Escape Velocity Calculator (v = √(2GM/r))
Escape Velocity Calculator (v = √(2GM/r))
Escape velocity is the minimum speed an object needs to break free of a celestial body's gravity without further propulsion, derived from setting kinetic energy equal to gravitational potential energy. Enter the mass and radius of any planet, moon, or star, and this calculator computes the escape velocity, shown alongside a graph of how it changes with distance from the body's center.
- v = √(2GM / r), where G is the gravitational constant, M is the body's mass, and r is its radius - for Earth, this gives about 11,186 m/s (11.2 km/s).
- A more massive or more compact body has a higher escape velocity - this is why escaping a black hole is impossible (its escape velocity exceeds the speed of light), while escaping the Moon only requires about 2.4 km/s.
- Escape velocity decreases with distance from the center - the graph shows this inverse-square-root relationship, which is why it's slightly easier to escape from a mountaintop than from sea level.
How do I calculate escape velocity?
Use v = √(2GM/r), where G = 6.674×10⁻¹¹ m³/(kg·s²), M is the mass of the body, and r is the distance from its center (usually its radius).
What is Earth's escape velocity?
Using Earth's mass (5.972×10²⁴ kg) and radius (6,371,000 m): v = √(2×6.674×10⁻¹¹×5.972×10²⁴ / 6,371,000) ≈ 11,186 m/s.
Escape Velocity Calculator (v = √(2GM/r))
Escape velocity is the minimum speed an object needs to break free of a celestial body's gravity without further propulsion, derived from setting kinetic energy equal to gravitational potential energy. Enter the mass and radius of any planet, moon, or star, and this calculator computes the escape velocity, shown alongside a graph of how it changes with distance from the body's center.
- v = √(2GM / r), where G is the gravitational constant, M is the body's mass, and r is its radius - for Earth, this gives about 11,186 m/s (11.2 km/s).
- A more massive or more compact body has a higher escape velocity - this is why escaping a black hole is impossible (its escape velocity exceeds the speed of light), while escaping the Moon only requires about 2.4 km/s.
- Escape velocity decreases with distance from the center - the graph shows this inverse-square-root relationship, which is why it's slightly easier to escape from a mountaintop than from sea level.
How do I calculate escape velocity?
Use v = √(2GM/r), where G = 6.674×10⁻¹¹ m³/(kg·s²), M is the mass of the body, and r is the distance from its center (usually its radius).
What is Earth's escape velocity?
Using Earth's mass (5.972×10²⁴ kg) and radius (6,371,000 m): v = √(2×6.674×10⁻¹¹×5.972×10²⁴ / 6,371,000) ≈ 11,186 m/s.