Incorrect output when computing the distance in kilometres of the Great Circle using Haversine formula in Java

Question

I'm trying to compute the distance in kilometres of the Great Circle using Haversine formula in Java as shown below

/* Program to demonstrate the Floating-point numbers and the Math library.
 * The great-circle distance is the length of the shortest path between two points (x1,y1) and (x2,y2) on the surface of a sphere, where the path is constrained to be along the surface.*/
public class GreatCircle 
{
    public static void main(String[] args) 
    {
        double r = 6371.0; // Equatorial radius of the Earth
        double x1 = Math.toRadians(Double.parseDouble(args[0]));
        double y1 = Math.toRadians(Double.parseDouble(args[1]));
        double x2 = Math.toRadians(Double.parseDouble(args[2]));
        double y2 = Math.toRadians(Double.parseDouble(args[3]));

        // Compute using Haversine formula
        double distance = 2 * r * Math.asin(Math.sqrt(Math.pow(Math.sin((x2 - x1) / 2),2 + Math.cos(x2) * Math.pow(Math.sin((y2 - y1) / 2),2)));

        // Output the distance
        System.out.println(distance + " kilometers ");
    }
}

I'm running with input java GreatCircle 60.0 15.0 120.0 105.0. The expected output is 4604.53989281927 kilometers, But I get 13406.238676180266 kilometers. Could someone please point out where am I going wrong?

This might be more appropriate on the [math stack exchange](https://math.stackexchange.com/). — bluevulture, Dec 22 '21 at 10:45
`Math.pow(Math.sin(y2 - y1 / 2)` y1 getscasted to an int in the last power i don’t think you want that you should probably write y1 / 2.0 instead of y1 / 2. — Gian Laager, Dec 22 '21 at 11:14
@user16320675 I thought there was an integer division since I had a similar problem some time ago — Gian Laager, Dec 22 '21 at 12:00

Alok Y · Accepted Answer · 2021-12-24T10:14:16.417

1

The formula was implemented incorrectly. It worked after making the following corrections. In the formula, we are taking the arc sin of the entire expression.


        // Compute using Haversine formula
        double distance = 2 * r * Math.asin(Math.sqrt(Math.pow(Math.sin((x2 - x1) / 2),2 + Math.cos(x2) * Math.pow(Math.sin((y2 - y1) / 2),2)));

        // Output the distance
        System.out.println(distance + " kilometers ");
    }
}

edited Dec 24 '21 at 10:14

answered Dec 24 '21 at 09:57

Alok Y

93
9

Your answer could be improved with additional supporting information. Please [edit] to add further details, such as citations or documentation, so that others can confirm that your answer is correct. You can find more information on how to write good answers [in the help center](/help/how-to-answer). – Community Dec 24 '21 at 10:02
Perhaps I need to rework on the implementation of the formula. I might get back to this sometime in the future. – Alok Y Dec 27 '21 at 10:24

Ragip Gashi · Answer 2 · 2021-12-27T13:58:40.083

0

You have forgotten to calculate Math.cos(x1) * Math.cos(x2), that's why you get a different result.

// Compute using Haversine formula<br>
double distance = 2 * r * Math.asin(Math.sqrt((Math.pow(Math.sin((x2 - x1) / 2),2) + Math.cos(x1) * Math.cos(x2) * Math.pow(Math.sin((y2 - y1) / 2),2))));```

edited Dec 27 '21 at 13:58

answered Dec 27 '21 at 13:53

Ragip Gashi

41
3

score 0 · Answer 3 · edited Jan 30 '22 at 08:40

0

double distance = 2 * r * Math.asin(Math.sqrt(Math.pow(Math.sin((x2 - x1) / 2),2)
            + Math.cos(x2) * Math.cos(x1) * Math.pow(Math.sin((y2 - y1) / 2),2)));

edited Jan 30 '22 at 08:40

Dada

6,313
7
24
43

answered Jan 30 '22 at 01:11

marypeng1020

21
2

3

As it’s currently written, your answer is unclear. Please [edit] to add additional details that will help others understand how this addresses the question asked. You can find more information on how to write good answers [in the help center](/help/how-to-answer). – Community Jan 30 '22 at 08:41

Incorrect output when computing the distance in kilometres of the Great Circle using Haversine formula in Java

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