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Problem 909

# If an observer could be suspended in the same spot in space over the equator and watch the world turn, how many miles of the equator would he observe to pass by in 1 hour?

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The observer would witness approximately 1037.54 miles of the equator pass by in 1 hour.
See the step by step solution

## Step 1: Understand the problem

This problem can be solved by understanding that the observer standing over the equator will be witnessing the rotation of the earth underneath them. Considering that the earth completes one full rotation (360 degrees) in a day (24 hours), we need to find out how far the earth rotates per hour.

## Step 2: Find the Earth's Circumference

Earth’s Equator is almost a perfect circle. Therefore, the best way to calculate the distance around the earth (its circumference) is by using the formula $$C = 2 \pi r$$, where $$r$$ is the radius of earth. According to NASA, Earth's equator radius is about 3965 miles. So, the earth's circumference is $$C = 2 \pi \times 3965 = 24901$$ miles.

## Step 3: Find the Distance Travelled in 1 Hour

We know that the earth completes one full rotation (360 degrees) in 24 hours. Therefore, in 1 hour, the earth will cover $$\frac{1}{24}^{th}$$ of its circumference. Let's call the distance covered in an hour as $$d$$. Therefore, $$d = \frac{C}{24} = \frac{24901}{24} = 1037.54$$ miles. So the observer would witness approximately 1037.54 miles of the equator pass by in 1 hour.

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