In astrodynamics or celestial mechanics, a hyperbolic trajectory or hyperbolic orbit is the trajectory of any object around a central body with more than enough speed to escape the central object's gravitational pull.

All interplanetary bodies such as comets or asteroids that approach the earth, or any spacecraft we want to send to other planets, must be on a hyperbolic trajectory. Whereas a parabolic trajectory has zero velocity at infinite radius, the hyperbolic trajectory has some non-zero velocity.

Lecture notes on hyperbolic orbits, Lagrange’s equations for hyperbolic orbits, hyperbolic injection velocity, injection from pericenter of a hyperbolic orbit, and out-of-plane injection from pericenter of a hyperbolic orbit.

Hyperbolic Periodic Orbits Definition. A Ck hypersurface in Rn is a pair (ψ,U) in which 1. Uis an open set in Rn−1. 2. ψis a 1-1 Ck map from Uinto Rn. 3. Dψ(x) has rank n−1 at each x∈ U. Given a Ck hypersurface (ψ,U) in Rn and a point p ∈ ψ(U), we let T pψ(U) denote the tangent space to ψ(U) at p. This is an affine hyperplane

For example, non-periodic comets describe hyperbolic orbits around the Sun; they approach the Sun, swing by once, and then move away along their hyperbolic path, to never come back.

You can read more about hyperbolic angles on Brilliant and on Wikipedia. We can relate \(F\) to the true anomaly \(\nu\) by plugging in \(y = r\sin\nu\) , and the orbit equation for \(r\) . We also note that \(b = a\sqrt{e^2 - 1}\) .

Subjects: Hyperbolic orbits. Interplanetary transfer. (1) Hyperbolic orbits The trajectory is still described by p r= , but now we have ε>1, so that the 1+!cos" radius tends to infinity at the asymptotic angle ! " = #$cos$1(1/%). The “parameter” p still has the geometrical significance indicated in the figure, and is therefore a positive ...

A hyperbolic orbit refers to an open curve trajectory with a negative semimajor axis, where the total energy is positive and the eccentricity is greater than unity. It is commonly observed in spacecraft escaping the earth's gravity during interplanetary missions or …

In this lecture, we will consider how to transfer from one orbit, to another or to construct an interplanetary trajectory. One of the assumptions that we shall make is that the velocity changes of the spacecraft, due to the propulsive effects, occur instantaneously.

The hyperbola is the locus of points for which the difference of the distance from the two foci is constant = 2 a. The whole transfer is split into legs described with two-body dynamics. The planets’ sphere of influences are infinitely large in planetary reference frame but points in heliocentric reference frame.