F = G·m₁·m₂/r²: Any two point masses attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.
The N-body problem studies the motion of multiple celestial bodies under mutual gravitational attraction. Even with just three bodies, the system can exhibit unpredictable chaotic behavior. This is a classic example in chaos theory.
Chaotic systems are extremely sensitive to initial conditions. In the three-body problem, tiny differences in initial conditions lead to completely different orbital evolutions. This is the famous 'butterfly effect'.
In an isolated system, total energy (kinetic + potential) remains constant. This is an important metric for validating numerical integrator accuracy.
Kepler's laws describe three rules governing planetary motion: elliptical orbits, equal areas swept in equal time, and the square of the period being proportional to the cube of the semi-major axis.
Click and drag to add a small mass body, giving it a tangential velocity. Watch how it orbits around the large mass. Adjust the initial velocity until you achieve a nearly circular orbit.
Select the 'Chaotic Three-Body' preset. Observe the complex motion of three similar-mass bodies. Slightly change one body's initial position and run again to see the huge difference in results.
Select the 'Gravity Assist' preset. Watch how a small body gains speed by approaching a large body. This is how spacecraft use planetary gravity to accelerate toward outer planets.
Create two small bodies orbiting the same central body. Adjust their orbital radii so their periods form a simple integer ratio (like 2:1). Watch how they periodically interact with each other.