Question
Derive the mass of the Earth from the Moon's orbital period of 27.3 days and orbital distance of $3.84 \times 10^{8} \mathrm{m}$
Step 1
We know the Moon's orbital period (T) is 27.3 days, which we need to convert to seconds: T = 27.3 days * 24 hours/day * 60 minutes/hour * 60 seconds/minute = 2,358,720 seconds Show more…
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"The moon takes about 27.3 days to revolve around the earth in a nearly circular orbit of radius 3.84×10^4 Km. Calculate the mass of the earth from these data"
Determine the mass of the Earth from the period $T$ and the radius $r$ of the Moon's orbit about the Earth: $T=27.3$ days and $r=3.82 \times 10^{5} \mathrm{~km}$.
Calculate the mass of Earth from the period of the moon, T = 27.3 d; its mean orbital radius, r_m = 3.84 x 10^8 m; and the known value of G.
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