This simulator launches a point satellite tangentially from a chosen altitude above a fixed spherical Earth, governed purely by Newtonian inverse-square gravity in a single orbital plane. Set the launch altitude and the ratio of initial speed to circular speed, then trace the resulting trajectory — circular, elliptical, surface-intersecting or hyperbolic escape — through a numerically integrated propagator.
• A real-time 3D view of spherical Earth with a latitude grid, a satellite bus with antenna and solar wings, a magenta numerical trajectory trail, teal velocity and orange gravitational-acceleration arrows, and a blue reference circle marking the initial orbital radius — with home view, focus-selected-part, auto-rotate, expand and toggleable labels. • Three live controls: initial altitude (300–20,000 km above the spherical surface), initial speed as a ratio to circular speed (0.5–1.6, where 1 = circular and √2 ≈ 1.414 is the escape threshold) and satellite mass (100–2000 kg, which affects gravitational force but not the trajectory). • Twelve live metrics: current altitude, orbital speed, circular speed, escape speed, gravitational force, initial conic eccentricity, specific orbital energy, specific angular momentum, periapsis and apoapsis altitude, bound-conic period and energy drift as a percentage. • A Curves & measurements tab charting altitude/speed and orbital invariants, the full model equations and snapshot measurements. • An Experiments tab with four guided scenarios (circular orbit, elliptical transfer, surface-intersecting path, escape trajectory), a model-verification bench of independent automated checks, and a timestamped event log with a copyable trial report. • A Learn & assess tab with guided lessons, a two-question knowledge-check quiz and a written scope/reference statement.
A satellite is always accelerating toward Earth at a = −μr⃗/|r⃗|³, exactly like anything else in free fall — what makes an orbit different from simply dropping straight down is that enough sideways (tangential) speed curves the fall's path around the planet instead of into it. Circular speed at a given radius is vc = √(μ/r) and escape speed is √(2μ/r); crucially, escape is defined by an energy condition, not by gravitational force ever reaching zero — gravity keeps acting on an escaping satellite the entire time, it just never manages to pull the trajectory back into a closed loop.
Negative specific orbital energy ε = v²/2 − μ/r gives a bound ellipse, zero energy gives the parabolic escape threshold, and positive energy gives an unbound hyperbola. But negative energy alone does not guarantee safety — the surface-intersecting experiment launches too slowly from a low 300 km altitude, and even though the resulting orbit is technically bound (negative energy), its calculated periapsis lies below Earth's surface, so the simulation stops at surface contact rather than completing a full revolution. With only central gravity acting, this two-body model conserves specific orbital energy and angular momentum exactly; the simulator reports numerical energy drift so you can see how closely the Velocity-Verlet integrator holds that conservation.
No. Doubling the satellite mass doubles the gravitational force acting on it, but dividing that force by twice the mass gives the exact same acceleration — so in this ideal two-body model, trajectory shape is completely independent of satellite mass. Mass only changes the displayed force value, never the path.
No. Negative energy only guarantees the orbit is mathematically bound (an ellipse) — it says nothing about whether that ellipse clears the planet. The surface-intersecting experiment shows a bound orbit whose calculated periapsis lies below Earth’s surface, so the simulation stops at surface contact well before completing a revolution.
No. Escape is defined by an energy condition — specific orbital energy reaching zero or above, at escape speed √(2μ/r) — not by gravitational force vanishing. Gravity continues decelerating an escaping satellite the entire time; it simply never has enough time or strength to pull the trajectory back into a closed orbit.
It models a fixed spherical Earth and a point satellite under pure Newtonian two-body gravity in one plane, with no atmospheric drag, Earth oblateness, thrust, lunar perturbation or relativistic effects. The Velocity-Verlet integrator uses time steps of one second or less, runs stop after 48 simulated hours or at 10 initial radii, and apoapsis/period are undefined for unbound (hyperbolic) trajectories — this is an educational propagator, not mission-planning software.