Lecture Notes: Calculating Latitude and Longitude Changes

Introduction

• Topic: Calculation of differences between latitudes and longitudes
• Scope: Basics of latitude and longitude, Greenwich Prime Meridian, measuring longitudes and latitudes, reasons for calculating changes, and detailed methodologies
• Target Audience: For anyone wanting to understand everything about latitudes and longitudes

Basics

What are Longitudes?

• Definition: Vertical lines running from pole to pole
• Prime Meridian: Passes through Greenwich, London (Greenwich Prime Meridian)
  • Terminology: Datum meridian, 0° East/West
  • Designation: Meridians to the west = West, to the east = East
  • Angles: Named according to the angle they make with the Prime Meridian

What are Latitudes?

• Definition: Parallel lines on either side of the equator
• Equator: Datum line, 0° North/South
  • Designation: Latitudes above equator = North, below = South
  • Angles: Named by the angle they make with the equator
• Great and Small Circles: Equator is a great circle; latitudes are small circles

Measuring Latitudes and Longitudes

• Latitudes: Measured by the angle between a line from a point on Earth and the equator
• Longitudes: Measured by the angle between a meridian and the Prime Meridian

Unit Conversions

• Degrees to Minutes/Seconds:
  • 1° = 60'
  • 1' = 60"
• Plotting Points: Use equator and prime meridian as references to plot coordinates

Practical Use

Importance of Calculating Changes

• Essential for finding distances between two points on Earth
• Example: Difference between two given coordinates to calculate distance.
• Scenarios: Finding shortest distance (departure) and changes using basic arithmetic operations

Addition and Subtraction of Degrees

Methodology

• Write degrees, minutes, and seconds separately
• Add or subtract corresponding units
• Convert overflow (e.g., 60 seconds to a minute)
• Example 1: Adding two latitudes
• Example 2: Subtracting longitudes
• Tools: Scientific calculators can simplify calculations

Finding Changes

Concept

• Shortest distance between two latitudes or longitudes
• Questions Types: Direct questions on change or calculating departure
• Additional Concept: Always look for shortest arc between longitudes

Examples and Diagrams

Example 1: Latitude Change

• 55°29’S to 31°48’S: Subtract to find the change
• Result: 23°41’ North

Example 2: Latitude Change across Hemispheres

• 26°57’S to 14°25’N: Add to find change
• Result: 41°22’ North

Tips

• Same hemisphere: Subtract
• Cross-hemispheres: Add

Longitude Change

• Example 1: 82°35’E to 132°42’E: Subtract to find the change
• Example 2: 4°32’W to 10°15’E: Add to find the change (shortest arc rule)
• Complex Example: Use step-by-step calculations and scientific calculator for simplification

Conclusion

Key Takeaways

• Always aim for the shortest arc in longitude calculations
• Always use diagrams and directional arrows for clarity
• Change in latitude or longitude is incomplete without direction

Exercises

• Homework questions for understanding application
• Encouragement to perform manual calculations even if calculators are allowed

Final Notes

• End of lecture. Inviting questions, comments, and suggestions.