Earth's moon is 3.8 X 10 8 m from the planet and is in freefall. Acceleration due to the Earth's gravity acting on the moon is 2.70X 10 -3. What is the moon's speed? How long does it take to make a complete orbit?
I can't believe they did not give you the units (dimensions) of acceleration along the number. In physics, that is a no-no. I will assume the units are m/s^2.
The acceleration of the moon toward the Earth is V^2/R = 2.7*10^-3 m/s^2
Since they told you the value of R, you can solve for V.
For the period P of one revolution can be obtained from for
V P = 2 pi R
P should turn out to be about 27 days. A month is a bit longer because the moon must travel more than one revolution to get back to the same phase, as a result of the Earth-moon system's motion around the sun
To find the moon's speed and the time it takes to make a complete orbit, we can use the equations of motion for circular motion.
1. First, let's find the moon's speed using the equation for centripetal acceleration:
a = (v^2) / r,
where a is the acceleration, v is the speed, and r is the distance from the center of the circle (in this case, the distance between Earth and the moon).
Rearranging the equation, we have:
v^2 = a * r.
Plugging in the values we have:
v^2 = (2.70 x 10^(-3)) * (3.8 x 10^8).
Now we can solve for v:
v^2 = 8.16 x 10^5.
Taking the square root of both sides:
v ≈ 902.74 m/s.
So, the moon's speed is approximately 902.74 m/s.
2. To find the time it takes for the moon to make a complete orbit, we can use the equation for the period of circular motion:
T = (2 * π * r) / v,
where T is the period, r is the distance from the center of the circle, and v is the speed.
Plugging in the values we have:
T = (2 * π * (3.8 x 10^8)) / 902.74.
Now we can solve for T:
T ≈ 1.67 x 10^6 seconds.
Therefore, it takes approximately 1.67 x 10^6 seconds for the moon to make a complete orbit around the Earth.