 What is the shape of the path a plane takes as it navigates on earth. Why is this path necessary? How can this be described in terms of distance and displacement?

 

The path a plane takes when navigating long distances on Earth is typically an *arc of a great circle*. This path is called a *great circle route*. A great circle is the largest possible circle that can be drawn on a sphere, and it divides the sphere into two equal halves. On Earth, great circles include the Equator, lines of longitude, and any circle that passes through the poles.

### Why is the Great Circle Path Necessary?
The great circle route is the shortest path between two points on a sphere. Due to the curvature of the Earth, following a straight line (in a flat, two-dimensional sense) would actually result in a longer distance. Therefore, planes follow the arc of a great circle to minimize travel distance, which saves fuel, time, and cost.

For example, if a plane travels from New York to London, the most efficient route on a flat map may look like a curve moving northwards, near Greenland. However, in three dimensions, it is the shortest distance between these two cities on the Earth's surface.

### Distance vs. Displacement in Great Circle Route
- **Distance** refers to the total length of the path traveled by the plane, which, in this case, is the arc length of the great circle.
- **Displacement**, on the other hand, is the straight-line distance between the starting point and the destination (ignoring the Earth's curvature). Displacement is measured as the shortest straight-line distance on a flat map but is not the most accurate representation when considering Earth's curvature.

### Summary of Key Points:
- **Path**: Arc of a great circle on Earth's surface.
- **Reason**: Minimizes travel distance due to Earth's curvature.
- **Distance**: Actual curved path length.
- **Displacement**: Straight-line distance connecting two points.

Would you like more details or have any questions?

---

Here are five relative questions:
1. How is a great circle route calculated mathematically?
2. Why are longitude lines considered part of great circles?
3. What is the impact of Earth's curvature on shorter flights?
4. How does the Coriolis effect impact the plane's path?
5. What tools or technology are used by pilots to navigate using great circles?

**Tip**: When visualizing the great circle route, think of the Earth as a three-dimensional sphere. Any "straight line" in this context means the shortest arc between two points on this sphere.

What is the shape of the path a plane takes as it navigates on Earth? Why is this path necessary? How can this be described in terms of distance and displacement?

Learn how the great circle route is the shortest path a plane takes on Earth, based on spherical geometry. This explanation covers key concepts like distance, displacement, and the great circle theorem, with practical examples from long-distance air travel. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation