Escape Velocity

Launch straight up from the surface and see where the projectile stops. The gold column is the apogee, on a single scale of distance from the centre in radii of the body. Escape velocity is a threshold: half of it buys a third of a radius, 70.7 % of it (the speed of a circular orbit skimming the surface) buys exactly one radius, and at 100 % the apogee runs away to infinity. v_esc = sqrt(2·G·M / r) — the mass of the thing you launch never appears.

Launch speed50.0 %
Body4 worlds
Escape velocity  v_esc = sqrt(2·G·M / r)
11.18 km/s
Launch speed  v = (% / 100) · v_esc
5.592 km/s
Outcome
Falls back
Apogee above the surface  r_max = R / (1 - (v / v_esc)²)
2123 km
Fraction of escape speed
50.0 % of escape
Surface circular orbit
7.909 km/s
Body
Earth
Mass M
5.97e24 kg
Radius R
6370 km
Apogee in body radii
1.333 R
G = 6.674e-11 N·m²/kg² · straight-up launch · no atmosphere, no thrust after release