Cosmic Velocity - First to Velocity of Sound in Pure Water

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.

The speed of sound in pure water at 20°C is approximately 1,482.7 m/s, significantly faster than in air due to water's higher density and bulk modulus.

Depends on water temperature, salinity, and pressure. At 20°C, pure water: ~1,483 m/s. Varies with depth and location.

To km/h: × 3.6. To ft/s: × 3.281. 1,483 m/s = 5,339 km/h = 3,317 mph.

Sonar (submarine detection, fish finding), ultrasound imaging, underwater communication, and oceanographic measurements.

Sound in water travels ~4.3× faster than in air. Whales can communicate over hundreds of km using this. SOFAR channel enables even longer distances.

Assuming sound speed in water equals sound in air — it's much faster. Also, forgetting temperature dependence.

~1,500 m/s in water (rule of thumb). 4–5× faster than in air. Increases with temperature, salinity, and depth.