Move a planet on a solved Kepler ellipse around a focus. Velocity, radius, equal-time swept sectors and an energy comparison update from the same orbital state. Explore why a planet travels faster near periapsis while conserving energy and angular momentum.
• A real-time 3D scene with 5 inspectable parts (Central star at a focus, Kepler ellipse, Planet and velocity arrow, Equal-time swept sector, Kinetic and potential energy indicators), with home view, focus-selected-part, auto-rotate, expand, instrument-cover and hide-labels scene tools, plus a model response curve beneath the scene. • Experiment controls: Semimajor axis (0.5-3 AU); Eccentricity (0-0.8); Central mass (0.5-2 solar masses); Initial mean anomaly (0-360 °); Days per animation second (0-30 days/s); pause/resume, 0.1 s and 1 s single-step buttons, four playback speeds and a restart button. • Live readouts: Orbital radius; Orbital speed; Orbital period; Specific orbital energy; Specific angular momentum; Area swept per day. • A Geometry & measurements tab with a parameter-comparison chart, a live-measurements chart, the model equations and snapshot readouts. • An Experiments tab with 3 guided presets (Circular orbit; Eccentric orbit; Larger orbit) and a Model verification bench that runs independent fresh models, plus a timestamped event log and a copyable trial report. • A Learn & assess tab with guided lessons, a knowledge-check quiz with reset and a written model-scope statement linking to a technical reference.
μ=1.32712440018×10¹¹ × Mstar km³/s²; AU=149597870.7 km M=E−e sinE; n=√(μ/a³); P=2π/n x=a(cosE−e); y=a√(1−e²) sinE v²=μ(2/r−1/a); ε=−μ/(2a); h=√(μa(1−e²)) Swept area rate=h/2
Exact two-body Kepler orbit around a fixed point mass. No planet–planet gravity, precession, relativity or collisions. Bodies are enlarged; orbit geometry preserves shape. Equal-time sector is one twentieth of a period, not a fixed number of days across different systems.
No. A Kepler orbit places the attracting body at a focus.
No. Equal time sweeps equal area; speed changes around the ellipse.
Exact two-body Kepler orbit around a fixed point mass. No planet–planet gravity, precession, relativity or collisions. Bodies are enlarged; orbit geometry preserves shape. Equal-time sector is one twentieth of a period, not a fixed number of days across different systems.