Cosmic Velocity - Second to Millimeter per Second

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.

Millimeter per second measures distance in millimeters traveled in one second. Used for small-scale movements and precise measurements.

1 mm/s = 0.001 m/s = 0.0036 km/h = 0.06 m/min.

To m/s: ÷ 1,000. To cm/s: ÷ 10. To km/h: × 0.0036.

Vibration measurements (machinery typically 0.1–50 mm/s RMS), small motor speeds, precision linear actuators, and tape/film transport speeds.

Machinery vibration: >10 mm/s indicates problems. Seismic activity: 0.001–100 mm/s. CD/DVD read head: 1.2–1.4 mm/s linear velocity.

Confusing mm/s with cm/s (10× different) or m/s (1000× different).

1,000 mm/s = 1 m/s. Very common in vibration analysis. 10 mm/s RMS is a typical machinery vibration threshold.