Formula: v_e = sqrt(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: (1/2)mv_e^2 = 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 = GMm/(2r).