Mass of Planet Given Period, Radius & G Constant

[the_d]

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?

 

[dextercioby]

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

Daniel.

 

[xanthym]

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?

{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} = M_moonv²/r =
= M_moon(18.9)²/{4.85e(+5)} =
= {7.37e(-4)}M_moon

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

{Centripetal Force} = {Gravitational Force}
::: ⇒ {7.37e(-4)}M_moon = {2.84e(-22)}*M_planetM_moon
::: ⇒ M_planet = {7.37e(-4)}/{2.84e(-22)} = {2.60e(+18) kg}

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