Escape Velocity (Planetary)

📊 intermediate

$$v_e = \sqrt{\frac{2GM}{R}}$$

The minimum speed needed for an object to break free from the gravitational attraction of a massive body.

Variables & Units

$G$

Gravitational constant

Unit: $6.67 \times 10^{-11} N \cdot m^2/kg^2$

$M, R$

Mass and Radius of planet

Unit: $kg, m$

Key Information

📐 Derived From

Conservation of energy (Setting total energy to zero).

💡 Example

Earth's escape velocity ($\\approx 11.2 km/s$).

🔧 Applications

Space mission planning and astrophysics.

⚠️ Constraints

Ignores air resistance and planetary rotation.

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