The Moon is about 3.8e5 km from the Earth. Find its average orbital speed about the Earth.
1026 m/s
To find the average orbital speed of the Moon around the Earth, we can use the formula:
Average Orbital Speed = 2πR / T
Where:
- R is the distance from the Moon to the center of the Earth
- T is the period of the Moon's orbit around the Earth
Given that the distance from the Moon to the Earth is 3.8e5 km, we can convert it to meters by multiplying by 1000 (since 1 km = 1000 m), giving us:
R = 3.8e5 km * 1000 = 3.8e8 m
The period of the Moon's orbit around the Earth is approximately 27.3 days, or 27.3 * 24 * 60 * 60 seconds. Converting this to seconds, we have:
T = 27.3 days * 24 hours/day * 60 minutes/hour * 60 seconds/minute = 2.36e6 seconds
Plugging these values into the formula, we get:
Average Orbital Speed = 2π * (3.8e8 m) / (2.36e6 seconds)
Simplifying the equation, we have:
Average Orbital Speed = 6.28 * (3.8e8 m) / (2.36e6 seconds)
Calculating this, we get:
Average Orbital Speed ≈ 10.08e2 m/s
So, the average orbital speed of the Moon around the Earth is approximately 1008 m/s.
To find the average orbital speed of the Moon around the Earth, we need to know the time it takes for the Moon to complete one orbit around the Earth.
The Moon takes approximately 27.3 days to complete one orbit around the Earth.
First, let's convert this time to seconds:
27.3 days * 24 hours/day * 60 minutes/hour * 60 seconds/minute = 2,360,800 seconds
Next, we need to calculate the circumference of the Moon's orbit. The circumference of a circle can be found using the formula:
Circumference = 2 * π * radius
The radius of the Moon's orbit can be calculated as the average distance between the Moon and the Earth, which is given as 3.8e5 km.
Now, let's convert this distance to meters:
3.8e5 km * 1000 m/km = 3.8e8 m
Plugging the values into the formula, we have:
Circumference = 2 * π * 3.8e8 m
Finally, we can calculate the average orbital speed by dividing the circumference by the time:
Average orbital speed = Circumference / Time taken
Average orbital speed = (2 * π * 3.8e8 m) / 2,360,800 s
By performing the calculation, we find that the average orbital speed of the Moon around the Earth is approximately 1,022 m/s.