# Trajectory (physics)

The orbits of the planets and comets around the sun are approximately flat ellipses. This movement is more or less disturbed by other planets. The picture shows an orbit (red) which has a large angle of inclination i compared to the plane of the earth's orbit (ecliptic, green) .

In physics , a trajectory , also a trajectory , a path or a path (sometimes after the English: orbit) is the course of the space curve along which a body or a point, for example the center of gravity of a rigid body , moves. A macroscopic body, such as a bullet or a ball, is also referred to as the trajectory . In a broader sense, the trajectory is a curve in the n-dimensional phase space .

For bodies that are subject to constraints, the shape of the trajectory is described mathematically by kinematics ; z. B. describes a pendulum an arc. For bodies that are only exposed to external forces, the trajectories result as solutions to systems of differential equations . The investigation of the trajectory as the time-dependent course of the location in a reference system is the subject of kinetics .

## Examples

Different trajectories for a crooked throw without any friction (black), with Stokes friction (blue) or with Newton friction (green)
• The trajectory of a ground level downed cannonball or a ballistic missile called ballistic curve .
• The trajectory of a natural or artificial celestial body in the gravitational field of a central body or in free space runs on a Kepler orbit . In the case of closed orbits in the solar system or in the galaxy , one speaks more of an orbit . According to the conservation of angular momentum , the path of a body in every central field is a plane curve.
• In a homogeneous magnetic field , charged particles describe spiral paths (helical lines) around the magnetic field lines.
• Due to the law of inertia , the trajectory of a body runs straight when there is no force acting on it or there is an equilibrium of forces .
• In road construction, the transition between a straight line and a circle is made in the form of a clothoid .
• In racing, the ideal line is the trajectory of a fixed point on the vehicle on which a section of the route can be driven at the greatest speed.
• The Bohr model describes the trajectory of the electrons around the nucleus as a closed circular paths .
• The meteorology knows the trajectory of a (hypothetical) air particle. A distinction is made between backward and forward trajectories. The former indicate where the air came from, the latter where it is going. Of the trajectory which is streamlined to distinguish; only in a steady flow do trajectories and streamlines coincide.
• In object tracking , a trajectory is represented as the movement path of an object through the temporal sequence of coordinates during the runtime.
• In technical chemistry , trajectories are used to describe the dynamic behavior of a chemical reaction. For this purpose, representations in the so-called state or phase level are used, in which the instantaneous concentration is plotted against the temperature . The trajectories then show the simultaneous change in concentration and temperature during a transition process. Time runs along the trajectory. The graphs can e.g. B. (depending on the starting conditions and of course other variables) have a spiral shape.${\ displaystyle \! \ c (t)}$${\ displaystyle \! \ T (t)}$
• Predator-prey relationships: Lotka-Volterra equations

## Practical determination

In the case of visible objects, the trajectory can usually be determined using photographic means, e.g. B. with photogrammetry .

The trajectory of an atomic or subatomic particle is only available as an illustrative aid, since these particles must be described by quantum mechanics . Such particle trajectories can approximately be made visible in bubble or cloud chambers or determined indirectly with hodoscopes or wire chambers .

## Individual evidence

1. Gerthsen: Physics . 18th edition. Springer, 1995, ISBN 978-3-662-07467-1 , pp. 968 ( limited preview in Google Book search).
2. Manfred Baerns , Arno Behr , Axel Brehm, Jürgen Gmehling , Hanns Hofmann , Ulfert Onken: Technische Chemie . Wiley-VCH, 2006, ISBN 3-527-31000-2 , pp. 158 .