coordinate system - What is a projection for Germany that preserves distance?

I have a point A (EPSG 4326) in Berlin, Germany:

{
   "type": "Point",
   "coordinates": [
     13.394994735717773,
     52.514849775310154
   ]
}

I want to create point B that is 500m to the east of point A and point C that is 500m to the north.

For this, I have to project point A to a projection that preserves distance.

Can you recommend a projection that works for this operation in entire Germany?

I am working with GeoPandas and Shapely for this project.

Answer

You don't need an equidistant projection, but geodetic distances calculated on a spheroid (Vincenty's formulae) or a sphere (Great-cicle distance). For instance, geopy is able to calculate them.

Here’s an example usage of Vincenty distance:

>>> from geopy.distance import vincenty

>>> newport_ri = (41.49008, -71.312796)
>>> cleveland_oh = (41.499498, -81.695391)
>>> print(vincenty(newport_ri, cleveland_oh).miles)
538.3904451566326

Using great-circle distance:

>>> from geopy.distance import great_circle
>>> newport_ri = (41.49008, -71.312796)
>>> cleveland_oh = (41.499498, -81.695391)
>>> print(great_circle(newport_ri, cleveland_oh).miles)

537.1485284062816

Source: https://pypi.python.org/pypi/geopy#measuring-distance

---

how to find point B with the above-described method?

You need to solve the direct problem, i.e. given an initial point, its azimuth and a geodesic distance calculate the final point. A Python implementation of the direct problem is available in the PyGeodesy package.

Example:

>>> from pygeodesy.ellipsoidalVincenty import LatLon 

>>> p = LatLon(-37.95103, 144.42487)
>>> d = p.destination(54972.271, 306.86816)
>>> print d.lon, d.lat
143.926497668 -37.6528177174