Velocity escape

The escape velocity required for gas molecules to overcome the earths gravity and go off to outer space is 1.12 X 103m/s at 15°C Calculate die molar mass of a species with that velocity. Would you expect to find He and H2 molecules in the earth s atmosphere How about argon atoms ... 

The abundance of light elements at high altitude leads to a finite flux of these substances escaping the Earth s gravitational field. This results from a combination of a very long mean free path and a few particles having the requisite escape velocity due to the high-velocity "tail" of the Boltzmann velocity distribution. 

The mass of the object appears on both sides of the equation and thus cancels, hence the escape velocity is an intrinsic property of the star or planet from which you are trying to escape. So the concept of a black hole requires that the escape velocity should be set at the speed of light, the fastest possible velocity and a point at which not even light can escape, hence it must be black. Setting ve = c we can rearrange Equation 4.12 to calculate the radius at which a star or body of known mass will become a black hole ... 

Meteors form when meteoroids enter the atmosphere. The mean orbital velocity of the Earth around the Sun is 29.7 kms-1, so a particle stationary in space will enter the Earth s atmosphere at this velocity. Gravity will further attract the particles up to a maximum of 11 kms-1 (the escape velocity) to make an entry velocity of order 40 kms-1 plus whatever additional velocity the particle may possess. This energy is converted into heat by the drag on the atmosphere, producing temperatures of order 2000 K - the glow seen from a shooting star. The final temperature depends on the properties of the particle, the atmospheric composition and the angle of incidence with the atmosphere. 

Fig. 11.14. Conditions for gas loss from a galaxy, as a function of axial ratio e (e = 1 for a spherical galaxy) and ratio of minimum vertical velocity to escape velocity. After Ferrara and Tolstoy (2000).

FI ox. Fluorine/Oxygen Mixture for Atlas Rockets. A research program of the Lewis Research Center of NASA using this new propellant indicates that the pay load capacity is increased by 90% for 160km high orbits and by 65% for tasks with escape velocity. About 30% fluorine 70% oxygen is taken as a basic mixt... 

When asteroid collisions are especially violent, sufficient kinetic energy may be imparted to launch fragments at greater than escape velocities. In that case, separate asteroids are formed. These fragments share similar orbital characteristics and are referred to as families. The members of most asteroid families share the same spectral characteristics, further linking them together. Families composed of fragments of differentiated asteroids can potentially provide important information on their internal compositions. 

For all comets visited by spacecraft, the measured albedo is <5%, making comet nuclei among the darkest objects in the solar system. This coloration is due to black crusts that cover most of the nuclei. The materials now comprising the crusts were presumably spewed out of the interior at speeds below the escape velocity, so they can be considered lag deposits. The parts of surfaces covered by such deposits are inert, and active areas releasing gas and dust constitute only a small percentage of a comet s total surface area. 

Fig, la The observed relation between terminal velocity vm and photospheric escape velocity v (from Abbott, 1982). esc... 

Fig. 6 The "alternative HR-diagram" of massive star evolution. Upper part Surface escape velocity vs. T . Lower part Terminal veolcity vs. eff The position of observed objects (see Fig. 5) is also shown.

Despite the observational identification of a possible site of dust formation, however, the dust-driven wind could not be applied to stars without dust envelope, as noted in Sect.II. Then, a more interesting possibility is a turbulence-driven wind,in which the high turbulent pressure of the transition layer(or cool corona) pushes the gas out of star,just as the high thermal pressure in corona does in solar-type stars. In fact, if the turbulent zone is extended to about 10 stellar radii, the local escape velocity there may already be small enough to be comparable with the observed flow velocities. Thus, the Maxwellian tail of the turbulent motion in the quasi-static molecular formation zone can directly lead to stellar mass-loss in all... 

During the active mass outflow episode in 1986 June, U Cephei was observed with the IUE (McCluskey, Kondo and Olson 1987) and from ground. The unusual nature of the mass flow is quite evident (1) partical covering, (2) secular and phase-dependent variation, and (3) maximum velocity of some 800 km/s, well in excess of the escape velocity from the binary. 

Liquid escape velocity from the downcomer onto the tray below. 

Escape velocity is defined as the velocity uesc needed for an object on the surface of a planet or satellite to escape its gravitational pull. This means that the total energy (kinetic plus potential, where the potential energy as r —oo vanishes, as in Equation 3.10) is at least zero. 

If the escape velocity of an atom is inversely proportional to a square root of its mass m,k (m) m, and from Equation (2.34) we have... 

This assumes that the initial velocity is below that needed to escape from the influence of the Earth s gravitational field, the so-called escape velocity. 

PROBLEM 2.4.4. Show that the escape velocity vesc from the earth s gravitational field is l.lxl04ms 1. Given the necessary escape kinetic energy (1/2) mv2sc = (3/2) kg T, where kB = 1.3807 x 10 23JK 1 atom-1 is Boltzmann s51 constant, which molecules, at an effective temperature of 30,000 K, can leak out from the earth s atmosphere into space Is this temperature reasonable ... 

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