[Proj] How can I convert between cartesian space and WGS84?

[David Grundberg]

Hello,

I'd like to have a cartesian space, ideally in meters, axis-aligned with 
north/east/up, centered on a WGS84 position, so that I can transform 
between this cartesian space and WGS84 coordinates. I attempted to make 
a Mercator projection but quickly ran into problems. Just to illustrate, 
I tested with geocentric projection and known coordinates.

I tested it with coordinates for a track and it should be 100 meters 
between the points.

<https://kartor.eniro.se/?c=63.821347,20.321247&z=18&l=aerial&d={%22l%22:[[63.821477,20.321209,63.820758,20.322454,null,0]]}> 
or https://tinyurl.com/ybcxe3sb

$ printf "63.821477N 20.321209E\n63.820758N 20.322454E" | cs2cs -v 
+proj=latlong +ellps=WGS84 +datum=WGS84 +no_defs +to +proj=geocent 
+datum=WGS84 +to_meters
# ---- From Coordinate System ----
#Lat/long (Geodetic alias)
#
# +proj=latlong +ellps=WGS84 +datum=WGS84 +no_defs +towgs84=0,0,0
#--- following specified but NOT used
# +ellps=WGS84
# ---- To Coordinate System ----
#Geocentric
#
# +proj=geocent +datum=WGS84 +ellps=WGS84 +towgs84=0,0,0
#--- following specified but NOT used
# +to_meters
2639773.20    5369807.65 2201077.86
2639819.46    5369731.56 2201207.11
$ octave
octave:1> norm([2639773.20 5369807.65 2201077.86] - [2639819.46 
5369731.56 2201207.11])
ans =  156.96 # Should be about 100.7 meters!
octave:2>
$

Any advice appreciated!
David