What is the centripetal acceleration of the Moon? The period of the Moon's orbit about the Earth is 27.3 days, measured with respect to the fixed stars. The radius of the Moon's orbit is RM = 3.85 · 108 m.
v=2•π•R/T= 2•π•3.85•10^8/27.3•24•3600 =1.025•10^ 3 m/s
a(centr) =v²/R = (1.025•10^ 3)²/ 3.85 • 10^8=2.73•10^-3 m/s²
To calculate the centripetal acceleration of the Moon, we need to use the formula for centripetal acceleration, which is given by:
ac = (v^2) / r
Where:
ac is the centripetal acceleration
v is the velocity of the Moon
r is the radius of the Moon's orbit
First, let's find the velocity of the Moon using the period of its orbit.
We can use the formula for the velocity of an object in circular motion:
v = (2πr) / T
Where:
v is the velocity
r is the radius
T is the period of the orbit
Plugging in the given values:
v = (2π * 3.85 * 10^8) / (27.3 * 24 * 60 * 60) (Converting the period from days to seconds)
Now, let's calculate the value of v:
v = 1022.72 m/s
Now that we have the value of v, we can calculate the centripetal acceleration:
ac = (1022.72^2) / (3.85 * 10^8)
Calculating ac:
ac ≈ 0.027 m/s^2
Therefore, the centripetal acceleration of the Moon is approximately 0.027 m/s^2.