[Python] Processing satellite conjunctions with numpy efficiently

Original Post: How to populate a 2-d numpy array with values from a third dimension?


New Post: I'm trying to analyze interference between satellites using numpy and sgp4 python libraries, and want to start with a very basic model which simply shows geometric conjunctions between objects. In this case a conjunction is defined as the angle between two spacecraft's position vectors being equal to 0 degrees (or close to).

To keep it simple, my example shows my current code for one GPS satellite and 10 OneWeb ones, at two points during the day. The GP data needed to load these is provided at the bottom.

Question: I don't know how to do this efficiently - and using loops will get very slow very quickly as I start to introduce more timesteps and more satellites. How can I do this in a vectorized manner?

Example: The following code gets the position vectors for each spacecraft and stores them in owR and gpsR:

# Imports
import numpy as np

from datetime import datetime as dt
from datetime import timedelta as td

from sgp4 import omm
from sgp4.api import jday, Satrec, SatrecArray

# Set up analysis period
startDate = dt(2025, 3, 17, 0)
endDate = startDate + td(days=1)
step = td(days=0.5)

dateArray = np.arange(startDate, endDate, step).astype(dt)
dateArray = np.array([np.array(jday(x.year, x.month, x.day, x.hour, x.minute, x.second)) for x in dateArray])

jdArray = np.ascontiguousarray(dateArray[:,0]) # Integer + 0.5 Julian day
frArray = np.ascontiguousarray(dateArray[:,1]) # Fraction past 1200UTC of Julian day

# Loading OMM data from CSV
owSats = {}
gpsSats = {}

with open('GP_DATA.csv') as f:
for fields in omm.parse_csv(f):
sat = Satrec()
omm.initialize(sat, fields)
if 'ONEWEB' in fields['OBJECT_NAME']:
owSats[fields['OBJECT_NAME']] = sat
elif 'NAVSTAR' in fields['OBJECT_NAME']:
gpsSats[fields['OBJECT_NAME']] = sat

# Arrays of Satrec objects for SGP4
owSatsArray = SatrecArray(list(owSats.values()))
gpsSatsArray = SatrecArray(list(gpsSats.values()))

# Calculate Position & Velocity for each satellite at each timestep, returns error codes too
owErr, owR, owV = owSatsArray.sgp4(jdArray, frArray)
gpsErr, gpsR, gpsV = gpsSatsArray.sgp4(jdArray, frArray)


I then define a function, angle_of_separation(u, v), which takes two vectors and calculates the angle between them using np.dot:

def angle_of_separation(u, v):
cosTheta = np.dot(u, v) / (np.linalg.norm(u)*np.linalg.norm(v))
thetaRad = np.arccos(cosTheta)
thetaDeg = np.degrees(thetaRad)

return thetaRad, thetaDeg


Then, the bit I'm trying to improve, I loop through and find the angle between the GPS satellite and all the OneWeb satellites at all timesteps:

m, n, r = owR.shape
res = np.ones(shape=[m,n])
for i in range(m):
for j in range(n):
rad, deg = angle_of_separation(gpsR[j,:], owR[i,j,:])
res[i,j] = deg


GP_DATA.csv

NAVSTAR 43 (USA 132),1997-035A,2025-03-18T23:55:30.358560,2.00562658,.0087553,55.7688,116.3810,53.8413,307.0378,0,U,24876,999,20282,0,.19E-6,0
ONEWEB-0012,2019-010A,2025-03-19T17:10:05.865888,13.16596004,.0002263,87.9081,319.3992,91.2044,268.9346,0,U,44057,999,29176,-.65808E-3,-.239E-5,0
ONEWEB-0010,2019-010B,2025-03-19T15:57:09.992736,13.16593707,.0001911,87.9085,319.3913,67.6783,292.4550,0,U,44058,999,29180,.17816E-3,.81E-6,0
ONEWEB-0008,2019-010C,2025-03-19T16:33:37.353888,13.16594232,.0001519,87.9084,319.3871,85.1200,275.0104,0,U,44059,999,29192,-.95577E-3,-.353E-5,0
ONEWEB-0007,2019-010D,2025-03-19T19:41:26.459232,13.15550961,.0002162,87.9140,349.7394,76.2670,283.8701,0,U,44060,999,29163,.44111E-3,.179E-5,0
ONEWEB-0006,2019-010E,2025-03-19T19:47:07.657152,13.15551703,.0002,87.9131,349.6962,72.9243,287.2106,0,U,44061,999,29168,.3057E-3,.128E-5,0
ONEWEB-0011,2019-010F,2025-03-19T19:03:48.012480,13.15548960,.0001684,87.9131,349.7085,71.9060,288.2254,0,U,44062,999,29167,-.43781E-4,-.4E-7,0
ONEWEB-0013,2020-008A,2025-03-19T16:06:50.603328,13.09419131,.0002857,87.8620,144.4872,114.4762,245.6663,0,U,45131,999,24658,-.20908E-2,-.707E-5,0
ONEWEB-0017,2020-008B,2025-03-19T16:08:33.371808,13.10369647,.0001894,87.8836,126.8843,89.6849,270.4495,0,U,45132,999,24842,.51902E-3,.194E-5,0
ONEWEB-0020,2020-008C,2025-03-19T15:25:31.641312,13.10377069,.0001741,87.8844,126.8744,100.3520,259.7803,0,U,45133,999,24881,.76903E-3,.281E-5,0
ONEWEB-0021,2020-008D,2025-03-19T15:47:03.423264,13.10373043,.0002105,87.8843,126.8999,96.8444,263.2922,0,U,45134,999,24912,.18627E-2,.663E-5,0

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