A planet has mass M = 8.00 × 10²³ kg.The centripetal acceleration of an orbiting space station is equal to the gravitational acceleration on Earth's surface.What is the speed of the space station? (G = 6.67 × 10^-¹¹ m³·kg^-1·s^-2) A)7.30 × 10⁶ m/s B)5.34 × 10¹³ m/s C)1.10 × 1017 m/s D)1.20 × 1034 m/s

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Quizplus · Accepted Answer

The speed of the space station can be found using the formula for gravitational acceleration $g = \frac{GM}{r^2}$, where $g$ is the gravitational acceleration on Earth's surface (9.8 m/s$^2$), $G$ is the gravitational constant (6.67 × 10$^{-11}$ m$^3$/kg·s$^2$), and $M$ is the mass of the planet. Since the centripetal acceleration is equal to $g$, we can also use the formula for centripetal acceleration $a_c = \frac{v^2}{r}$, where $v$ is the speed of the space station and $r$ is the radius of the orbit. Equating the two expressions for acceleration gives us a way to solve for $v$, the speed of the space station, which matches the value in choice A when calculated correctly.

A Planet Has Mass M = 8