with value [tex]m_e =  5.978 *10^{24} \  kg[/tex]

           [tex]r_e[/tex] is the radius of the earth with value  [tex]r_e  =  6371  \ km  =  6371000 \ m[/tex]

       G is the gravitational constant with value [tex]G  =  6.67 *10^{-11}  \  m^3/ kg\cdot s^2[/tex]

    So

         [tex]W =  \frac{ 6.67 *10^{-11} *  70 *  5.978 *10^{24}}{ (275000 + 6371000)^2}[/tex]

         [tex]W =  631.92 \  N[/tex]

    Converting to  pounds

        [tex]W =  \frac{631.92  }{4.45}[/tex]

            [tex]W  = 142 \ lb[/tex]

         

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