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  1. Mar 8, 2005 #1
    Given: G = 6.67259 x 10^11 N x m^2/kg^2
    A small Moon of a planet has an orbital
    period of 1.86 days and an orbital radius of
    485000 km.
    What is the mass of the planet?
     
  2. jcsd
  3. Mar 8, 2005 #2

    dextercioby

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    Well,what have you done/attempted to do so far...?

    Daniel.
     
  4. Mar 8, 2005 #3

    xanthym

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    {Orbital Period} = T = (1.86 days) = {1.61e(+5) sec}
    {Orbital Radius} = r = (4.85e(+5) km)
    {Orbital Velocity} = v = 2*Pi*r/T = 2*Pi*(4.85e(+5) km)/{1.61e(+5) sec} = (18.9 km/sec)

    {Centripetal Force} = Mmoonv2/r =
    = Mmoon(18.9)2/{4.85e(+5)} =
    = {7.37e(-4)}Mmoon

    {Gravitational Force} = GMplanetMmoon/r2 =
    = {6.67e(-11)}*MplanetMmoon/(4.85e(+5) km)2 =
    = {2.84e(-22)}*MplanetMmoon

    {Centripetal Force} = {Gravitational Force}
    ::: ⇒ {7.37e(-4)}Mmoon = {2.84e(-22)}*MplanetMmoon
    ::: ⇒ Mplanet = {7.37e(-4)}/{2.84e(-22)} = {2.60e(+18) kg}

    ~~
     
    Last edited: Mar 8, 2005
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