The Moon orbits Earth in an approximately circular orbit at a distance of 380000 km in 27.3216 days. What is the centripetal acceleration of the Moon? A)0.0272 m/s² B)0.0068 m/s² C)0.0027 m/s² D)0.0014 m/s²

Question

Quizplus · Accepted Answer

The centripetal acceleration $a_c$ can be calculated using the formula $a_c = \frac{v^2}{r}$, where $v$ is the orbital speed and $r$ is the radius of the orbit. The orbital speed $v$ can be found from $v = \frac{2\pi r}{T}$, where $T$ is the orbital period. Substituting the given values, $r = 380,000$ km (or $380,000,000$ m) and $T = 27.3216$ days (or $27.3216 \times 86400$ seconds), we find $v$ and then calculate $a_c$, which results in approximately $0.0027 m/s^2$.

The Moon Orbits Earth in an Approximately Circular Orbit at a Distance