Understanding the Distances Between New York and Moscow: Great-Circle vs Rhumb-Line Paths
When traveling between New York and Moscow, one might be curious about why the straight-line distance is approximately 8905 km while the distance along a specific course is 7500 km. This article explores the differences between these two distance measurements and explains the underlying reasons.
Great-Circle Distance
The great-circle distance is the shortest distance between two points on the surface of a sphere. This measurement assumes a direct path over the Earth's surface, following the curvature of the planet. For New York City (40°42.8’N 74°00.4’W) and Moscow (55°45.3’N 37°37.0’E), the great-circle distance is approximately 8905 km. This path is the closest point between the two cities and represents the theoretical minimum distance.
When plotting this path on a Mercator map, it appears as a curve. The departure bearing from New York City is 34°28.6’ and the arrival bearing in Moscow is 130°19.0’. The distance along the great-circle path is 7505 km, which is closer to the 7500 km mentioned in the question, possibly due to rounding.
Rhumb-Line Distance
The rhumb-line distance, or rhumb course, is a different type of distance measurement. This path is a straight line if drawn on a Mercator projection map, making it easy to navigate. On the globe, this path appears as a spiral called a loxodrome, connecting the two specified points. The rhumb-line bearing from New York City to Moscow is approximately 78°28.9’, and the path length is 8371 km.
While this distance is slightly less than the 8905 km great-circle distance, it is 6 km less than the value mentioned in the question, suggesting this value might have been the writer's intent.
Why Are These Distances Different?
The key difference lies in the nature of the measurements. The great-circle distance is the shortest possible path between the two points, taking into account the curvature of the Earth. On the other hand, the rhumb-line distance is easier to navigate because it follows a constant bearing. However, due to the Earth's curvature, this path is longer than the great-circle path.
The shortest path, the great-circle path, is always the optimal choice for purposes of distance and time efficiency. In contrast, the rhumb-line path, which is easier to navigate, is not the shortest but is often used in practical navigation due to its straightforward nature.
Conclusion
In summary, the difference in distances between New York and Moscow arises from the nature of the measurements: one represents the theoretical minimum distance (great-circle distance), while the other is a practical distance based on actual travel routes (rhumb-line distance). Understanding both measurements helps in comprehending the complexities of geodesic paths on a spherical Earth.