Relative speed

In classical mechanics , the relative speed is the difference between the speeds of two objects. These may be either in the same reference system are or denote the speed of an object in a reference system moves which no inertial system is. An example is the relative speed of two objects during impact processes or the speed of a body that is described in a rotating reference system.

Special theory of relativity

The special theory of relativity is based on the constancy of the speed of light c in all inertial systems . Among other things, this leads to the fact that

• Relative velocities outside the Newtonian limit case are not additive, and
• the speed difference between A and B is not equal to their relative speed and in particular has a larger amount. While the maximum differential speed between two objects relative to a third inertial system has the limit value 2c, this is c for the maximum relative speed compared to each system.

To change from any laboratory system from and to calculate, one must latter by means of a Lorentz transformation convert in the rest system of A. The formula is if and are collinear ${\displaystyle {\vec {v}}_{\mathrm {BA} }}$ ${\displaystyle {\vec {v}}_{\mathrm {A} }}$ ${\displaystyle {\vec {v}}_{\mathrm {B} }}$ ${\displaystyle {\vec {v}}_{\mathrm {A} }}$ ${\displaystyle {\vec {v}}_{\mathrm {B} }}$

${\displaystyle v_{\mathrm {BA} }={\frac {v_{\mathrm {B} }-v_{\mathrm {A} }}{1-{\frac {v_{\mathrm {A} }v_{\mathrm {B} }}{c^{2}}}}}}$.

Examples

Airplanes have a speed relative to the air that surrounds them. With no wind, this would correspond to the speed over the ground . Tail wind increases ground speed; Headwind lowers them.

Ships also have a speed over ground (“speed over ground”). Water currents affect this.

Many satellites have a fixed location (“ geostationary ”) when viewed from the earth ; seen from space they orbit the earth.

Individual evidence

1. ↑ Jürgen Dankert, Helga Dankert: Technical mechanics: statics, strength theory, kinematics / kinetics . 5th edition. Vieweg + Teubner, 2009, ISBN 978-3-8351-0177-7 . : ( limited preview in Google Book search)