Relative velocity

The relative velocity is the velocity of an object B in the rest frame of another object A. If it is constant, applies

The latter is the velocity of A in the rest frame of B.

Classical Mechanics

In the Newtonian limit case in which approximate the Galilean transformations

Applicable, the relative velocity is identical to the speed difference, ie the vector difference of the velocities relative to any observer considered to be at rest, the laboratory system, ie

In general this is not true, especially not in the light developed by Albert Einstein special theory of relativity.

Special Theory of Relativity

The special theory of relativity is, however, of the constancy of light velocity c in all reference systems. This leads, among other things, that

• Velocities outside the Newtonian limiting case are not additive, and
• The difference in speed between A and B is not equal to its relative speed, and in particular has a smaller amount. While the maximum speed difference between the two objects is relative to a third reference system 2c, the maximum relative velocity with respect to a stationary coordinate system considered as equal to c.

To get out of any laboratory system and to calculate, you have to convert the latter by means of a Lorentz transformation to the rest frame of A. Are collinear and so the formula is

Examples

Aircraft have a speed relative to the air that surrounds them. In calm weather this would correspond to the speed over the ground. Tailwind increases the speed over the ground; Headwind it lowers.

Ships also have a ground speed ( " speed over ground "). Water currents influence them.

Many satellites have a seen from the Earth fixed location ( " geostationary "); seen from space orbit around the earth.

• Classical Mechanics
• Special Theory of Relativity