Respuesta :

DeanR
Let's call [tex]M[/tex] the mass of the star and [tex]m[/tex] the mass of the planet, which should cancel.  The gravitational force should equal the centripetal force:

[tex]\dfrac{GMm}{r^2} = \dfrac{mv^2}{r}[/tex]

[tex]M=rv^2/G[/tex]

We compute [tex]v = \dfrac{2 \pi r}{T}[/tex]

[tex]M=\dfrac{4 \pi^2 r^3}{G T^2}[/tex]  

This is Keppler's Law.  We convert to MKS as we plug in and get

[tex]M=\dfrac{4\pi^2(3 \cdot 1.496 \times 10^{11}) ^3}{6.674\times 10^{-11} ( 1200 \cdot 24 \cdot 60 \cdot 60 )^2 }[/tex]

[tex]M=4.9744\times 10^{30}[/tex] kg

which is about two and a half solar masses if I haven't made any errors.




  

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