The potential energy U of an object of mass m that is separated by a distance R from an object of mass M is given by U= -GMm/RA. What is the

Question

The potential energy U of an object of mass m that is separated by a distance R from an object of mass M is given by U= -GMm/RA. What is the kinetic energy K of the satellite?Express your answer in terms of the potential energy .
B. Find an expression for the square of the orbital period.

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Dulcie 5 months 2021-08-04T06:59:23+00:00 1 Answers 41 views 0

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    2021-08-04T07:01:16+00:00

    Answer:

    A)  K = ½ U / r
    , B)     T² = (4π² / G M) r³

    Explanation:

    A) It asks us for the kinetic energy of the satellite and they give us the relation of the potential synergy

             U = – G M m / r

    the force can be found from this expression

              F = – dU / dr

              F = – G M m / r²

    The kinetic energy is given by the formula

              K = ½ m v²

    let’s use Newton’s second law

            F = m a

            G M m / r² = m a

    where the acceleration is centripetal

            a = v² / r

             G M r² = v² / r

             v² = G M r³

    we substitute the expression for the kinetic energy

             K = ½ m v²

             K = ½ m G M r³

    in terms of potential energy is

             K = ½ (G M m r²) 1 / r

             K = ½ U / r

    B) The period of the orbit

             

    We write Newton’s second law

                G M m / r² = m a

                a = v² / r

               

    in a circular orbit the speed of the velocity is constant

                v = d / t

               

    the longitude of the orbit is

                 d = 2π r

                v = 2π r / T

    we substitute

                G Mm / r² = m (2πr / T)² / r

                G M / r³ = 4π² / T²

                T² = (4π² / G M) r³

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