A satellite is in a circular orbit about the Earth at a distance of two Earth radii above the surface.What is the speed of the satellite? (The radius of the Earth is 6.4 × 10⁶ m,and G = 6.67 × 10−¹¹ N × m²/kg². ) A)2 800 m/s B)4 600 m/s C)5 600 m/s D)17 000 m/s

Question

Quizplus · Accepted Answer

The speed $v$ of a satellite in circular orbit at a distance $r$ from the center of the Earth is given by the formula $v = \sqrt{\frac{GM}{r}}$, where $G$ is the gravitational constant and $M$ is the mass of the Earth. The distance $r$ from the center of the Earth to the satellite is three Earth radii (one radius to get to the surface, plus two more to the satellite), so $r = 3 \times 6.4 \times 10^6 \, \text{m}$. Plugging in the values for $G$ and $M$ (where $M = \frac{4}{3} \pi R^3 \rho$, but since we're looking for a direct relationship involving $G$, $M$, and $r$, we can simplify our calculations by directly substituting the given values), we find that the speed falls into the range of the provided options, with the correct calculation aligning with option B, 4 600 m/s, after solving the equation with the given and derived values.

A Satellite Is in a Circular Orbit About the Earth