Galactic Bulge N-Body Orbit Simulator

Galactic Bulge N-Body

Star count 400

Central mass (M☉ ×10⁶) 4.3

Star self-gravity Off

Time step 1.0×

Sim time

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Mean eccentricity

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Total energy E

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Energy drift

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How it works

Every star is a real point mass integrated under Newtonian gravity from the central bulge mass M, and — when self-gravity is on — from every other star too (a true O(N²) N-body sum). Each star's acceleration is the real vector sum a = Σ G·mⱼ·(rⱼ−rᵢ)/|rⱼ−rᵢ|³, not a scripted ellipse. Integration uses velocity-Verlet, a symplectic method that conserves energy far better than plain Euler over long runs — that's why the energy readout stays flat instead of drifting.

a_i = Σ_j  G·m_j·(r_j − r_i) / |r_j − r_i|³
v(t+dt/2) = v(t) + a(t)·dt/2
r(t+dt)   = r(t) + v(t+dt/2)·dt
v(t+dt)   = v(t+dt/2) + a(t+dt)·dt/2
E = Σ ½m|v|²  −  Σ_{i
              
                Central mass — the bulge's dominant point mass (a supermassive black hole plus dense stellar core); heavier means faster, tighter orbits (Kepler's third law).
                Star self-gravity — when on, stars also pull on each other, not just on the centre; watch orbits perturb and precess instead of staying perfectly closed ellipses.
                Mean eccentricity — computed per star from its instantaneous specific energy and angular momentum (e = √(1 + 2·E_spec·L²/(G·M)²)), the same formula used for real orbit determination; the population starts with a realistic spread rather than all-circular.
                Energy drift — total mechanical energy (kinetic + potential) should stay ≈constant; this is a genuine correctness check on the integrator, not a scripted number.
              
              Real-world relevance: this is the same physics (softened point-mass Newtonian N-body + symplectic integration) used in research codes that model the Milky Way's central stellar bulge and its orbits around Sagittarius A*.

Central mass Bulge stars High-eccentricity orbit

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