Question

One of Saturn’s moons is named Mimas. The orbital radius of Mimas is 1.87 x ${10}^8$ m from Saturn. The mean orbital period of Mimas is approximately 23 hours. Its speed with which it revolves around Saturn is ________. (Assume that the path taken is circular.)

• A. $21,274m{s}^{-1}$
• B. $28,366m{s}^{-1}$
• C. $14,183m{s}^{-1}$
• D. $12,200m{s}^{-1}$

Answer 1

The correct option is C $14,183m{s}^{-1}$

Given,
Orbital radius, $r=1.87\times {10}^{8}m$
Time period, t = 23 hours = 23 × 3,600 = 82,800 seconds
From the definition of speed,
$Speed\left(v\right)=\frac{Circumference}{Timeperiod}$
$v=\frac{2\pi r}{t}$
$v=\frac{2\times 3.14\times 1.87\times {10}^8}{82,800}$
$v=14,183m{s}^{-1}$
Therefore, the speed of Mimas with which it revolves around Saturn is $14,183m{s}^{-1}.$