**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.

Concept# Hyperbolic trajectory

Summary

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. The name derives from the fact that according to Newtonian theory such an orbit has the shape of a hyperbola. In more technical terms this can be expressed by the condition that the orbital eccentricity is greater than one.
Under simplistic assumptions a body traveling along this trajectory will coast towards infinity, settling to a final excess velocity relative to the central body. Similarly to parabolic trajectories, all hyperbolic trajectories are also escape trajectories. The specific energy of a hyperbolic trajectory orbit is positive.
Planetary flybys, used for gravitational slingshots, can be described within the planet's sphere of influence using hyperbolic trajectories.
Like an elliptical orbit, a hyperbolic trajectory for a given system can be defined (ignoring orientation) by its semi major axis and the eccentricity. However, with a hyperbolic orbit other parameters may be more useful in understanding a body's motion. The following table lists the main parameters describing the path of body following a hyperbolic trajectory around another under standard assumptions and the formula connecting them.
Characteristic energy
The semi major axis () is not immediately visible with an hyperbolic trajectory but can be constructed as it is the distance from periapsis to the point where the two asymptotes cross. Usually, by convention, it is negative, to keep various equations consistent with elliptical orbits.
The semi major axis is directly linked to the specific orbital energy () or characteristic energy of the orbit, and to the velocity the body attains at as the distance tends to infinity, the hyperbolic excess velocity ().
or
where: is the standard gravitational parameter and is characteristic energy, commonly used in planning interplanetary missions
Note that the total energy is positive in the case of a hyperbolic trajectory (whereas it is negative for an elliptical orbit).

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related courses (29)

Related publications (91)

Related people (26)

Related units (3)

Related concepts (20)

Related MOOCs (10)

Ontological neighbourhood

Related lectures (143)

PHYS-100: Advanced physics I (mechanics)

La Physique Générale I (avancée) couvre la mécanique du point et du solide indéformable. Apprendre la mécanique, c'est apprendre à mettre sous forme mathématique un phénomène physique, en modélisant l

PHYS-101(a): General physics : mechanics

Le but du cours de physique générale est de donner à l'étudiant les notions de base nécessaires à la compréhension des phénomènes physiques. L'objectif est atteint lorsque l'étudiant est capable de pr

PHYS-101(e): General physics : mechanics

Le cours "Physique générale" fournit les notions de base nécessaires à la compréhension de phénomènes physiques comme la mécanique du point matériel. L'objectif est atteint lorsque que l'on peut prédi

, , , , , , , , ,

Space Mission Design and Operations

Learn the concepts used in the design of space missions, manned or unmanned, and operations, based on the professional experience of the lecturer.

Space Mission Design and Operations

Learn the concepts used in the design of space missions, manned or unmanned, and operations, based on the professional experience of the lecturer.

Parabolic trajectory

In astrodynamics or celestial mechanics a parabolic trajectory is a Kepler orbit with the eccentricity equal to 1 and is an unbound orbit that is exactly on the border between elliptical and hyperbolic. When moving away from the source it is called an escape orbit, otherwise a capture orbit. It is also sometimes referred to as a C3 = 0 orbit (see Characteristic energy). Under standard assumptions a body traveling along an escape orbit will coast along a parabolic trajectory to infinity, with velocity relative to the central body tending to zero, and therefore will never return.

Elliptic orbit

In astrodynamics or celestial mechanics, an elliptic orbit or elliptical orbit is a Kepler orbit with an eccentricity of less than 1; this includes the special case of a circular orbit, with eccentricity equal to 0. In a stricter sense, it is a Kepler orbit with the eccentricity greater than 0 and less than 1 (thus excluding the circular orbit). In a wider sense, it is a Kepler orbit with negative energy. This includes the radial elliptic orbit, with eccentricity equal to 1.

Orbital eccentricity

In astrodynamics, the orbital eccentricity of an astronomical object is a dimensionless parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is a circular orbit, values between 0 and 1 form an elliptic orbit, 1 is a parabolic escape orbit (or capture orbit), and greater than 1 is a hyperbola. The term derives its name from the parameters of conic sections, as every Kepler orbit is a conic section.

Explores non-Cartesian coordinates, dynamics of a point particle, and motion in three dimensions.

Introduces the fundamentals of advanced physics, emphasizing mechanics and historical developments from Aristotle to Newton.

Covers application exercises with a ball in a loop and analyzes a scenario involving a monkey and a mirror.

, , ,

Planning multicontact motions in a receding horizon fashion requires a value function to guide the planning with respect to the future, e.g., building momentum to traverse large obstacles. Traditionally, the value function is approximated by computing traj ...

, ,

Does gravity affect decision-making? This question comes into sharp focus as plans for interplanetary human space missions solidify. In the framework of Bayesian brain theories, gravity encapsulates a strong prior, anchoring agents to a reference frame via ...

Michael Herzog, Leila Drissi Daoudi - Kleinbauer, Lukas Vogelsang

Integration across space and time is essential for the analysis of motion, low contrast, and many more stimuli. A crucial question is what determines the duration of integration. Based on classical models of decision-making, one might expect that integrati ...

2023