🪐 Escape Velocity Calculator
Calculate the minimum velocity to escape a celestial body's gravitational field
Earth: 5.972 × 10²⁴ kg | Moon: 7.342 × 10²² kg | Mars: 6.39 × 10²³ kg
Earth: 6,371,000 m | Moon: 1,737,000 m | Mars: 3,390,000 m
How to Use This Calculator
Enter Planetary Mass
Input the mass of the celestial body in kilograms. For Earth, use 5.972 × 10²⁴ kg. You can use scientific notation (e.g., 5.972e24).
Enter Planetary Radius
Input the radius of the celestial body in meters. For Earth, use 6,371,000 m (6,371 km). The radius should be measured from the center to the surface.
Calculate and Interpret
Click "Calculate" to get the escape velocity. This is the minimum speed an object needs to escape the gravitational field without further propulsion. Compare to orbital velocity (which is √2 times smaller).
Formula
v = √(2GM/R)
Where:
- v = Escape velocity (m/s)
- G = Gravitational constant = 6.67430 × 10⁻¹¹ m³kg⁻¹s⁻²
- M = Mass of the celestial body (kg)
- R = Radius of the celestial body (m)
Example Calculation: Earth
Given:
- Mass: M = 5.972 × 10²⁴ kg
- Radius: R = 6,371,000 m
- Gravitational constant: G = 6.67430 × 10⁻¹¹ m³kg⁻¹s⁻²
Calculation:
v = √(2GM/R)
v = √(2 × 6.67430×10⁻¹¹ × 5.972×10²⁴ / 6,371,000)
v = √(1.2504×10⁸)
v ≈ 11,186 m/s ≈ 11.2 km/s
Escape Velocities for Common Bodies:
- Earth: 11.2 km/s
- Moon: 2.38 km/s
- Mars: 5.03 km/s
- Jupiter: 59.5 km/s
- Sun: 617.5 km/s
About the Escape Velocity Calculator
The Escape Velocity Calculator determines the minimum velocity an object needs to escape a celestial body's gravitational field without further propulsion. This fundamental concept in orbital mechanics is essential for space mission planning, rocket launches, and understanding why some objects can leave a planet while others cannot.
When to Use This Calculator
- Space Mission Planning: Determine minimum launch velocity for leaving Earth or other planets
- Rocket Design: Calculate fuel requirements for escape trajectories
- Educational Purposes: Understand gravitational physics and orbital mechanics
- Interplanetary Travel: Plan missions to other planets and moons
- Astronomy: Understand why some objects escape planetary systems
Why Use Our Calculator?
- ✅ Accurate Formula: Uses the standard escape velocity equation from physics
- ✅ Works for Any Body: Calculate escape velocity for Earth, Moon, Mars, or any celestial object
- ✅ Quick Results: Instant calculations for mission planning
- ✅ Educational Tool: Learn about gravitational escape and orbital mechanics
- ✅ Free to Use: No registration required
- ✅ Mobile Friendly: Works on all devices
Understanding Escape Velocity
Escape velocity is the minimum speed needed to escape a gravitational field:
- Definition: The velocity at which an object's kinetic energy equals the gravitational potential energy
- Direction: Escape velocity is independent of direction - it's the speed, not the angle
- Comparison to Orbital Velocity: Escape velocity is √2 times the circular orbital velocity at the same distance
- No Propulsion Needed: Once escape velocity is achieved, no further propulsion is needed to escape (in theory)
- Mass Independent: Escape velocity is the same for all objects, regardless of their mass
Physical Derivation
Escape velocity is derived from energy conservation. An object at escape velocity has:
- Kinetic Energy: KE = ½mv²
- Gravitational Potential Energy: PE = -GMm/R (negative because it's bound)
- Total Energy: At escape velocity, total energy = 0 (object can reach infinity with zero velocity)
- Solving: ½mv² - GMm/R = 0 → v = √(2GM/R)
Real-World Applications
- Spacecraft Launches: Rockets must reach escape velocity to leave Earth's orbit
- Satellite Deployment: Understanding escape velocity helps design orbital insertion
- Interplanetary Missions: Calculating escape velocities for different planets
- Atmospheric Escape: Explaining why light gases (hydrogen, helium) escape planetary atmospheres
- Black Holes: At the event horizon, escape velocity equals the speed of light
Tips for Using This Calculator
- Remember that escape velocity is independent of the object's mass - a feather and a spacecraft need the same speed
- Escape velocity decreases with distance - it's easier to escape from higher altitudes
- For real launches, rockets don't reach escape velocity immediately - they accelerate gradually
- Atmospheric drag and other factors mean real escape requires more energy than the theoretical minimum
- Escape velocity is the same regardless of launch direction (though practical launches are usually vertical initially)
Frequently Asked Questions
What is escape velocity?
Escape velocity is the minimum speed an object needs to escape a celestial body's gravitational field without further propulsion. At this velocity, the object's kinetic energy equals the gravitational potential energy, allowing it to reach infinity with zero velocity.
Why is Earth's escape velocity 11.2 km/s?
Earth's escape velocity is calculated from its mass (5.972 × 10²⁴ kg) and radius (6,371 km). Using the formula v = √(2GM/R), this gives approximately 11.2 km/s. This is the speed needed to escape Earth's gravity from the surface.
Does escape velocity depend on the object's mass?
No, escape velocity is independent of the object's mass. Both a small probe and a large spacecraft need the same escape velocity (11.2 km/s for Earth). However, the larger spacecraft needs more energy to reach that velocity because energy = ½mv².
How is escape velocity different from orbital velocity?
Orbital velocity is the speed needed to maintain a circular orbit. For Earth's surface, orbital velocity is about 7.9 km/s. Escape velocity (11.2 km/s) is √2 times larger. Escape velocity allows the object to leave the orbit entirely, while orbital velocity keeps it in orbit.
Can you escape at less than escape velocity?
If you have continuous propulsion, yes. Escape velocity is the minimum speed needed if you stop propelling after reaching that speed. With continuous thrust (like a rocket), you can escape at lower speeds, but you'll need more total energy (fuel) over time.
Why is the Moon's escape velocity so low?
The Moon's escape velocity is only 2.38 km/s because it has much less mass (7.342 × 10²² kg) and a smaller radius (1,737 km) than Earth. Smaller mass means weaker gravity, and smaller radius means you're closer to the center, both contributing to a lower escape velocity.