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An alternative expression for the escape velocity v e particularly useful at the surface on the body is: = where r is the distance between the center of the body and the point at which escape velocity is being calculated and g is the gravitational acceleration at that distance (i.e., the surface gravity). [11]
"The first 1000-year-old is probably only ~10 years younger than the first 150-year-old."–Aubrey de Grey, 2005 [1]. In the life extension movement, longevity escape velocity (LEV), actuarial escape velocity [2] or biological escape velocity [3] is a hypothetical situation in which one's remaining life expectancy (not life expectancy at birth) is extended longer than the time that is passing.
In astrodynamics, the characteristic energy is a measure of the excess specific energy over that required to just barely escape from a massive body. The units are length 2 time −2, i.e. velocity squared, or energy per mass.
Similarly, a system of particles that eventually all escape each other at exactly the escape velocity will approximate a central configuration in the limit as time tends to infinity. And any system of particles that move under Newtonian gravitation as if they are a rigid body must do so in a central configuration.
One classical thermal escape mechanism is Jeans escape, [1] named after British astronomer Sir James Jeans, who first described this process of atmospheric loss. [2] In a quantity of gas, the average velocity of any one molecule is measured by the gas's temperature, but the velocities of individual molecules change as they collide with one another, gaining and losing kinetic energy.
The blue path in this image is an example of a hyperbolic trajectory. A hyperbolic trajectory is depicted in the bottom-right quadrant of this diagram, where the gravitational potential well of the central mass shows potential energy, and the kinetic energy of the hyperbolic trajectory is shown in red.
One of the best-known examples of an event horizon derives from general relativity's description of a black hole, a celestial object so dense that no nearby matter or radiation can escape its gravitational field. Often, this is described as the boundary within which the black hole's escape velocity is greater than the speed of light.
Here, the total turn is analogous to turning number, but for open curves (an angle covered by velocity vector). The limit case between an ellipse and a hyperbola, when e equals 1 , is parabola. Radial trajectories are classified as elliptic, parabolic, or hyperbolic based on the energy of the orbit, not the eccentricity.