Calculate the escape velocity from the surface of Mars, taking GM = 4.25×10¹³ m³/s² and the planet's radius R = 3.4×10⁶ m.

Gravity Challenge #3 — Escape Velocity

The escape velocity
of Mars.

Gravity Hard

Problem

Calculate the escape velocity from the surface of Mars. Take \( GM = 4.25 \times 10^{13}\ \mathrm{m^3/s^2} \) and the planet’s radius \( R = 3.4 \times 10^6\ \mathrm{m} \).

Mars GM\( 4.25 \times 10^{13}\ \mathrm{m^3/s^2} \)
Mars radius\( R = 3.4 \times 10^6\ \mathrm{m} \)
Answer inm/s

Escape means reaching infinity with nothing to spare — zero speed, zero energy.

Hint: give the rocket just enough kinetic energy to pay off its gravitational debt: \( \tfrac{1}{2}mv^2 = \tfrac{GMm}{R} \). The rocket’s own mass cancels.

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The escape velocityof Mars.

Problem

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The escape velocity
of Mars.