From geographical coordinates to local coordinates

Description:

There are coordinates of objects in the format returned by the Google Api. That is, latitude, longitude, etc.

For example, I have 3 objects, take the object (1) its local coordinates become [0,0]. Object (2) is located 5 meters to the north and 2 meters to the east relative to object (1), its coordinates should become [5,2]. Object number (3) is located 75 meters to the south and 35 meters to the west, its coordinates should become [-75, -35].

Question:

How to translate objects to the local coordinate system knowing their latitude and longitude, please help?

Visible solutions:

• There was an idea to get the distance between objects using the following solution. (however, here the accuracy is in km, how can I increase it to meters?) And then calculate the angle between the geographical coordinate of the north pole, object (1) (which is taken as [0,0] in local) and object (2) and already knowing the distance and angle calculate the coordinate of object (2) in local coordinates. Will there be a distortion at the angle if I apply similar calculations? The earth is not square .

P.S. It is necessary to calculate on the phone, and such calculations will be up to 50 pieces at a time, or even more, preferably the most optimal solution, but accuracy is important up to 1 meter. (Similar calculations on the phone cause me to concerns)

P. P. S. Can you please provide the C# code for solving this issue?

P. P. P. S. According to the idea, this is all similar to a system where the object (1) is a person, and you need to calculate the position of objects in meters in local coordinates (meters). However, I couldn't find how this is implemented in gps navigators.