Cosmic Velocity - Second to Cosmic Velocity - Third

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.

The third cosmic velocity is approximately 16,700 m/s (16.7 km/s), the minimum speed to escape the Sun's gravity from Earth's orbital position.

v₃ = √(v_sun² - v_Earth²) where v_sun is solar escape velocity from Earth's orbit. Approximately 16.7 km/s relative to Earth.

To km/h: × 3,600. To mph: × 37,282. 16.7 km/s = 60,120 km/h = 37,344 mph.

Voyager missions, future interstellar probes, and calculations for leaving the solar system.

Voyager 1: ~17 km/s relative to Sun (achieved via Jupiter gravity assist). Parker Solar Probe: 163 km/s peak (but toward Sun, not away).

Thinking Voyager was launched at 16.7 km/s — it used gravity assists. Also, confusing with speed needed to escape from Sun's surface (618 km/s).

~17 km/s to leave the solar system from Earth's orbit. Voyagers achieved this with gravity assists from planets.