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Escape velocity

2006-01-18 00:00Wikipedia

Escape velocity

In physics, for a given gravitational field and a given position, the escape velocity is the minimum speed an object without propulsion, at that position, needs to have to move away indefinitely from the source of the field, as opposed to falling back or staying in an orbit within a bounded distance from the source. The object is assumed to be influenced by no forces except the gravitational field; in particular there is no propulsion, as by a rocket, there is no friction, as between the object and the Earth's atmosphere (these conditions correspond to freefall) and there is no gravitational radiation. This definition may need modification for the practical problem of two or more sources in some cases. In any case, the object is assumed to be a point with a mass that is negligible compared with that of the source of the field, usually an excellent approximation. It is commonly described as the speed needed to "break free" from a gravitational field.

One somewhat counterintuitive feature of escape velocity is that it is independent of direction, so that "velocity" is a misnomer; it is a scalar quantity and would more accurately be called "escape speed". The simplest way of deriving the formula for escape velocity is to use conservation of energy, thus: in order to escape, an object must have at least as much kinetic energy as the increase of potential energy required to move to infinite height.

Defined a bit more formally, "escape velocity" is the initial speed required to go from an initial point in a gravitational potential field to infinity with a residual velocity of zero, relative to the field. Conversely, an object starting at rest and at infinity, dropping towards the attracting mass, would reach its surface moving at the escape velocity. In common usage, the initial point is on the surface of a planet or moon. On the surface of the Earth the escape velocity is about 11.2 kilometres per second. However, at 9000 km altitude in "space", it is slightly less than 7.1 km/s.

For a body rotating about its axis the escape velocity with respect to the surface does depend on direction e.g., for the Earth the rotational velocity is 465 m/s to the east at the equator, and the escape velocity to the east, with respect to the Earth's surface, is ca. 10.7 km/s.

List of escape velocities

Location with respect to Ve Location with respect to Ve
on the Sun, the Sun's gravity: 617.5 km/s
on Mercury, Mercury's gravity: 4.4 km/s at Mercury, the Sun's gravity: 67.7 km/s
on Venus, Venus' gravity: 10.4 km/s at Venus, the Sun's gravity: 49.5 km/s
at the Earth, the Earth's gravity: 11.2 km/s at the Earth/Moon, the Sun's gravity: 42.1 km/s
on the Moon, the Moon's gravity: 2.4 km/s at the Moon, the Earth's gravity: 1.4 km/s
on Mars, Mars' gravity: 5.0 km/s at Mars, the Sun's gravity: 34.1 km/s
on Jupiter, Jupiter's gravity: 59.5 km/s at Jupiter, the Sun's gravity: 18.5 km/s
on Saturn, Saturn's gravity: 35.5 km/s at Saturn, the Sun's gravity: 13.6 km/s
on Uranus, Uranus' gravity: 21.3 km/s at Uranus, the Sun's gravity: 9.6 km/s
on Neptune, Neptune's gravity: 23.5 km/s at Neptune, the Sun's gravity: 7.7 km/s
on Pluto, Pluto's gravity: 1.3 km/s at Pluto, the Sun's gravity: 6.7 km/s
at the solar system, the Milky Way's gravity: ~1000 km/s

Due to the atmosphere it is not useful and hardly possible to give an object near the surface of the Earth a speed of 11.2 km/s, as these speeds are too far in the hypersonic regime for most practical propulsion systems. For an actual escape orbit a spacecraft is first placed in low Earth orbit and then accelerated to the escape velocity at that altitude, which is a little less, ca. 10.9 km/s. The required extra velocity, however, is less because the spacecraft has already been accelerated to about 8 km/s.

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