Question

Calculate the escape velocity needed to launch a rocket from the surface of Mars.

Answer 1

We know, (1/2) * mv² = GMm/r

=> The escape velocity, V_escape = √(2GM_Mars / R_Mars)

The mass of a planet Mars, M_Mars = 6.39 × 10^₂₃ kg

The radius of the planet Mars, R_Mars = 3390 x 10³ m

The universal gravitational constant, G = 6.67 x 10^-11 m³ / (kg. sec²)

V_escape = √(2GM_Mars / R_Mars)

= √[(2 * 6.67 x 10^-11 m³ / (kg. sec²) * (6.39 × 10²³ kg)] / (3390 x 10³ m )

= √ [(85.24 * 10¹² m³/sec² ) / (3390 * 10³ m)]

= √ [(8524 / 3390) * 10⁶] m / sec

= 5.01 x 10³  m/sec

= 5.01 Km/sec