I am trying to estimate the crossing time of a circle given two point P1, P2 one inside and the other one outside of the buoy.

So given the following (Coords in WGS):

lat1, lon1, t1 = 45.965467, 8.509283, datetime(2024, 6, 19, 11, 46, 39) # P1 
lat2, lon2, t2 = 45.968483, 8.5089, datetime(2024, 6, 19, 11, 57, 12) # P2 
lat_c, lon_c, r = 45.987168002, 8.452897189, 4500  # Bouy center coordinates and radius

I need to find an estimated crossing time. Typically, if it all works, I have a sample per second and take the last outside to define the crossing time, but sometimes GPS get lost, especially in mountain hiking races and I need to interpolate.

What is the best approach with Python? I believe it must include (haversine distance calculations, bearings since it can be crossed sideways, speeds etc etc)?