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The moon takes about 27.3 days to revolve round the earth in a nearly circular orbit of radius 3.84 × 105 km. Calculate the mass of the earth from these data.

The moon takes about 27.3 days to revolve round the earth in a nearly circular orbit of radius 3.84 × 105 km. Calculate the mass of the earth from these data.

Grade:upto college level

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
6 years ago
Sol. T = 2π √r^3/GM 27.3 = 2 * 3.14 √(3.84 * 10^5)^3/6.67 * 10^-11 * M or 2.73 * 2.73 = 2 * 3.14 * (3.84 * 10^5)^3/6.67 * 10^-11 * M or M = 2 * (3.14)^2 * (3.84)^3 * 10^15/3.335 * 10^-11 (27.3)^2 = 6.02 * 10^24 kg ∴ mass of earth si found to be 6.02 * 10^24 kg.

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