Answer:
The radius of the moon's orbit, R = 7.715 x 10⁷ m
The orbital period of the moon, T = 14.48 hr
Explanation:
Given,
The orbital speed of the moon, v = 9.3 x 10³ m/s
The mass of Neptune, M = 1.0 x 10²⁶ Kg
The orbital velocity of the moon is given by the relation
[tex]v = \sqrt{\frac{GM}{r+h}}[/tex] m/s
Where,
r + h = R → radius of the moon's orbit
Therefore squaring the above equation and solving for r +h. The equation becomes
r + h = GM / v²
Substituting the given values in the above equation
R = (6.673 x 10⁻¹¹ x 1.0 x 10²⁶) / (9.3 x 10³)²
= 7.715 x 10⁷ m
The radius of the moon's orbit, R = 7.715 x 10⁷ m
The orbital period of the moon is given by the relation
T = 2π/ω
= 2πR/v ∵ ω = v/r
Substituting the values in the above equation
T = (2 x π x 7.715 x 10⁷ )/ 9.3 x 10³
= 52125.72969 s
= 14.48 hr
The orbital period of the moon, T = 14.48 hr
