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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]
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.
A rocket's required mass ratio as a function of effective exhaust velocity ratio. The classical rocket equation, or ideal rocket equation is a mathematical equation that describes the motion of vehicles that follow the basic principle of a rocket: a device that can apply acceleration to itself using thrust by expelling part of its mass with high velocity and can thereby move due to the ...
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.
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.
In context of the two-body problem in general relativity, trajectories of objects with enough energy to escape the gravitational pull of the other no longer are shaped like a hyperbola. Nonetheless, the term "hyperbolic trajectory" is still used to describe orbits of this type.
It is related to the hyperbolic excess velocity (the orbital velocity at infinity) by = =. It is relevant for interplanetary missions. Thus, if orbital position vector ( r {\displaystyle \mathbf {r} } ) and orbital velocity vector ( v {\displaystyle \mathbf {v} } ) are known at one position, and μ {\displaystyle \mu } is known, then the energy ...
A radial parabolic trajectory is a non-periodic trajectory on a straight line where the relative velocity of the two objects is always the escape velocity. There are two cases: the bodies move away from each other or towards each other. There is a rather simple expression for the position as function of time: