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Gravity lab

Three bodies

gravity simulator · 2D / 3D

t = 0.00 E = 0 ΔE/E₀ = 0 |P| = 0 d_min = 0 collisions = 0

Simulation

Speed×1.0

Constant G1.00

Trail length700

Collisions

velocity vectors acceleration vectors centre of mass follow the centre of mass radius ∝ ∛m rotate in 3D

Energy over time

kineticpotentialtotal

Units and method

Dimensionless units: G = 1, mass in m₀, distance in u, time in t. Integrator: leapfrog (kick-drift-kick) with an adaptive step based on the closest pair, softening ε = 10⁻³. The radius determines collisions and the size of the body. Dragging a body holds it in place while it moves, and E₀ is reset after every change.

From the universe to a star

cosmic web · galaxy collisions · star formation

Computing the cosmic web…

Cosmic web

Redshift8.0

Time rate×1.0

Hubble const.

box edges loop

Galaxy collision

Mass ratio1.00

Pericentre5 kpc

Disc 1 tilt60°

Disc 2 tilt−60°

Starburst×1.0

Time rate×1.0

follow the centre of mass

A restricted N-body model in the spirit of Toomre & Toomre (1972): two cores with dark haloes (Plummer potential) attract each other and are slowed by dynamical friction, while the disc stars are test particles. During a close passage the gas is compressed and blue stars are born (a starburst). Units: 10 kpc, 10¹¹ M☉, 1 time unit = 47 million years.

Star formation in a galaxy

Formation efficiency50 %

Pattern speed25

Arm pitch angle14°

Time rate15 Myr/s

Number of arms

old stars gas young stars H II regions

Density wave theory: the spiral pattern rotates more slowly (pattern speed in km/s/kpc) than the stars and gas. Gas is compressed as it passes through an arm and a star forms in it. Its lifetime is ≈ 10 billion yr · M⁻²·⁵, so massive blue stars explode as supernovae while still in the arm and older yellow ones spread across the disc. The rotation curve is flat, 220 km/s.

Main-sequence star

Mass1.00 M☉

Rotation×0.40

spots

Main-sequence relations: R ∝ M⁰·⁸ (below 1 M☉) or M⁰·⁵⁷, L ∝ M³·⁵ and T from L = 4πR²σT⁴. The surface shows convective granulation, the edge of the disc darkens (limb darkening) and the corona is visible as a glow.

Controls

Dragging rotates the view, the right button or Shift + drag pans it. The wheel or two fingers zoom. When you keep zooming at the edge of a scale, you move to the next level: cosmic web → galaxy collision → galaxy → star.

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