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Hyperbolic trajectories followed by objects approaching central object (small dot) with same hyperbolic excess velocity (and semi-major axis (=1)) and from same direction but with different impact parameters and eccentricities. The yellow line indeed passes around the central dot, approaching it closely.
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.
The velocity equation for a hyperbolic trajectory is = ... The hyperbolic excess velocity is related to the specific orbital energy or characteristic energy by ...
Thus the hyperbolic excess velocity (the theoretical orbital velocity at infinity) is given by = / However, Voyager 1 does not have enough velocity to leave the Milky Way. The computed speed applies far away from the Sun, but at such a position that the potential energy with respect to the Milky Way as a whole has changed negligibly, and only ...
Hyperbolic trajectories are escape trajectories with excess velocity, and will be covered under Interplanetary flight below. Elliptical orbits are characterized by three elements. [ 9 ] The semi-major axis a is the average of the radius at apoapsis and periapsis : a = r a + r p 2 {\displaystyle a={\frac {r_{a}+r_{p}}{2}}}
Pages for logged out editors learn more. Contributions; Talk; Hyperbolic excess velocity
If the body has a velocity greater than escape velocity then its path will form a hyperbolic trajectory and it will have an excess hyperbolic velocity, equivalent to the extra energy the body has. A relatively small extra delta- v above that needed to accelerate to the escape speed can result in a relatively large speed at infinity.
Hyperbolic trajectory An "orbit" with eccentricity greater than 1. The object's velocity reaches some value in excess of the escape velocity, therefore it will escape the gravitational pull of the Earth and continue to travel infinitely with a velocity (relative to Earth) decelerating to some finite value, known as the hyperbolic excess velocity.