How to Calculate Distance Between Two Points on Earth Using Latitude and Longitude?

Introducing Latitude and Longitude-Based Distance Calculations

Calculating the distance between two points on the Earth's surface using their latitude and longitude coordinates is a fundamental task in various applications. Below, we'll explore the intricacies of calculating this distance using a snippet of Java code and delve into an improved implementation that accounts for altitude differences.

Calculating Distance Using a Snippet of Java Code

The code provided by Dommer utilizes a simplified formula to compute the distance between two points on the Earth's surface:

<code class="java">double temp = Math.cos(Math.toRadians(latA))
            * Math.cos(Math.toRadians(latB))
            * Math.cos(Math.toRadians((latB) - (latA)))
            + Math.sin(Math.toRadians(latA))
            * Math.sin(Math.toRadians(latB));
    return temp * RADIUS * Math.PI / 180;</code>

This formula assumes a spherical Earth and yields reasonable results for small distances. However, it fails to consider altitude differences, which can lead to inaccuracies for significant distances.

Introducing the Haversine Formula for Altitude-Aware Distance Calculation

To address the limitations of the formula used by Dommer, we turn to the Haversine formula, which incorporates a more precise model for representing the Earth's shape. This formula explicitly accounts for the distance and height difference between the two points:

<code class="java">public static double distance(double lat1, double lat2, double lon1,
        double lon2, double el1, double el2) {

    final int R = 6371; // Radius of the earth
    
    double latDistance = Math.toRadians(lat2 - lat1);
    double lonDistance = Math.toRadians(lon2 - lon1);
    double a = Math.sin(latDistance / 2) * Math.sin(latDistance / 2)
            + Math.cos(Math.toRadians(lat1)) * Math.cos(Math.toRadians(lat2))
            * Math.sin(lonDistance / 2) * Math.sin(lonDistance / 2);
    double c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1 - a));
    double distance = R * c * 1000; // convert to meters

    double height = el1 - el2;

    distance = Math.pow(distance, 2) + Math.pow(height, 2);

    return Math.sqrt(distance);
}</code>

This formula provides a more accurate representation of distance, making it valuable for applications requiring precise geographic calculations.

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