Another Way

Mearth = w2Rearth-moon3/G

where w = 2pf = 2p/T and

T = 1 month (actually 27.3 days = 2.36 x 106s

Rearth-moon = 250,000 miles = 3.84 x 108 m

Mearth = (2p/2.36 x 106s)2 * (3.84 x 108 m)3 / 6.67 x 10-11 Nt-m2/kg2 = 6.0 x 1024 kg

which matches the first answer for mearth !

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