A spacecraft is in a circular orbit close to Earth's surface. The additional speed required to escape Earth's gravity is, for g = 10 m s⁻² and R = 6400 km:
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A spacecraft is in a circular orbit close to Earth's surface. The additional speed required to escape Earth's gravity is, for g = 10 m s⁻² and R = 6400 km:

G1 Physics · Accepted Answer

Near Earth's surface, orbital speed v₀ = √(GM/R) = √(gR) = √(10×6.4×10⁶) = 8 km s⁻¹. Escape speed v(e) = √2 v₀. Additional speed Δv = v(e) - v₀ = 8(√2-1) km s⁻¹.