# What is the value of the escape speed

## Escape speed

The escape speed or *Escape speed* is the speed that a body has to reach in order to escape the gravitational field of a mass.

### A little bill

The frame dragging of the means of Newtonian gravitational physics can be done quickly by equating the kinetic energy with the potential energy of a test mass in the gravitational field of a large mass *M.* the escape speed v_{esc} calculate (result on the right). The gravitational field is assumed to be spherically symmetrical and the smaller test mass at location R._{surf}e.g. the surface of the great mass *M.*, localized. G is Newton's gravitational constant with the numerical value 6.672 × 10^{-11} m^{3} kg^{-1} s^{-2} in SI units.

### Examples

The speed of escape from the earth is 11.2 km / s or a good 40,000 km / h. That is quite a decent speed that rockets have to achieve in order, for example, to bring satellites into Earth orbit.

The extreme is a black hole in these considerations: here the escape speed corresponds to the speed of light in a vacuum *c*, a whopping 300,000 km / s or 1.08 billion km / h! According to the special theory of relativity is *c* however, the general top speed. Only light can achieve this 300,000 km / s, but not matter. In other words, not even light can escape a black hole at a critical distance, the event horizon. Therefore, when viewed from the outside, the hole is black.

### further names

The escape speed will too *parabolic speed* called because the escaping body escapes on a parabolic path. Another name for the escape speed is*second cosmic speed*. **Annotation:** The *first cosmic speed* is the minimum speed that a body must have in order to orbit a mass on a circular path; it is less than the escape speed. Upon reaching the *third cosmic speed* the body also leaves the mass, but on a hyperbolic path (therefore also *hyperbolic speed*); it is even greater than the escape speed.

### Limits of Newton's Theory

It should be noted that with such a compact mass as a black hole it cannot be calculated with the means of Newtonian gravitational physics. Here begins the regime of a new theory of gravity, namely Einstein's General Theory of Relativity (GTR). She understands gravitation geometrically as a curved space-time. It is a coincidence that the equation above still produces the correct result, namely the so-called Schwarzschild radius; thus Newton's gravity fails in the analog calculation for the case of a rotating black hole. This is correctly described by the Kerr solution of ART.

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