The discussion focuses on calculating the distance on the ground corresponding to one minute or one second of arc at specific points on the Earth's surface, considering latitude and longitude. It explores both simplified and more complex models of the Earth's shape, including the implications of using a spherical versus a geoid model.
Participants express differing views on the implications of using a spherical model versus a geoid model, and there is no consensus on the best approach to calculate distances based on latitude and longitude.
Participants highlight the need for precision in defining latitude and the potential inaccuracies when using simplified models. The discussion does not resolve the mathematical complexities involved in these calculations.
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.Pollock said: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