Escape Velocity Calculator
Calculate the minimum velocity needed to escape gravitational pull of celestial bodies
Calculate Escape Velocity
Our home planet
1 Earth mass = 5.972×10²⁴ kg
1 Earth radius = 6.371×10⁶ m
Escape Velocity Results
Additional Parameters
Comparison to Earth
Escape Velocity Formula: v = √(2GM/R)
First Cosmic Velocity Formula: v = √(GM/R)
Calculation: √(2 × 6.674e-11 × 5.972e+24 / 6.371e+6) = 11186 m/s
Velocity Category: Moderate escape velocity - terrestrial planet
Solar System Escape Velocities
Example: Earth's Escape Velocity
Given Parameters
Mass: 5.972×10²⁴ kg
Radius: 6.371×10⁶ m
G: 6.674×10⁻¹¹ m³/kg⋅s²
Calculation
v = √(2GM/R)
v = √(2 × 6.674×10⁻¹¹ × 5.972×10²⁴ / 6.371×10⁶)
v = √(7.968×10¹⁴ / 6.371×10⁶)
v = √(1.251×10⁸)
v = 11,186 m/s ≈ 11.2 km/s
Cosmic Velocities
First Cosmic Velocity
Minimum speed for circular orbit
Second Cosmic Velocity
Escape velocity from surface
Third Cosmic Velocity
Escape from Solar System (42.1 km/s)
Fourth Cosmic Velocity
Escape from Milky Way (~550 km/s)
Physics Facts
Escape velocity is independent of object mass
Earth's escape velocity is 25,020 mph
Jupiter has highest planetary escape velocity
Black holes have escape velocity = speed of light
Escape velocity = √2 × orbital velocity
Understanding Escape Velocity
What is Escape Velocity?
Escape velocity is the minimum speed needed for an object to break free from a celestial body's gravitational pull without further propulsion. It's the speed at which kinetic energy equals gravitational potential energy.
Conservation of Energy
The escape velocity formula derives from energy conservation. At escape velocity, total energy (kinetic + potential) equals zero, meaning the object just barely escapes with zero velocity at infinite distance.
Independence from Mass
Remarkably, escape velocity doesn't depend on the escaping object's mass. A feather and a spacecraft need the same velocity to escape Earth's gravity (ignoring atmospheric resistance).
Escape Velocity Formula
v = √(2GM/R)
- v: Escape velocity (m/s)
- G: Gravitational constant (6.674×10⁻¹¹ m³/kg⋅s²)
- M: Mass of celestial body (kg)
- R: Radius of celestial body (m)
First Cosmic Velocity
v₁ = √(GM/R) = v_escape/√2
The first cosmic velocity is the minimum speed for circular orbit. It's exactly 1/√2 ≈ 0.707 times the escape velocity. This is the velocity needed for satellites to orbit without falling back to the surface.
Energy at Launch
- • Kinetic energy: ½mv²
- • Potential energy: -GMm/R
- • Total energy: KE + PE = 0
- • Object barely escapes
- • Final velocity approaches zero
- • Maximum possible distance: infinity
Space Applications
- • Rocket launch calculations
- • Interplanetary mission planning
- • Satellite deployment
- • Space probe trajectories
- • Gravitational slingshot maneuvers
- • Asteroid deflection missions
Practical Considerations
- • Atmospheric drag effects
- • Fuel mass requirements
- • Multi-stage rocket design
- • Launch window optimization
- • Earth's rotation assistance
- • Gravitational assist trajectories