🚀 Escape Velocity

📖 The Physics

Throw a ball up and it always comes back. So how does a rocket ever leave Earth for good? As it climbs, gravity keeps pulling it back — but gravity also gets weaker with distance.

The escape velocity is the launch speed just big enough that gravity, adding up its pull over the whole (infinite) journey, can never quite bring the rocket to a stop.

v_escape = √(2·g·R) = √(2·G·M / R) (independent of the rocket's mass)

Below 1×v_esc the rocket rises, stops and falls back. At 1× and above it escapes. Notice how much larger Jupiter's escape speed is than the Moon's — that's why small bodies can't hold onto an atmosphere.

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