Mechanical & Aerospace
Kepler Orbit Lab
Give a satellite a sideways nudge and gravity does the rest. Launch exactly at the circular speed v_c = √(GM/r) and you get a perfect circle; launch slower or faster and the orbit becomes an ellipse with the central mass at one focus. Keep adding speed and the ellipse grows until, at the escape speed √2·v_c, the path opens into a parabola — and beyond that, a hyperbola that never returns. The trajectory is integrated with a symplectic stepper that conserves orbital energy, so the shapes are faithful, and the readouts show the eccentricity, the specific energy ε (negative = bound, ≥ 0 = escaping) and the live radius and speed — which trade off exactly as the vis-viva equation v² = GM(2/r − 1/a) predicts. It is the whole logic of orbital mechanics in one picture.
Ellipse
Orbit type
0.190
Eccentricity e
2.00
Current radius
0.636
Current speed
0.707
Circular v_c
-0.297
Specific energy ε
The body launches sideways at a fraction of the circular speed v_c = √(GM/r). Exactly 1× gives a circle; below it, an ellipse with the launch point at apoapsis; above it, a bigger ellipse — until 1.41× (escape, √2·v_c) opens the path into a parabola and beyond into a hyperbola. Energy ε < 0 stays bound; ε ≥ 0 escapes.
How to use this simulation
Give a satellite a sideways nudge and gravity does the rest. Launch exactly at the circular speed v_c = √(GM/r) and you get a perfect circle; launch slower or faster and the orbit becomes an ellipse with the central mass at one focus. Keep adding speed and the ellipse grows until, at the escape speed √2·v_c, the path opens into a parabola — and beyond that, a hyperbola that never returns. The trajectory is integrated with a symplectic stepper that conserves orbital energy, so the shapes are faithful, and the readouts show the eccentricity, the specific energy ε (negative = bound, ≥ 0 = escaping) and the live radius and speed — which trade off exactly as the vis-viva equation v² = GM(2/r − 1/a) predicts. It is the whole logic of orbital mechanics in one picture.
Everything runs in your browser — no sign-up, no download. Change a value and the result updates instantly, so you can build a feel for how each input shapes the outcome. It pairs with Crameleon's practice exams and step sheets when you want to go from intuition to working the problems.