A planet has mass M = 8.00 × 10²³ kg.At what distance will the centripetal acceleration of an orbiting space station be equal to the gravitational acceleration on Earth's surface? (G = 6.67 × 10^-11 m³·kg^-1·s^-1) A)2.33 × 10⁶ m B)5.44 × 1012 m C)5.23 × 10¹⁴ m D)1.18 × 1035 m

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Quizplus · Accepted Answer

The gravitational acceleration on Earth's surface is 9.8 m/s^2. To find the distance where the centripetal acceleration equals Earth's gravitational acceleration, use the formula for gravitational force $F = \frac{G \cdot M \cdot m}{r^2}$ and set the acceleration equal to 9.8 m/s^2. Solving for $r$, we get $r = \sqrt{\frac{G \cdot M}{9.8}}$. Plugging in the values $G = 6.67 \times 10^{-11} \, \text{m}^3/\text{kg} \cdot \text{s}^2$ and $M = 8.00 \times 10^{23} \, \text{kg}$, we find $r \approx 2.33 \times 10^{6} \, \text{m}$.

A Planet Has Mass M = 8