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# Great Circle Distance

### Great Circle Distance

The great circle distance is the shortest distance between two points on the surface of a sphere. The great circle is a circle on the sphere whose centers coincide with the center of the sphere. The tool named “Great Circle  Distance” allows the calculation of distance between two points of latitude and longitude which the geodetic coordinates must be based on WGS84. The tool use the formula is known as the haversine formula.

When you start the Surveyor Pocket Tools you will see the Great Circle Distance in the main window. Double click to run and the window will be displayed as the screenshot below. On the top of the window, there is a text box “Earth Radius” that the default value is 6371 Km. The coordinates to be computed the great circle distance are on the left and the the right panel. You can define the angle display format at the combo boxes on the left and on the right side as well. The great circle distance computation is denoted by the button. At the bottom of the window there is a “Great Circle Distance” text box displayed as the result which its unit are available in kilometer or meter. The another four small buttons are function to:

• The button use to store/save point to database.
• The button use to restore point from database.
• The button use to pin location to Google maps.
• The button use to save KML file and display location on Google Earth.

The default value for Earth radius that provided by the tool is about 6371 km (recommended) was derived from the the shape of the earth closely resembles a flattened sphere (a spheroid) with equatorial radius(a)  6378.137 km; distance(b) from the center of the spheroid to each pole is 6356.752 km. A good choice for the radius is the mean earth radius, R = 1/3 * ( 2a + b ) ≈ 6371 km (for the WGS84 ellipsoid).

#### Define Display Formats and Input Geodetic Coordinates

There are many possible display formats for geographic or geodetic coordinates (latitude/longitude). Follow the link below for tutorial how to define angle display settings and input geodetic coordinates.

How to define angle display formats and input geodetic coordinates?

#### Store the Point to Database and Restore the point from database

If you need to save a input or output point into database called Geo Database. Please follow the tutorial link:

How to use Geo Database?

#### Compute Great Circle Distance

Great circle distance by haversine formula is used to determine distance between two points on a sphere for navigation a vessel (a ship or aircraft) along a great circle. Even if the Earth isn’t exactly spherical, but the formulas are simpler and are often accurate enough for navigation.

#### Example 1

Compute the great circle distance from  Valparaíso, latitude = −33°, longitude = −71.6°, to Shanghai, lattitude = 31.4°, longitude = 121.8°. Enter the coordinate values of Valparaíso on the left panel and Shanghai on the right. Click the button to compute great circle distance. The great circle distance is about 18743 km, compare to the geodesic distance is more accurately at 18752 km. The difference is about 9 km (±1%) that is enough for navigation.

#### Example 2

This example will use the points that stored in the Geo Database. The procedure start from display the table of the database and then restore the point to the text boxes of the tool by the mean of drag and drop. Click the button on the tool and the table will be displayed. Scroll the mouse until you meet the point name “George Town“. Click to this row as the screenshot below. Drag this point to the rectangle of “Coordinate point 1” and drop. Locate the coordinates of the “Luanda” and do the same as previous method just drop the coordinates to “Coordinate point 2” on the right panel. The coordinate of two points were input by dropped values from the table and then click the button to compute great circle distance. The result is “10815 km“. #### Conclusion

The Great Circle Distance tool calculate the shortest distance on the surface of the sphere which is accurate enough for navigation.