Formula: $v_e$ = sqrt$\frac{2GM}{R}$ = sqrt(2gR)

For Earth: $v_e$ = sqrt(2 * 9.8 * 6.4 x 10^6) = 11.2 km/s

Key properties:

• Independent of the mass of the projected body
• Independent of the direction of projection (only speed matters)
• $v_e$ = sqrt(2) * $v_{orbital}$ (near surface)
• Depends on the planet's mass and radius

Energy interpretation: \frac{1}{2}$$mv_e^2 = $\frac{GMm}{R}$. The KE must equal the magnitude of gravitational PE at the surface.

From orbit: If a satellite is already in circular orbit at radius r, the escape velocity from that orbit is sqrt(2) times the orbital velocity at r. The additional energy needed = $\frac{GMm}{2r}$.