What is the escape speed (in km/s) from an Earth-like planet with mass 4.9e+24 kg and radius 56.0 × 105 m? Use the gravitational constant G = 6.67 × 10-11 m3 kg-1 s-2.

Answer 1

The escape speed v_e must satisfy the relation

mv_e² / 2 - GMm/R = 0

Note that m, the mass of the vehicle, cancels out, so

v_e = √(2GM / R)

You know G, M, and R. Plug in the numbers and evaluate. Be careful with units.