# How does one calculate the distance (or length) on the ground

1. Oct 25, 2008

### Pollock

How does one calculate the distance (or length) on the ground suspended by one minute of arc (or one second of arc) at a particular point on the earth's surface,given its latitude/longitude in degrees/ minutes /seconds ?.Where would one get the earth radius of sufficient accuracy as a function of latitude ?.

Pollock

2. Oct 25, 2008

### mgb_phys

Re: Latitude/longitude

For a simple answer you can assume the Earth is a sphere then the length of an arc segment is failry simple to work out.

More complete answer require more terms to account for the Earth's shape (geoid) see http://en.wikipedia.org/wiki/Latitude

3. Oct 26, 2008

### Pollock

Re: Latitude/longitude

The distance on the ground equivalent to one degree of arc will be the same at any latitude (assuming the earth as a perfect sphere).But this will not be so for the distance equivalent to a degree of longitude as circles of constant latitude get smaller towards the poles.How does one take account of this to calculate distance on the ground in terms of both latitude and longitude anywhereon the earth's surface

4. Oct 26, 2008

### D H

Staff Emeritus
Re: Latitude/longitude

The arc length of one degree change in latitude is very, very close to constant everywhere on the non-spherical surface of the Earth. The reason why is that latitude of a point on the surface is not the angle subtended between the Earth's equatorial plane and the line connecting the center of the Earth and the point in question. The latitude of a point is instead the angle subtended between the Earth's equatorial plane and the line defined by the normal to an idealization of the Earth's non-spherical surface. This angle is more precisely called the geodetic latitude of the point. The word "latitude" without a qualifier means geodetic latitude.