The Moon, which revolves around Earth with a period of about 27.3 d in a nearly circular orbit has a centripetal acceleration of 2.7x10^-3 m/s^2. What is the average distance from Earth to the moon.
(Would appreciate a response without the use of radians).
To find the average distance from Earth to the Moon, we can use the formula for centripetal acceleration:
a = v^2 / r
where:
a = centripetal acceleration (2.7x10^-3 m/s^2)
v = orbital velocity of the Moon
r = distance from Earth to the Moon
We know that the period of revolution of the Moon is 27.3 days. The formula for orbital speed is:
v = 2πr / T
where:
v = orbital velocity
r = distance from Earth to the Moon
T = period of revolution
Substituting this value of v into the formula for centripetal acceleration:
2.7x10^-3 m/s^2 = [(2πr / T)^2] / r
Simplifying the equation:
2.7x10^-3 m/s^2 = (4π^2r) / T^2
Rearranging the equation to solve for r:
r = (2.7x10^-3 m/s^2 * (T^2)) / (4π^2)
Substituting the value of T (27.3 days = 2358720 seconds):
r = (2.7x10^-3 m/s^2 * (2358720 s)^2) / (4π^2)
Calculating this expression:
r ≈ 384,400 km
Therefore, the average distance from Earth to the Moon is approximately 384,400 kilometers.
To find the average distance from Earth to the Moon, we can use the centripetal acceleration and the period of revolution.
The centripetal acceleration of an object moving in a circular path is given by the formula:
a = v^2 / r
Where:
a = centripetal acceleration
v = velocity of the object
r = radius of the circular path
We know the centripetal acceleration of the Moon is 2.7×10^-3 m/s^2. However, we need to find the velocity of the Moon in order to calculate the radius.
The velocity of the Moon can be calculated using the formula:
v = 2πr / T
Where:
v = velocity of the Moon
r = radius of the circular path
T = period of revolution of the Moon
The period of revolution of the Moon is 27.3 days, which we need to convert into seconds to match the units in the equation. One day is equal to 24 hours, and one hour is equal to 60 minutes, and one minute is equal to 60 seconds, so:
T = 27.3 days × 24 hours/day × 60 minutes/hour × 60 seconds/minute
Now we can substitute the values into the equation to find the velocity:
v = 2πr / (27.3 days × 24 hours/day × 60 minutes/hour × 60 seconds/minute)
After finding the velocity, we can substitute it back into the formula for centripetal acceleration:
2.7×10^-3 m/s^2 = (v^2) / r
Now we have two equations with two unknowns (v and r). We can solve them simultaneously to find the value of r, which represents the average distance from Earth to the Moon.
You need to learn radians quickly, or get left behind.
acceleration=v^2/r=(2PIr/Period)^2 / r
acceleration= 4PI^2*r/Period^2
or r=Period^2*acceleration/(4PI^2)
so convert period in days to seconds, and you have it.