Cosmic Velocity - First to Millimeter per Second

The first cosmic velocity (escape velocity from Earth's surface to orbit) is approximately 7,900 m/s (7.9 km/s), the minimum speed needed to achieve Earth orbit.

v₁ = √(GM/r) where G is gravitational constant, M is Earth's mass, r is Earth's radius. Approximately 7.9 km/s.

To km/h: × 3,600. To mph: × 17,672. 7.9 km/s = 28,440 km/h = 17,672 mph.

Minimum speed for satellites, space station orbit, and low Earth orbit (LEO) calculations.

ISS orbits at ~7.66 km/s. Below this speed, you fall back to Earth. Above it, you stay in orbit (if horizontal).

Confusing with escape velocity (second cosmic velocity, 11.2 km/s) — orbital velocity is lower.

Remember: ~8 km/s for orbit, ~11 km/s to escape. v₁ is minimum for orbit, not escape.

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.