Escape Velocity

Because escape velocity comes from setting kinetic energy (½mv²) equal to gravitational potential energy (GMm/R) and solving for v -- the escaping object's mass m appears in both terms and cancels out algebraically. Physically, a heavier object has more kinetic energy at a given speed, but gravity also pulls on it harder in exact proportion, so the two effects offset perfectly. This is the same mass-independence that makes all objects fall at the same rate in a vacuum (ignoring air resistance) -- it's a direct consequence of gravitational and inertial mass being equal.

Because surface gravity depends on how close the surface is to the center of mass, not just on total mass. Spreading the same mass over a larger radius moves the surface farther from the center, weakening the gravitational pull felt there and reducing the speed needed to escape from it. This is why radius sits in the denominator, inside a square root, in the escape velocity formula -- and why comparing two bodies of similar mass but very different density (and therefore radius) can produce meaningfully different escape velocities.

It's the theoretical minimum for an object launched with no further propulsion from Earth's surface, ignoring the atmosphere -- not a literal launch requirement. Real rockets burn fuel continuously along a curved ascent trajectory rather than being fired once at 11.2 km/s, and they lose energy to atmospheric drag and to fighting gravity during the slower parts of ascent (gravity losses). 11.2 km/s remains the correct physical benchmark for the total energy an escaping trajectory ultimately needs relative to Earth's surface, even though no real launch reaches it in one instantaneous burst.

The Moon's escape velocity is about 2.4 km/s, less than a quarter of Earth's 11.2 km/s, because both its mass and radius are much smaller than Earth's. Its mass is about 1.2% of Earth's, which alone would push escape velocity down sharply since it depends on the square root of mass, and its smaller radius (about 27% of Earth's) partly offsets that by putting the Moon's surface closer to its own center of mass -- but the mass difference dominates, which is the main reason lunar spacecraft need far less fuel to leave the Moon's surface than Earth's.