Escape Velocity of the Earth

From √(2GM⊕/R) with the mean radius, escape velocity is 11.19 km/s: Mach 33, and exactly √2 times the 7.91 km/s needed merely to circle the planet at the surface. No chemical rocket reaches it in a single impulsive burn; launchers climb gradually while fighting gravity and drag losses, so the real delta-v to escape from the ground is closer to 13–14 km/s. Launching eastward near the equator gets you up to 0.46 km/s of it for free from Earth's rotation, which is why Kourou and Cape Canaveral are where they are.

Escape velocity also governs what an atmosphere can keep. Molecules in the high-temperature exosphere follow a Maxwell–Boltzmann distribution, and any species whose typical thermal speed climbs within about a sixth of escape velocity leaks away over geological time, which is why Earth retains nitrogen, oxygen and water vapour but has lost essentially all of its primordial hydrogen and helium.