He was actually timing how long between the entry and exit of the darker (umbral) shadow. Which to him appeared to be around 2.6 hours. Next, he compared this with the time it takes the moon to move a distance equal to it’s diameter. In the previous article we determined that this was about 1 hour. So he’s left with two numbers:
- time it takes the moon to travel 1 moon diameter = 1 hour
- time it takes the moon to travel 1 earth diameter = 2.6 hours
How could we figure out the size of the moon from this?
If the times were equal than it would imply that the moon is the same size as the earth. However the time of a lunar eclipse is much longer, which means the earth must be larger. How much larger? We need to setup a basic proportion:
time #1 / time #2 = moon diameter / earth diameter
1 / 2.6 = moon diameter / earth diameter
This led him to claim that the earth was about 8/3 the diameter of the moon. This is pretty close to the actual difference: the earth is about 3.7 times bigger than the moon. The main reason he underestimated was because the umbral shadow is narrower than the earth.
Actual size of the moon
We now know the relative size of the moon compared to earth. We also know the actual size of the earth from a previous calculation. Finally we can determine the approximate size of the moon!
moon diameter = earth Diameter / 3.7
moon diameter = 12742/3.7 = 3444 km
This is very close to the actual diameter of the moon: 3474.8 km
Mukul Tanwar 6 years, 11 months ago
He was actually timing how long between the entry and exit of the darker (umbral) shadow. Which to him appeared to be around 2.6 hours. Next, he compared this with the time it takes the moon to move a distance equal to it’s diameter. In the previous article we determined that this was about 1 hour. So he’s left with two numbers:
How could we figure out the size of the moon from this?
If the times were equal than it would imply that the moon is the same size as the earth. However the time of a lunar eclipse is much longer, which means the earth must be larger. How much larger? We need to setup a basic proportion:
time #1 / time #2 = moon diameter / earth diameter
1 / 2.6 = moon diameter / earth diameter
This led him to claim that the earth was about 8/3 the diameter of the moon. This is pretty close to the actual difference: the earth is about 3.7 times bigger than the moon. The main reason he underestimated was because the umbral shadow is narrower than the earth.
Actual size of the moon
We now know the relative size of the moon compared to earth. We also know the actual size of the earth from a previous calculation. Finally we can determine the approximate size of the moon!
moon diameter = earth Diameter / 3.7
moon diameter = 12742/3.7 = 3444 km
This is very close to the actual diameter of the moon: 3474.8 km
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