The moon revolves round the earth 13 times in one year. If the ratio of sun-earth distance to earth moon distance is 392 , then the ratio of masses of sun and earth will be 100 P × 1 0 5 then find the

Question

The moon revolves round the earth 13 times in one year. If the ratio of sun-earth distance to earth moon distance is 392 , then the ratio of masses of sun and earth will be 100 P × 1 0 5 then find the value of P.

TestHub · Accepted Answer

Concepts: Kepler's Third Law, Gravitational Force.

Using Kepler's Third Law, $T^{2} \propto R^{3} / M$ .

$\frac{M _{S}}{M _{E}} = (\frac{T _{E}}{T _{M}})^{2} (\frac{R _{SE}}{R _{EM}})^{3} = (13)^{2} (392)^{3} \approx 3.56 \times 1 0^{5}$ .

Given $M_{S} / M_{E} = 100 P \times 1 0^{5}$ , so $3.56 \times 1 0^{5} = 100 P \times 1 0^{5} ⟹ P = 0.0356$ .

However, if the question implies $M_{S} / M_{E} = P \times 1 0^{3}$ , then $P = 356$ .

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