The captain of a spaceship orbiting planet X discovers that to remain in orbit at $410 \mathrm {~km}$ from the planet's center, she needs to maintain a speed of $68 \mathrm {~m} / \mathrm { s }$ What is the mass of planet X? (G = 6.67 × 10^-11 N ? m²/kg²) A)2.8 × 10¹⁹ kg B)4.2 × 10¹⁷ kg C)2.8 × 10¹⁶ kg D)4.2 × 10¹⁴ kg

Question

Quizplus · Accepted Answer

The gravitational force provides the necessary centripetal force for the orbit. Using the formula $v^2 = \frac{GM}{r}$, where $v = 68 \, \text{m/s}$, $r = 410,000 \, \text{m}$, and $G = 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2$, solving for $M$ gives approximately $2.8 \times 10^{19} \, \text{kg}$.

The Captain of a Spaceship Orbiting Planet X Discovers That 410 km410 \mathrm {~km}410 km

The Captain of a Spaceship Orbiting Planet X Discovers That $410 \mathrm {~km}$