Answer:
option A
Explanation:
given,
distance of the moon 1 from planet = 0.7 AU
Time period of moon 1 = 27.8 earth days
distance of the moon 2 from the planet = 1.2 AU
time period of the moon 2 = ?
using Kepler's formula
[tex]T^2 = \dfrac{4\pi^2}{GM}\ R^3[/tex]
now,
only variable in the formula is time period and distance.
so,
[tex]\dfrac{T_2^2}{T_1^2}=\dfrac{R_2^3}{R_1^3}[/tex]
[tex]\dfrac{T_2^2}{27.8^2}=\dfrac{1.2^3}{0.7^3}[/tex]
T₂² = 3893.49
T₂ = 62.3 earth days
Hence, the correct answer is option A
