A 4,000 kg satellite is traveling in a circular orbit 200 km above the surface of the Earth. A 30.0 gram marble is dropped inside the satellite. What is the magnitude of the acceleration of the marble as viewed by the observers on the Earth? (M_E = 5.98 × 10²⁴ kg, R_E = 6.37 × 10⁶ m, G = 6.67 × 10⁻¹¹ N·m²/kg²) A) 9.80 m/s² B) 9.24 m/s² C) 8.90 m/s² D) 8.62 m/s² E) 7.95 m/s²

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Quizplus · Accepted Answer

The acceleration of the marble as viewed by observers on Earth can be calculated using the formula for gravitational acceleration at a distance $r$ from the center of the Earth: $a = \frac{G \cdot M}{r^2}$, where $G$ is the gravitational constant, $M$ is the mass of the Earth, and $r$ is the distance from the center of the Earth to the object. The distance $r$ is the sum of the Earth's radius and the altitude of the satellite: $r = 6.37 \times 10^6 m + 200 \times 10^3 m$. Substituting the given values and solving for $a$ gives an acceleration of approximately $9.24 m/s^2$, which corresponds to choice B.

A 4,000 Kg Satellite Is Traveling in a Circular Orbit