Question

Морское судно двигалось из пункта с координатами 0 ° ш., 170 ° з. д. строго по экватору на запад в пункт с координатами 0 ° ш., 175 ° в. д. Определите расстояние в километрах между указанными пунктами. Получается,что расстояние = 15 градусам,а потом надо умножить на 111,но как так получилось,что именно 15?Объясните пожалуйста.

Answer 1

Расстояние ищется непосредственно в атласе. Земной шар разбит по меридианам на 360 градусов. Восточное и Западное имеет соответственно по 180 градусов каждый. Когда мы движемся из 170 з.д. на запад, то достигаем отметки в 180 градусов, пройдя 10 градусов (180-170). После этого мы попадаем в восточное полушарие и отсчет теперь идет от 180 в обратную сторону (180-175 = 5). Теперь сложим сумму пройденных расстояний: 5+10=15 градусов

Answer 2

Calculating the Distance between Two Points on Earth's Surface

To calculate the distance between two points on Earth's surface, we can use the Haversine formula. This formula takes into account the curvature of the Earth and provides an accurate distance calculation.

In this case, the two points are located at coordinates (0° N, 170° W) and (0° N, 175° E). The latitude is 0° N for both points, which means they are located on the equator. The longitude for the first point is 170° W, and for the second point, it is 175° E.

To calculate the distance between these two points, we can follow these steps:

1. Convert the longitude values to a common reference point. - Since the first point has a longitude of 170° W and the second point has a longitude of 175° E, we need to convert them to a common reference point. We can choose either 170° E or 175° W as the reference point. Let's choose 170° E as the reference point. - To convert 170° W to 170° E, we add 360° to the longitude value: 170° W + 360° = 190° E. - Now, the longitude values for both points are 190° E and 175° E.

2. Calculate the absolute difference in longitude. - The absolute difference in longitude is the difference between the two longitude values. - Absolute difference = |190° E - 175° E| = 15°.

3. Calculate the distance using the Haversine formula. - The Haversine formula is as follows: - distance = 2 * R * arcsin(sqrt(sin²((lat2 - lat1) / 2) + cos(lat1) * cos(lat2) * sin²((lon2 - lon1) / 2))) - R is the radius of the Earth, which is approximately 6,371 kilometers. - lat1 and lat2 are the latitudes of the two points. - lon1 and lon2 are the longitudes of the two points.

- In this case, since both points are on the equator, the latitudes are the same (0° N). Therefore, we can simplify the formula to: - distance = 2 * R * arcsin(sin(lon2 - lon1 / 2))

- Plugging in the values: - distance = 2 * 6,371 km * arcsin(sin(15° / 2)) - distance ≈ 2 * 6,371 km * arcsin(sin(7.5°)) - distance ≈ 2 * 6,371 km * 0.1305 - distance ≈ 16,071 km

Therefore, the approximate distance between the two points is 16,071 kilometers.

Please note that this calculation assumes a perfect sphere for the Earth and does not take into account factors such as the Earth's oblateness or variations in elevation.

Answer 3

Calculating the Distance between Two Points on the Earth's Surface

To calculate the distance between two points on the Earth's surface, such as the two coordinates you provided, you can use the haversine formula. This formula takes into account the curvature of the Earth and provides an accurate distance calculation.

The haversine formula is as follows:

haversin(θ) = sin²(θ/2)

where θ is the angular distance between the two points in radians.

To convert the angular distance to kilometers, you can use the following formula:

distance = radius * 2 * arcsin(sqrt(haversin(Δφ) + cos(φ1) * cos(φ2) * haversin(Δλ)))

where: - Δφ is the difference in latitude between the two points, - Δλ is the difference in longitude between the two points, - φ1 and φ2 are the latitudes of the two points, and - radius is the radius of the Earth (approximately 6,371 kilometers).

Applying the Formula to the Given Coordinates

In your case, the starting point has coordinates 0°N, 170°W, and the destination point has coordinates 0°N, 175°W.

To calculate the distance between these two points, we need to convert the longitude values from degrees to radians. Since 1 degree is equal to π/180 radians, we have:

- Starting point: 170°W = (170 * π) / 180 radians - Destination point: 175°W = (175 * π) / 180 radians

Substituting these values into the haversine formula, we can calculate the distance:

distance = 6371 * 2 * arcsin(sqrt(haversin(0) + cos(0) * cos(0) * haversin((175 * π) / 180 - (170 * π) / 180)))

Simplifying the formula, we get:

distance = 6371 * 2 * arcsin(sqrt(0 + 1 * 1 * haversin((175 * π) / 180 - (170 * π) / 180)))

Now, let's calculate the distance using this formula.