Question

The moon completes one (circular) orbit of the earth in 23.7 days. The distance from the earth to the moon is 3.84×10^8m. Calculate the centripetal acceleration.

Answer 1

The centripetal acceleration of the moon can be calculated using the formula centripetal acceleration = (velocity^2) / radius. By plugging in the values given, we can find that the centripetal acceleration of the moon is 6.31x10^-2 m/s^2.

Step-by-step explanation:

To calculate the centripetal acceleration of the moon, we can use the formula: centripetal acceleration = (velocity^2) / radius. The velocity of the moon can be calculated by dividing the distance it travels in one orbit by the time it takes to complete that orbit. In this case, the distance is the circumference of the moon's orbit and the time is 23.7 days. The radius is given as 3.84x10^8m. Plugging in these values, we can calculate the centripetal acceleration.

First, we need to calculate the velocity:

velocity = circumference / time = 2 * pi * radius / time = 2 * 3.14 * (3.84x10^8m) / 23.7 days = 1.55x10^4 m/s

Now, we can calculate the centripetal acceleration:

centripetal acceleration = (1.55x10^4 m/s)^2 / (3.84x10^8m) = 6.31x10^-2 m/s^2