Cosmic Velocity - First to Mach (SI Standard)

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.

Mach (SI standard) uses the speed of sound at 0°C and 1 atm (295.0464 m/s) as the reference, based on SI standard conditions.

Mach (SI) = velocity / 295.0464 m/s. At 0°C, 1 atm: speed of sound ≈ 295 m/s (colder than 20°C).

To m/s (at 0°C): × 295.05. To km/h (at 0°C): × 1,062. To Mach (20°C): × 0.859.

Rarely used in practice. Theoretical aerodynamics at SI conditions, some scientific papers.

Mach 1 (SI) = 295 m/s, while Mach 1 (20°C) = 343.6 m/s. Same Mach number, different actual speeds depending on definition.

Assuming all Mach numbers use the same reference — they don't. Always check temperature and pressure conditions.

Rarely encountered. Mach 1 (SI) = 295 m/s at 0°C. Standard aviation Mach uses different conditions. Know your reference!