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Physics

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The moon Europa, of the planet Jupiter, has an orbital period of 3.55 days and
an average distance from the center of the planet equal to 671,000 km. If the
magnitude of the gravitational acceleration at the surface of Jupiter is 2.36 times greater than that on the surface of the Earth, what is the radius of Jupiter?
(Hint: begin by calculating the rotation speed.)

  • Physics -

    radius of orbit of Europa, rm = 671000km
    rotational period of Europa, T = 3.55 days
    Rotational velocity of Europa, ω
    = 2π/(3.55*86400) radians/second
    Centripetal acceleration, a
    =rmω²


    radius of Jupiter, r = to be determined
    Acceleration due to gravity on Jupiter
    = GM/r² = 2.36g
    Gravitational acceleration on Europa
    =GM/(rm)²
    =(GM/r²)*r²/(rm)²
    =(2.36g)(r/rm)²

    Equating gravitational acceleration with centripetal acceleration,
    (2.36g)(r/rm)² = rmω²
    r=(rm)³ω²/(2.36g)
    =74,038 km

    According to Google, r(Jupiter) = 71,492 km

    Check my numbers and my thinking please.

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