Escape velocity is the minimum speed an object needs to break free from a celestial body’s gravity without further propulsion, calculated as Ve = √2GM/r , where G is the gravitational constant, M is the body’s mass, and r is the distance from its center. For Earth, it’s about 11.2 km/s (25,000 mph), while the Moon’s is lower (around 2.4 km/s) due to its smaller mass, and larger bodies like Jupiter have much higher escape velocities.
How it works
- Concept: It’s the speed where an object’s kinetic energy equals the gravitational potential energy, allowing it to travel infinitely far away.
- Dependence: It depends on the mass (M) and radius (r) of the celestial body, not the mass of the escaping object.
- Direction: It’s a scalar, meaning the direction doesn’t have to be straight up, but launching from the equator towards the east is easier due to Earth’s rotation.
Examples
- Earth: ~11.2 km/s (25,000 mph).
- Moon: ~2.4 km/s (1.5 miles/second).
- Mars: ~5 km/s (5,000 m/s).
- Jupiter: Much higher than Earth’s due to its immense mass.
Calculation Formula
- Ve = √2GM/r
- G: Gravitational constant (6.674×10-11 N • m2/kg2)
- M: Mass of the planet/body (in kg)
- r: Radius of the planet/body (in meters)
The above information was provided by Gemini.
es·cape ve·loc·i·ty
/əˈskāp vəˌläsədē/
noun: escape velocity
plural noun: escape velocities
the lowest velocity which a body must have in order to escape the gravitational attraction of a particular planet or other object.