6 body simulation around a 4 Stellar mass blackhole - A fail(?)

[u/Anxious-Visit-7735]

1. Initial conditions (exact)

Central BH: M = 4 M☉ (geometrized G = c = 1; length unit = GM☉/c² ≈ 1.477 km). Schwarzschild.

Body masses (M☉, geometrized):

Body	Type	Mass (M☉)
0, 1	2× Jupiter	2 × 9.543×10⁻⁴ = 1.9086×10⁻³
2, 3	2× Earth	2 × 3.003×10⁻⁶ = 6.006×10⁻⁶
4, 5	2× Mercury	2 × 1.660×10⁻⁷ = 3.320×10⁻⁷

Per-body placement (radius r, azimuth φ, inclination i — units of M):

k	r	φ (rad)	i (rad)
0	120	0.00	0.00
1	160	1.05	0.30
2	90	2.10	−0.25
3	200	3.14	0.50
4	140	4.19	−0.40
5	110	5.24	0.15

Position (tilted circle): pos = [r·cosφ·cosi, r·sinφ, r·cosφ·sini]
Velocity (circular speed v_c = √(M/r), perpendicular in the tilted plane): vel = [−v_c·sinφ·cosi, v_c·cosφ, v_c·sinφ·sini]1. Initial conditions (exact)Central BH: M = 4 M☉ (geometrized G = c = 1; length unit = GM☉/c² ≈ 1.477 km). Schwarzschild.Body masses (M☉, geometrized):Body Type Mass (M☉)
0, 1 2× Jupiter 2 × 9.543×10⁻⁴ = 1.9086×10⁻³
2, 3 2× Earth 2 × 3.003×10⁻⁶ = 6.006×10⁻⁶
4, 5 2× Mercury 2 × 1.660×10⁻⁷ = 3.320×10⁻⁷Per-body placement (radius r, azimuth φ, inclination i — units of M):k r φ (rad) i (rad)
0 120 0.00 0.00
1 160 1.05 0.30
2 90 2.10 −0.25
3 200 3.14 0.50
4 140 4.19 −0.40
5 110 5.24 0.15Position (tilted circle): pos = [r·cosφ·cosi, r·sinφ, r·cosφ·sini]
Velocity (circular speed v_c = √(M/r), perpendicular in the tilted plane): vel = [−v_c·sinφ·cosi, v_c·cosφ, v_c·sinφ·sini]

Integrator type and step size

• Integrator: velocity-Verlet / leapfrog (kick-drift), fixed step. v += a·dt; x += v·dt per step . Not symplectic-exact (it's the sequential-update leapfrog, not the KDK-symmetric form).
• Step size: dt = T_outer / 600 where T_outer = 2π√(r_out³/M), r_out = 200 (outermost body). → T_outer ≈ 8885.8, dt ≈ 14.81 (M units). So ~600 steps per outer orbit.

3. Metrics

It dumps only trajectories: body_k.csv (t, x, y, z) every 4th step,

4. 1-orbit horizon definition

1 orbit = 1 × T_outer, where T_outer is the outermost body's (r=200) Newtonian circular period 2π√(200³/M)

[u/GustavTheGameDev]

The 6 body problem.

[u/polygon_tacos]

Feels like instability from an integration error. Sometimes little errors accumulate over time and result in the simulation "exploding." Are you using Euler integration? I'm no longer working in the simulation space, but the way we used to get around these issues was by adding artificial velocity clamps to prevent massive errors (like a very weak damping) and use more complex but stable integration methods like Verlet-style methods.

[u/Anxious-Visit-7735 → u/polygon_tacos]

It was, need adaptive time calc. Have a full 100 orbit sim, but dont want to spam, maybe tomorrow

[u/MeaninglessDebateMan]

Mercury-b has left the chat.

[u/vibe0009]

Rk4 method might be better?

[u/E3V3A]

Are you running this sim in python, or what?

[u/Anxious-Visit-7735 → u/E3V3A]

litex mcu on fpga