|
In physics, escape velocity is the minimum speed needed for an object to "break free" from the gravitational attraction of a massive body. The escape velocity from Earth is about 40,270 km/h (25,020 mph). 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.〔The gravitational potential energy is negative since gravity is an attractive force and the potential energy has been defined for this purpose to be zero at infinite distance from the centre of gravity.〕 At escape velocity the object will move away forever from the massive body, without additional acceleration (like propulsion) 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 : 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.〔The value ''GM'' is called the standard gravitational parameter, or ''μ'', and is often known more accurately than either ''G'' or ''M'' separately.〕 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. A rocket moving out of a gravity well does not actually need to attain escape velocity to escape, but could achieve the same result (escape) at any speed with a suitable mode of propulsion and sufficient propellant to provide the accelerating force on the object to escape. Escape velocity is only required to send a ballistic object on a trajectory that will allow the object to escape the gravity well of the mass ''M''. The term ''escape velocity'' is actually a misnomer, and it is more accurately referred to as ''escape speed'' since the necessary speed is a scalar quantity (not a vector quantity) which is independent of direction (assuming a non-rotating planet and ignoring atmospheric friction or relativistic effects). ==Overview== A barycentric velocity is a velocity of one body relative to the center of mass of a system of bodies. A relative velocity is the velocity of one body with respect to another. Relative escape velocity is defined only in systems with two bodies. For systems of two bodies the term "escape velocity" is ambiguous, but it is usually intended to mean the barycentric escape velocity of the less massive body. In gravitational fields "escape velocity" refers to the escape velocity of zero mass test particles relative to the barycenter of the masses generating the field. The existence of escape velocity is a consequence of conservation of energy. For an object with a given total energy, which is moving subject to conservative forces (such as a static gravity field) it is only possible for the object to reach combinations of places and speeds which have that total energy; and places which have a higher potential energy than this cannot be reached at all. For a given gravitational potential energy at a given position, the escape velocity is the minimum speed an object without propulsion needs to be able to "escape" from the gravity (i.e. so that gravity will never manage to pull it back). For the sake of simplicity, unless stated otherwise, we will assume that an object is attempting to escape from a uniform spherical planet by moving directly away from it (along a radial line away from the center of the planet) and that the only significant force acting on the moving object is the planet's gravity. Escape velocity is actually a speed (not a velocity) because it does not specify a direction: no matter what the direction of travel is, the object can escape the gravitational field (provided its path does not intersect the planet). The simplest way of deriving the formula for escape velocity is to use conservation of energy. Imagine that a spaceship of mass ''m'' is at a distance ''r'' from the center of mass of the planet, whose mass is ''M''. Its initial speed is equal to its escape velocity, . At its final state, it will be an infinite distance away from the planet, and its speed will be negligibly small and assumed to be 0. Kinetic energy ''K'' and gravitational potential energy ''U''g are the only types of energy that we will deal with, so by the conservation of energy, : ''K''''ƒ'' = 0 because final velocity is zero, and ''U''gƒ = 0 because its final distance is infinity, so : : Defined a little more formally, "escape velocity" is the initial speed required to go from an initial point in a gravitational potential field to infinity and end at infinity with a residual speed of zero, without any additional acceleration. All speeds and velocities measured with respect to the field. Additionally, the escape velocity at a point in space is equal to the speed that an object would have if it started at rest from an infinite distance and was pulled by gravity to that point. 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 kilometers per second (~6.96 mi/s), which is approximately 33 times the speed of sound (Mach 33) and several times the muzzle velocity of a rifle bullet (up to 1.7 km/s). However, at 9,000 km altitude in "space", it is slightly less than 7.1 km/s. The escape velocity ''relative to the surface'' of a rotating body depends on direction in which the escaping body travels. For example, as the Earth's rotational velocity is 465 m/s at the equator, a rocket launched tangentially from the Earth's equator to the east requires an initial velocity of about 10.735 km/s ''relative to Earth'' to escape whereas a rocket launched tangentially from the Earth's equator to the west requires an initial velocity of about 11.665 km/s ''relative to Earth''. The surface velocity decreases with the cosine of the geographic latitude, so space launch facilities are often located as close to the equator as feasible, e.g. the American Cape Canaveral (latitude 28°28' N) and the French Guiana Space Centre (latitude 5°14' N). The barycentric escape velocity is independent of the mass of the escaping object. It does not matter if the mass is 1 kg or 1,000 kg, what differs is the amount of energy required. For an object of mass the energy required to escape the Earth's gravitational field is ''GMm / r'', a function of the object's mass (where ''r'' is the radius of the Earth, ''G'' is the gravitational constant, and ''M'' is the mass of the Earth, ''M''=5.9736×1024 kg). For a mass equal to a Saturn V rocket, the escape velocity relative to the launch pad is 253.5 am/s (8 nanometers per year) faster than the escape velocity relative to the mutual center of mass. When the mass reaches the Andromeda Galaxy, Earth will have recoiled 500 m away from the mutual center of mass. Ignoring all factors other than the gravitational force between the body and the object, an object projected vertically from the surface of a spherical body will attain a maximum height of , where is the ratio between the original speed and escape velocity, and is the radius of the body. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Escape velocity」の詳細全文を読む スポンサード リンク
|