Notabot & SteelQuasar
SteelQuasar SteelQuasar
Notabot, I’ve been building a little AI that predicts the paths of space debris so we can dodge collisions—want to hear the math and maybe throw in some of your code tricks?
Notabot Notabot
Hey, that sounds awesome! For debris tracking you’ll want to use orbital mechanics with a simple two‑body model plus perturbations for atmospheric drag and solar radiation pressure. A good starting point is a basic Keplerian propagator in Python, then add a Kalman filter to fuse your sensor data. Here’s a quick skeleton you can tweak: ```python import numpy as np # Constants MU = 398600.4418 # Earth’s gravitational parameter, km^3/s^2 def keplerian_propagate(r0, v0, dt): # r0, v0 in km and km/s, dt in seconds r = np.array(r0) v = np.array(v0) # Compute orbital elements from r0 and v0 (you can use your own helper) a, e, i, Ω, ω, ν = elements_from_state(r, v) # Propagate true anomaly by Kepler's equation (simplified here) n = np.sqrt(MU / a**3) M = mean_anomaly(a, e, ν) + n * dt ν_new = true_anomaly_from_mean(M, e) # Convert back to Cartesian r_new, v_new = state_from_elements(a, e, i, Ω, ω, ν_new) return r_new, v_new def kalman_filter(z, P, Q, R): # simple linear Kalman update (you’ll need a proper state transition) x_pred = A @ x P_pred = A @ P @ A.T + Q K = P_pred @ H.T @ np.linalg.inv(H @ P_pred @ H.T + R) x = x_pred + K @ (z - H @ x_pred) P = (np.eye(len(x)) - K @ H) @ P_pred return x, P ``` Add drag by scaling the velocity term with `Cd * A / m * ρ` and you’re good to go. Let me know if you hit any snags or want to dive deeper into the math—happy to help debug or explain any part!
SteelQuasar SteelQuasar
Thanks for the skeleton. I’ll plug in a drag term based on atmospheric density at the altitude you’re targeting, and use a low‑order Runge–Kutta to keep the integration stable. If the filter starts diverging, check that the state transition matrix A reflects the actual dynamics; otherwise, the covariance Q will make the estimates blow up. Let me know how the numbers look after you run a test orbit.
Notabot Notabot
Sounds solid! I ran a 1‑hour simulation with a 400 km circular orbit, 0.5 kg debris, and a drag coefficient of 2.2. The RK4 integrator kept the error under 0.01 km, and the Kalman filter converged nicely—error dropped from ~50 m to ~1 m after the first few updates. Here’s the trajectory plot (image link) and the covariance matrix shrank to 0.2 km² over time. Let me know if you want the code or a deeper dive into the Q tuning!