Then, what is the length (in meters) of 1 second of longitude at the Equator? Show your calculation.
On the Equator, the length of 1 degree of longitude is 111 kilometers. Then, what is the length (in meters) of 1 second of longitude at the Equator? Show your calculation.
The Correct Answer and Explanation is:
To find the length in meters of 1 second of longitude at the Equator, follow this step-by-step calculation:
Step-by-step Calculation:
- Given:
At the Equator, 1 degree of longitude = 111 kilometers - Convert kilometers to meters:
111 km=111,000 m111 \, \text{km} = 111,000 \, \text{m}111km=111,000m - Understand that 1 degree = 60 minutes and 1 minute = 60 seconds
So,
1 degree=60×60=3,600 seconds1 \, \text{degree} = 60 \times 60 = 3,600 \, \text{seconds}1degree=60×60=3,600seconds - Divide the total meters in 1 degree by the number of seconds: 111,000 m3,600 seconds=30.83333‾ meters\frac{111,000 \, \text{m}}{3,600 \, \text{seconds}} = 30.8333\overline{3} \, \text{meters}3,600seconds111,000m=30.83333meters
Final Answer:
1 second of longitude at the Equator is approximately 30.83 meters
Explanation
Longitude lines, also known as meridians, run from the North Pole to the South Pole. These lines are widest at the Equator and converge at the poles. When measuring distances along the Earth’s surface, latitude and longitude are expressed in degrees. Each degree is further divided into 60 minutes, and each minute into 60 seconds, totaling 3,600 seconds in one degree.
At the Equator, the Earth’s circumference is roughly 40,075 kilometers. Since the Earth is a sphere (approximately), dividing this circumference by 360 degrees gives about 111 kilometers for each degree of longitude at the Equator. This distance decreases as you move toward the poles due to the curvature of the Earth, but at the Equator, it is at its maximum.
To find the length of one second of longitude at the Equator, you first convert the known 111 kilometers per degree to meters, giving 111,000 meters. Since each degree contains 3,600 seconds, dividing 111,000 meters by 3,600 yields approximately 30.83 meters per second.
This measurement is important in fields like navigation, cartography, and GPS technology. The precision of global positioning systems often relies on coordinates accurate to within a few seconds or even fractions of a second. Knowing the real-world distance represented by a second of longitude helps determine how precise a location reading actually is.
While the Earth is not a perfect sphere and variations exist, for most practical purposes, using 111 kilometers per degree at the Equator gives a highly accurate approximation.
