Mach (20°C, 1 atm) to Cosmic Velocity - Second

Mach number is the ratio of an object's speed to the speed of sound in the surrounding medium. Mach 1 at 20°C, 1 atm equals approximately 343.6 m/s (1,235 km/h).

Mach = velocity ÷ speed_of_sound. At 20°C: Mach 1 = 343.6 m/s. Speed of sound = √(γRT/M) where γ = heat capacity ratio.

To m/s (at 20°C): × 343.6. To km/h (at 20°C): × 1,237. Note: changes with altitude and temperature.

Fighter jets (Mach 1.5–2.5), commercial aircraft (Mach 0.8–0.85), space shuttle reentry (Mach 25), and missile speeds.

Concorde: Mach 2.04. SR-71 Blackbird: Mach 3.3. X-15: Mach 6.7. Meteorites enter at Mach 50+. Subsonic <1, supersonic >1, hypersonic >5.

Thinking Mach is constant — it varies with temperature/altitude. At 30,000 ft, Mach 1 ≈ 295 m/s (colder air = slower sound).

Mach 1 = speed of sound. Below Mach 1 = subsonic. Mach 1–5 = supersonic. Above Mach 5 = hypersonic. It's a ratio, not a fixed speed.

The second cosmic velocity (Earth's escape velocity) is approximately 11,200 m/s (11.2 km/s), the minimum speed to escape Earth's gravity completely.

v₂ = √(2GM/r) = √2 × v₁ ≈ 11.2 km/s. Exactly √2 times the first cosmic velocity.

To km/h: × 3,600. To mph: × 25,000. 11.2 km/s = 40,320 km/h = 25,053 mph.

Moon missions, Mars missions, deep space probes (Voyager, New Horizons), and any mission leaving Earth's gravity well.

Apollo missions: ~11.2 km/s. Voyager probes: exceeded v₂ to leave solar system. New Horizons: launched at record 16.26 km/s (fastest ever from Earth).

Thinking you need this speed everywhere — you only need it at launch. In space, much less Δv is needed.

~11 km/s to escape Earth. √2 × orbital velocity. Remember: orbit ≈ 8 km/s, escape ≈ 11 km/s.