Assuming that the Earth is spherical and recalling that latitudes range from 0° at the Equator to 90° N at the North Pole, how far apart, measured on the Earth's surface, are Copenhagen (55.67° N latitude), and Rome (41.90° N latitude)? The two cities lie on approximately the same longitude. Do not neglect the curvature of the Earth in determining this distance.
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To determine the distance between Copenhagen and Rome, we need to use the concept of spherical geometry, taking into account the curvature of the Earth. To calculate this distance, we can use the formula for the arc length on a sphere.
The arc length formula on a sphere is given by:
s = r * Δθ
Where:
s is the arc length,
r is the radius of the sphere (which we assume to be the radius of the Earth), and
Δθ is the difference in latitude between the two points.
First, we need to convert the latitudes from degrees to radians by multiplying them by π/180. So, the latitude of Copenhagen, 55.67° N, in radians is (55.67 * π / 180), and the latitude of Rome, 41.90° N, in radians is (41.90 * π / 180).
Next, we find the difference in latitude between the two cities:
Δθ = (latitude of Copenhagen in radians) - (latitude of Rome in radians)
Now, plug in the values into the formula:
s = r * Δθ
The radius of the Earth is approximately 6,371 kilometers. Hence, we can use this value in the equation to calculate the distance.