Simulate planetary orbits with adjustable mass, velocity, and eccentricity. Visualize Kepler laws, transfer orbits, and escape velocity.
Drop a probe beside a central mass, set its speed, and this simulator computes the path under the inverse-square gravity law and draws the orbit. Mass, starting distance, velocity, and eccentricity are adjustable; the tool classifies the result as circular, elliptical, parabolic, or hyperbolic, and reports period, perigee and apogee, and speed along the path. It can also overlay Kepler's equal-area sweep and a Hohmann transfer arc. The common first surprise: the circular speed at a given radius is one exact value. A little faster, the circle stretches into an ellipse; about 1.41 times faster, the probe escapes entirely.
A concrete input and expected output from the current implementation.
Input
Planet: Earth (5.972e24 kg). Release point 7,000 km from the center. Tangential speed 8.0 km/s.
Expected output
Elliptical orbit. Eccentricity 0.12, period about 1 h 58 min. Perigee 7,000 km at the release point, apogee about 8,980 km. For reference: circular speed here is 7.55 km/s and escape speed is 10.67 km/s.
8.0 km/s exceeds the circular speed of 7.55 km/s but stays below the escape speed of 10.67 km/s, so the probe is bound in an ellipse with the release point at perigee. The vis-viva equation determines the semi-major axis and eccentricity; Kepler's third law gives the period.
At each moment of simulated time, the probe's acceleration points toward the central body with magnitude GM/r^2, and the simulator advances the probe's position and velocity from that acceleration, repeating as long as the run continues. The trace left behind is a conic section - a closed ellipse or an open parabola or hyperbola - decided by the speed the probe has at the radius where it starts.
The simulator compares the launch speed with the circular speed sqrt(GM/r) and the escape speed sqrt(2GM/r) at the starting radius: below circular, the ellipse has the start point at apogee; between the two, a normal ellipse; at escape speed, a parabola; above it, a hyperbola. For closed orbits it derives semi-major axis and eccentricity from the vis-viva relation v^2 = GM(2/r - 1/a), and the period from Kepler's third law, T = 2*pi*sqrt(a^3/GM).
That is Kepler's second law: the line from the central body to the probe sweeps out equal areas in equal times. Close in, the radius is short, so the probe must travel a longer arc, and therefore move faster, to sweep the same area each second. The equal-area overlay shows this directly; it is also why comets linger far from the Sun but race past it quickly.
You still get an ellipse, but the start point becomes the apogee and perigee drops closer in - possibly below the planet's surface, in which case the path intersects the body. Whether the simulator stops at impact or lets the trace continue through the planet depends on how it models the central body's surface, so check the visual behavior rather than assuming.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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