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 GraphSearch.
Concept
Radial trajectory
Summary
In astrodynamics and celestial mechanics a radial trajectory is a Kepler orbit with zero angular momentum. Two objects in a radial trajectory move directly towards or away from each other in a straight line.
There are three types of radial trajectories (orbits).
Radial elliptic trajectory: an orbit corresponding to the part of a degenerate ellipse from the moment the bodies touch each other and move away from each other until they touch each other again. The relative speed of the two objects is less than the escape velocity. This is an elliptic orbit with semi-minor axis = 0 and eccentricity = 1. Although the eccentricity is 1 this is not a parabolic orbit. If the coefficient of restitution of the two bodies is 1 (perfectly elastic) this orbit is periodic. If the coefficient of restitution is less than 1 (inelastic) this orbit is non-periodic.
Radial parabolic trajectory, a non-periodic orbit where the relative speed of the two objects is always equal to the escape velocity. There are two cases: the bodies move away from each other or towards each other.
Radial hyperbolic trajectory: a non-periodic orbit where the relative speed of the two objects always exceeds the escape velocity. There are two cases: the bodies move away from each other or towards each other. This is a hyperbolic orbit with semi-minor axis = 0 and eccentricity = 1. Although the eccentricity is 1 this is not a parabolic orbit.
Unlike standard orbits which are classified by their orbital eccentricity, radial orbits are classified by their specific orbital energy, the constant sum of the total kinetic and potential energy, divided by the reduced mass:
where x is the distance between the centers of the masses, v is the relative velocity, and is the standard gravitational parameter.
Another constant is given by:
For elliptic trajectories, w is positive. It is the inverse of the apoapsis distance (maximum distance).
For parabolic trajectories, w is zero.
For hyperbolic trajectories, w is negative, It is where is the velocity at infinite distance.
Official source
About this result
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 concepts (13)
Vis-viva equation
In astrodynamics, the vis-viva equation, also referred to as orbital-energy-invariance law or Burgas formula, is one of the equations that model the motion of orbiting bodies. It is the direct result of the principle of conservation of mechanical energy which applies when the only force acting on an object is its own weight which is the gravitational force determined by the product of the mass of the object and the strength of the surrounding gravitational field.
Orbit equation
In astrodynamics, an orbit equation defines the path of orbiting body around central body relative to , without specifying position as a function of time. Under standard assumptions, a body moving under the influence of a force, directed to a central body, with a magnitude inversely proportional to the square of the distance (such as gravity), has an orbit that is a conic section (i.e. circular orbit, elliptic orbit, parabolic trajectory, hyperbolic trajectory, or radial trajectory) with the central body located at one of the two foci, or the focus (Kepler's first law).
Radial trajectory
In astrodynamics and celestial mechanics a radial trajectory is a Kepler orbit with zero angular momentum. Two objects in a radial trajectory move directly towards or away from each other in a straight line. There are three types of radial trajectories (orbits). Radial elliptic trajectory: an orbit corresponding to the part of a degenerate ellipse from the moment the bodies touch each other and move away from each other until they touch each other again. The relative speed of the two objects is less than the escape velocity.
Related courses (22)
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
Related MOOCs (1)