# Calculating Minimum Distance Between Two Co-ordinates on Earth

• lbass
In summary, the minimum distance between two coordinates on Earth can be found using a method called great circles. The formula for calculating the distance involves the radius of the Earth and the central angle between the two points, which can be determined from their latitude and longitude.

#### lbass

Could somebody please please explain how to work out the minimum distance between two co-ordinates on the earth, eg hobart(43 S,147 E) to Beijing (39 N, 117 E). Apparently there is a method incorporating great circles which finds min distant. If anyone knows the formula and could give me a quick explanation, would be much appreciated.
Cheers

Yes, the shortest distance between two points on the surface of a sphere is along a "great circle" which is a circle having the center of the sphere as its center. The length of an arc of radius R and subtending central angle $\theta$, in radians, is R$/theta$. If $\theta$ is in degrees that is $R\theta (\pi/180)$. Here R is the radius of the Earth and you will need to work out the angle $\theta$ from the latitude and longitude.

## 1. How is the minimum distance between two coordinates on Earth calculated?

The minimum distance between two coordinates on Earth is calculated using the Haversine formula. This formula takes into account the curvature of the Earth's surface and uses the latitude and longitude of the two points to calculate the shortest distance between them.

## 2. What factors affect the minimum distance between two coordinates on Earth?

The factors that affect the minimum distance between two coordinates on Earth include the latitude and longitude of the two points, the curvature of the Earth's surface, and any obstacles such as mountains or bodies of water that may be between the two points.

## 3. Can the minimum distance between two coordinates on Earth be calculated using a straight line?

No, the minimum distance between two coordinates on Earth cannot be accurately calculated using a straight line. This is because the Earth is not a flat surface and the shortest distance between two points on a spherical surface is not a straight line.

## 4. What units are used to measure the minimum distance between two coordinates on Earth?

The minimum distance between two coordinates on Earth is typically measured in kilometers or miles. However, other units such as meters or nautical miles may also be used depending on the specific application.

## 5. How accurate is the calculation of the minimum distance between two coordinates on Earth?

The calculation of the minimum distance between two coordinates on Earth can be quite accurate, especially if the Haversine formula is used. However, it should be noted that this calculation is an approximation and factors such as weather conditions or variations in the Earth's surface may affect the actual distance between the two points.