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Okay, problem reads :

The moon orbits the earth in an approximately circular path of radius 3.8 X 10^8 m. It takes about 27 days to complete one orbit. What is the mass of the earth as obtained from these data?

I started with

[tex] \frac {mv^2}{r} = G \frac {Mm}{r^2}[/tex]

I did some simplification all the way to

[tex]\frac {v^2r}{G} = M[/tex]

From here, the book then re-writes it as [tex] \frac {\Omega^2r^3}{G} = M[/tex]. How did they do that?

The moon orbits the earth in an approximately circular path of radius 3.8 X 10^8 m. It takes about 27 days to complete one orbit. What is the mass of the earth as obtained from these data?

I started with

[tex] \frac {mv^2}{r} = G \frac {Mm}{r^2}[/tex]

I did some simplification all the way to

[tex]\frac {v^2r}{G} = M[/tex]

From here, the book then re-writes it as [tex] \frac {\Omega^2r^3}{G} = M[/tex]. How did they do that?

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