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Escape velocity

Escape Velocity in the solar system

 Automatic translation  Automatic translation Updated May 04, 2014

Gravitas (depth of character) was one of the Roman virtues, with Pietas (duty, devotion), Dignitas (charisma, self-esteem) and Virtus (moral excellence). The opposite of virtue is vice.
But in astronomy, gravity is a term which dates from the Middle Ages and used by Isaac Newton to speak of gravity exerted on any mass nearby. It is the force of the gravitational field that holds us to the surface of the Earth. In fact it makes us fall continuously towards the center of the Earth, but we are retained by the solid surface of our planet. Gravitation is universal, it acts at a great distance in all directions, on all objects with mass, in other words it is a force invisible and universal attraction of matter directly related to its mass.
This concept is fundamental to astronomy because it explains all the trajectories of space orbits.
But how a body can escape from the attraction of another body?
The escape velocity allows a body to escape definitively of the gravitational attraction of another body, this speed depends on the mass and radius of the star. On a tiny body like Deimos,  the moon of Mars, whose dimensions are 7.8 × 6.0 × 5.1 km, it is sufficient to run at 20 km / h (5.556 m/s) to leave the ground and definitively escape Deimos. But the Earth has a mass of 5.972E24 kg and a radius of 6371 km, the escape velocity is more difficult to achieve, it is 11,186 km/s or 40,270 km/h. On a more massive or smaller than Earth planet, the release rate will be even more difficult to achieve.
For example, the Sun is 333,000 times more massive and 109 times larger than Earth. The release rate of the Sun is ≈ 617 km/s.

Bodies Mass
Mercury0.0552440 4.25
Venus0.8156052 10.36
Earth16371 11.18
Moon0.01231737 2.38
Mars0.1073389 5.02
Ceres0.00015476 1.85
Jupiter317.869911 59.5
Saturn95.1558232 35.5
Uranus14.5325362 21.3
Neptune17.1424622 23.5
Soleil333000696342 617.7
Sirius B3350005850 5200
Neutron star100000010 200000

Table: Escape velocities of the planets and stars.

NB: For galaxies, the escape velocity depends on the mass of the galaxy but especially the distance to the center of the galaxy, yet the mass distribution of galaxies is still very uncertain. The center of our galaxy harbors a black hole, the escape velocity is greater than the speed of light (300,000 km/s). At the periphery of the galaxy escape velocity remains high (several hundred km/s) because of the presence of dark matter.
 escape velocity

Image: Earth has a mass 5.972E24 kg and a radius of 6371 km, its release or minimum escape velocity is 11,186 km/s or 40,270 km/h. The minimum escape velocity is also known as the second cosmic velocity, it corresponds to the escape velocity of a body moving away definitely from the Earth. The first cosmic speed is the minimum escape velocity (7.9 km/s) to bring a machine in low orbit (<2,000 km). The third cosmic velocity is the escape velocity to bring a machine outside the solar system (42.1 km/s) from Earth orbit.

Escape velocity of the stars


Much of stars in the Galaxy have a speed of escape or release of a few hundred kilometers per second.
If we want to measure much larger escape velocity, we must be observe white dwarfs, as a white dwarf of 1 solar mass has a radius of the order of that of the Earth. So a machine placed on the surface will have much difficulties to escape, the escape velocity at the surface of white dwarfs is a few thousand kilometers per second, as Sirius B (5200 km/s).
In neutron stars, the escape velocity are even higher. Indeed neutron stars are very small and very dense. They concentrate the mass of a star like the Sun within a radius of about 10 km. As the radius is very small, gravity field at the surface is much higher and it is even more difficult to escape. The escape velocity can reach to 200,000 km/s, or 66% of the speed of light.
But it is with black holes that we reach the limit of the escape velocity that is that of light. Black holes are massive objects whose gravitational field is so intense that it prevents any form of matter or radiation to escape. The black holes theory stipulates that objects are so dense that their escape velocity is greater than the speed of light (300,000 m/s).
Black holes are described by the theory of general relativity. When the heart of the dead star is too massive to become a neutron star, it shrinks inexorably to form this astronomical object invisible.


NB: White dwarfs are stars off residues. This is the penultimate phase of the evolution of stars whose mass is between 0.3 and 1.4 times that of the Sun. The density of a white dwarf is very high. A white dwarf of 1 solar mass has a radius of the order of that of the Earth. The diameter of the white dwarf does not depend on temperature, but its mass, more its mass is hight, more its diameter is small. However, there is a value above which a white dwarf can exist is the Chandrasekhar limit. Beyond this mass, the pressure due to electrons is insufficient to compensate the gravity and the star continues its contraction to become a neutron star.

NB: Neutron stars are very small but very dense objects. They concentrate the mass of a star like the Sun, within a radius of about 10 km. These are the  remains of very massive stars more than ten solar masses. When a massive star reaches the end of its existence, it collapses on itself, producing an impressive explosion called a supernova. This explosion scatters huge amounts of matter in space but savings the dense heart of the star. This heart is contracting further and is transformed largely a gigantic nucleus of neutrons.

 black hole and escape velocity

Image: Considered from the 18th century, the theory supporting the existence of black holes, stipulates that it is an objects so dense that its escape velocity exceeds the speed of light. As light can not overcome their gravitational surface and remains trapped, they were naturally called "black holes". This disturbing feature from the terms "black" but the more accurate term would probably "invisible" because it is indeed a total absence of light. The theory also defines precisely the gravitational field of a black hole. It is such that no particle crossing its horizon, theoretical border, can not escape. Credit image: V. Beckmann (NASA's GSFC) et al., ESA.

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