Escape Velocity: v_e = sqrt(2GM/R) = sqrt(2gR)

• Independent of mass, direction, and angle of projection
• For Earth: 11.2 km/s
• Derived from energy: (1/2)mv_e^2 = GMm/R

Orbital Velocity: v_o = sqrt(GM/r)

• Near surface: v_o = sqrt(gR) ≈ 7.9 km/s
• Decreases with altitude (outer orbits are slower)

Key Relation: v_e = sqrt(2) * v_o (at any altitude)

• To escape from circular orbit, increase speed by factor sqrt(2)
• Additional speed needed: v_o(sqrt(2) - 1) ≈ 0.414*v_o

For a body projected at speed v (v < v_e): Maximum height h = v^2*R/(2gR - v^2) At v = v_e: h -> infinity At v = v_e/2: h = R/3