Same leap. Different world.

A controlled physics experiment

Both jumpers start with the same upward speed, mass, frontal area and drag coefficient. This compares equal launch speeds, not equal muscular effort. Feet begin and land at height zero. The displayed height is displacement from launch, not body height.

We integrate vertical motion using fourth-order Runge–Kutta at 240 steps per second, locating the apex and ground contact within a step. Gravity decreases with height as g(h) = g₀[R/(R+h)]². Air density follows ρ(h) = ρ₀ exp(−h/H). Drag opposes motion: F = −½ρ Cᴅ A v|v|. Buoyancy is ρ V g, with displaced volume V = 0.08 m³ for the jumper, or 0.00724 m³ for a 24 cm ball. Vacuum mode removes both drag and buoyancy on both worlds.

This is a point-mass model with a fixed posture, still air, a level landing surface, and no propulsion after launch. The 1.8 m astronaut is a scale reference, not a modeled spacesuit. Temperature and pressure are contextual facts. They do not model human survival, suit deformation, winds or biomechanics. Venus is a thought experiment. Gas and ice giants use an imaginary platform and force vacuum physics on both worlds. Their rounded effective gravity is a local approximation at the one-bar level, including rotation in the reference value; inverse-square scaling is approximate away from that level.

Earth uses standard gravity 9.80665 m/s² and representative surface density 1.217 kg/m³. Other gravity references are Moon 1.62, Mercury 3.70, Mars 3.73 and Venus 8.87 m/s². Mars density is uncertain (0.016 ± 0.006 kg/m³); Venus density is approximately 65 kg/m³. Local gravity, weather and posture vary, so extra solver precision does not imply an exact prediction for every real jump.

Landscapes are illustrative. The two foreground rulers and avatars share a physical scale; distant terrain uses artistic perspective. Animation uses real seconds. Pause or scrub to inspect it. Reduced motion shows the selected world at its apex.

Additional moon mass and radius data: NASA Jovian satellites and Saturnian satellites. Planet reference table. Reference data: NASA Earth · Moon · Mars · Mercury · Venus.