gen-define-escape-velocity-and-give-one-short-worked-example-4c3f

Define escape velocity and give one short worked example.

# Escape Velocity **Definition:** Escape velocity is the minimum speed an object needs to escape the gravitational pull of a celestial body without any further propulsion, reaching an infinite distance with zero final velocity. The formula is: $$v_{esc} = \sqrt{\frac{2GM}{r}}$$ where: - G = gravitational constant (6.67 × 10⁻¹¹ N·m²/kg²) - M = mass of the celestial body - r = distance from the center of the body ## Worked Example **Find the escape velocity from Earth's surface.** Given: - M = 5.97 × 10²⁴ kg - r = 6.37 × 10⁶ m (Earth's radius) $$v_{esc} = \sqrt{\frac{2(6.67 \times 10^{-11})(5.97 \times 10^{24})}{6.37 \times 10^6}}$$ $$v_{esc} = \sqrt{\frac{7.96 \times 10^{14}}{6.37 \times 10^6}}$$ $$v_{esc} = \sqrt{1.25 \times 10^8}$$ $$v_{esc} = 11,200 \text{ m/s} = \textbf{11.2 km/s}$$ This is approximately **25,000 mph** – the speed needed for a rocket to leave Earth without further thrust.