Question

If mass of earth is $5.98\times {10}^{24}$ kg and earth moon distance is $3.8\times {10}^5$ km, the orbital period of moon, in days is

• A. 27 days
• B. 2.7 days
• C. 81 days
• D. 8.1 days

Answer 1

Answer: (A)

27 days

$M=5.98\times {10}^{24}kg$

$R=3.8\times {10}^{8}km$

The orbital time period of moon,

$T=2\pi \sqrt{\frac{R^3}{GM}}$

$T=2\times 3.14\sqrt{\frac{(3.8{)}^3\times {10}^{24}}{6.67\times {10}^{-11}\times 5.48\times {10}^{24}}}$

$T=23.2427\times {10}^{5}sec$

In days,

Time period, $T=\frac{23.2427\times {10}^5}{60\times 60\times 24}day$

$T=27days$

The correct option is A.