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Saturday, October 3, 2015

Escape Velocity

In physics, escape velocity is the minimum speed needed for an object to "break free" from the gravitational attraction of a massive body. More particularly, escape velocity is the velocity (speed traveled away from the starting point) at which the sum of an object's kinetic energy and its gravitational potential energy is equal to zero. At escape velocity the object will move away forever from the massive body, without additional acceleration applied to the object. As the object moves away from the massive body, the object will continually slow and asymptotically approach zero speed as the object's distance approaches infinity.
For a spherically symmetric massive body such as a (non-rotating) star or planet, the escape velocity at a given distance is calculated by the formula
v_e = \sqrt{\frac{2GM}{r}},
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 mass M to the object. Notice that 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.
In this equation atmospheric friction (air drag) is not taken into account.
Source: Wikipedia

In hyperPhysics website you can input some data and it gives the escape velocity:

See the escape velocity of Earth and Mars here:

full computaion here

Listen about escaping probes in this Astronomy Cast:

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