Orbits & Escape Velocity
Launch a rocket — crash, orbit, or escape. Builds on Universal Gravitation.
A rocket is launched from Earth's surface at exactly escape velocity (11.2 km/s). It flies straight up without any further thrust.
How fast is it traveling when it's infinitely far from Earth?
Zero! Escape velocity is defined as the speed where ALL kinetic energy exactly converts to potential energy: ½mv² = GMm/R. At infinity, PE = 0 and KE = 0. Go any slower and gravity wins. Go any faster and you arrive at infinity with leftover speed.
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Launch rockets at different speeds. Below escape velocity — they fall back. At escape velocity — they just barely get away. Above — they fly free!
v_esc = √(2GM/R)
Escape velocity = √2 × orbital velocity. To orbit Earth you need 7.9 km/s. To escape, you need 11.2 km/s = 7.9 × √2. Just 41% more speed, but it takes you to infinity!
Apollo spacecraft reached 10.8 km/s — less than escape velocity! They didn't need to escape Earth entirely, just reach the Moon's gravitational influence (about 380,000 km away).
To leave the Solar System, you need 42 km/s relative to the Sun. Voyager 1 achieved this using gravity assists from Jupiter and Saturn — it's now in interstellar space.
A black hole's escape velocity at the event horizon equals the speed of light — 300,000 km/s. Since nothing can exceed c, nothing escapes. That's what 'black' means.
“Orbit vs escape is a question of energy, not direction. It doesn't matter which way you throw — only how fast. Below escape velocity, you're bound. Above it, you're free.”
Launch Pad
Launch rockets from different planets. Compare escape velocities and see how gravity wells differ across the solar system.
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Launch from the Moon (v_esc = 2.4 km/s) vs Jupiter (v_esc = 59.5 km/s). Jupiter's gravity well is 25× deeper! Then try to orbit vs escape at each planet.
Escape velocity depends only on mass and radius: v_esc = √(2GM/R). Earth, Moon, Jupiter — same formula, wildly different results.