Gravity Well Simulator

Fixed-source sandbox: compare trajectories by changing the configuration

Single-source orbit mode explores one particle's trajectory and energy from its initial radius and velocity. The fixed-source sandbox lets you place sources and compare the forces on multiple test particles. Both are planar softened-force models, not simulations of general relativity or of a real solar system, binary star or galaxy.

An example to try first

Select Single-source circular orbits to place a fixed source of mass 200 at the centre and five particles at radii 80, 120, 160, 200 and 250. At the default G=1, their tangential speeds are $v_c=\sqrt{200r/(r^2+100)}$. The particle at radius 200 starts at approximately 0.998752 model speed. Play the simulation and check whether its radius remains nearly constant.

Pause and change G: source positions and particle velocities are retained, but the gravitational force changes. The previous circular-orbit condition therefore no longer applies. Select the preset again to rebuild its initial configuration with circular speeds for the current G. Do not compare energies before and after changing G as the same system's conserved quantity.

In Two fixed sources and Two-source particle groups, only the test particles move. The sources receive no reaction force from particles and do not move relative to one another. Two-source particle groups is not a galaxy-collision calculation.

Controls and interpreting the results

Click or tap an empty position to add a source with the selected mass; drag a source to move it. On a desktop, right-click a source to remove it individually. On mobile, Remove sources clears all sources so you can rebuild the configuration. Add particles adds 30 particles. Grid density changes the drawing only, not the force or integration time step.

Total particle KE is $\sum_i |\mathbf v_i|^2/2$, with each test-particle mass set to one. It excludes potential energy and is not conserved on its own. For a particle moving among fixed sources at constant G, with no capture or display-domain stopping, the conserved quantity is kinetic plus potential energy.

Equations, units and stopping conditions

With distance $r_j$ from source $j$ and outward unit vector $\hat{\mathbf r}_j$, acceleration and potential per unit mass are given below. Particle motion, force vectors and grid depth use the same model. Grid depth is capped for readability; it is not a calculation of spacetime curvature.

The softening length is fixed at $s=10$ in sandbox mode and $s=18$ in single-source mode. Although the acceleration has the same form, softening lengths and input definitions differ, so the displayed numbers are not interchangeable without checking these conditions. Distance, speed, mass and time use model units, with no defined conversion to m, km/s or kg. The sandbox uses RK4 with a maximum step of 0.03 model time, reduced further near a source.

Each source has a capture radius of $1.5(4+0.55\sqrt{m_j})$. A captured particle stops being calculated; post-collision motion and mass merging are not simulated. Particles farther than 4000 from the origin stop as a display-domain condition, not an energy-based escape classification. Safety limits are 128 sources and 2048 particles.

The visible domain runs from −360 to 360 on each axis, but particles do not bounce at its edges and their speeds are not capped. They continue to be calculated outside the picture up to the stopping radius. Resizing the display does not change world positions or velocities. Shared links save current sources, active particle states and display settings and restore them paused. Trail history, elapsed time and captured particles are excluded.