Suppose that a satellite is in a circular orbit at a height of 2.00 $\times$ 10⁶ m above Earth's surface.What is the acceleration due to gravity at this elevation? A)9.80 m/s² B)3.22 m/s² C)5.67 m/s² D)7.68 m/s² E)None of these is correct.

Question

Quizplus · Accepted Answer

The acceleration due to gravity at a distance $r$ from the center of the Earth is given by $g = \frac{G M}{r^2}$, 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. At a height of $2.00 \times 10^6$ m above the Earth's surface, the total distance $r$ from the center of the Earth is the sum of the Earth's radius ($6.38 \times 10^6$ m) and the height above the surface, giving $r = 8.38 \times 10^6$ m. Plugging these values into the formula for $g$, we find that the acceleration due to gravity is closer to the value given in option C, $5.67 m/s^2$, than to any of the other provided options.

Suppose That a Satellite Is in a Circular Orbit at a Height