Find the orbital speed of an ice cube in the rings of Saturn.The mass of Saturn is 5.68 × 10²⁶ kg and the rings have an average radius of 100,000 km.(G = 6.67 × 10^-11 N ∙ m²/kg²) A)19.5 km/s B)27.5 km/s C)13.8 km/s D)1.95 km/s

Question

Quizplus · Accepted Answer

The orbital speed $v$ can be found using the formula $v = \sqrt{\frac{GM}{r}}$, where $G$ is the gravitational constant $6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2$, $M$ is the mass of Saturn $5.68 \times 10^{26} \, \text{kg}$, and $r$ is the average radius of the rings $100,000 \, \text{km} = 100,000,000 \, \text{m}$. Plugging in the values, we get $v = \sqrt{\frac{6.67 \times 10^{-11} \times 5.68 \times 10^{26}}{100,000,000}} \approx 19.5 \, \text{km/s}$.

Find the Orbital Speed of an Ice Cube in the Rings