Escape velocity

In physics, escape velocity is the minimum speed needed for an object to escape from a massive body, in the sense of becoming neither on the surface nor in closed orbit of any radius no matter how great, without the aid of thrust, or suffering the resistance from friction. The escape velocity from Earth is about 11.186 km/s (6.951 mi/s; 40,270 km/h; 25,020 mph) at the surface. More generally, escape velocity is the speed at which the sum of an object's kinetic energy and its gravitational potential energy is equal to zero. With escape velocity in a direction pointing away from the ground of a massive body, the object will move away from the body, slowing forever and approaching but never reaching zero speed. Once escape velocity is achieved, no further impulse need be applied for it to continue in its escape. In other words, if given escape velocity, the object will move away from the other body, continually slowing and will asymptotically approach zero speed as the object's distance approaches infinity, never to return.

For a spherically symmetric massive body such as a star or planet, the escape velocity for that body, at a given distance is calculated by the formula

where G is the universal gravitational constant (G = 6.67×10⁻¹¹ m³ kg⁻¹ s⁻²), M the mass of the body to be escaped, and r the distance from the center of mass of the body to the object. The relation is independent of the mass of the object escaping the mass body M. Conversely, a body that falls under the force of gravitational attraction of mass M from infinity, starting with zero velocity, will strike the mass with a velocity equal to its escape velocity.

When given a speed ${\displaystyle V}$ greater than the escape speed ${\displaystyle v_{e},}$ the object will asymptotically approach the hyperbolic excess speed ${\displaystyle v_{\infty },}$ satisfying the equation:

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