Escape Velocity Calculator
Calculate escape velocity and circular orbit velocity for planets, moons, and stars. Compare multiple celestial bodies, analyze launch speeds, and estimate kinetic energy requirements.
Ready to Calculate Escape Velocity
Select a celestial body or enter custom mass and radius to compute escape velocity, circular orbit velocity, and energy requirements.
vesc = √(2μ/r) — Escape velocity
vcirc = √(μ/r) — Circular orbit velocity
vesc = √2 × vcirc ≈ 1.414 × vcirc
Understanding Escape Velocity
What is Escape Velocity?
Escape velocity is the minimum speed an object needs to break free from a celestial body's gravitational pull without any additional propulsion. At this speed, the object's kinetic energy exactly equals the gravitational potential energy binding it to the body.
Key insight: Escape velocity depends only on the mass and radius of the celestial body—not on the mass of the escaping object. A feather and a rocket have the same escape velocity from Earth.
The Key Formulas
Escape velocity:
vesc = √(2GM/r) = √(2μ/r)
Circular orbit velocity:
vcirc = √(GM/r) = √(μ/r)
Where: G = gravitational constant, M = body mass, r = distance from center, μ = GM = gravitational parameter
The √2 Relationship
A remarkable fact: escape velocity is always exactly √2 (≈1.414) times the circular orbit velocity at any given altitude:
This means to escape, you need about 41.4% more speed than to orbit. Or equivalently, you need exactly twice the kinetic energy (since KE ∝ v²).
Effect of Altitude
Escape velocity decreases with altitude. The farther you are from a body's center, the easier it is to escape:
- • At Earth's surface: vesc ≈ 11.2 km/s
- • At 400 km (ISS orbit): vesc ≈ 10.9 km/s
- • At Moon's distance: vesc ≈ 1.4 km/s
This is why rockets continue accelerating as they climb—the required velocity keeps dropping.
Solar System Escape Velocities
| Body | vesc | Surface g |
|---|---|---|
| Moon | 2.4 km/s | 1.6 m/s² |
| Mars | 5.0 km/s | 3.7 m/s² |
| Earth | 11.2 km/s | 9.8 m/s² |
| Jupiter | 59.5 km/s | 24.8 m/s² |
| Sun | 617 km/s | 274 m/s² |
Real-World Considerations
The theoretical escape velocity is just the starting point. Real rockets need more delta-v because of:
- Gravity losses: Fighting gravity during ascent
- Atmospheric drag: Air resistance on Earth, Venus, etc.
- Rotation bonus: Launching east from equator saves ~0.5 km/s on Earth
- Trajectory constraints: Real missions rarely launch straight up
Frequently Asked Questions
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