The gamma factor

For relative velocities which are small compared to the speed of light, the relativistic gamma factor y^ 1. The Lorentz transformation becomes the Galilean transformation and relativistic effects become negligible.

In practice, astronauts travelling in satellites in orbit around the earth or space vehicles to the moon never reach speeds even remotely close to relativistic speeds. Concorde was a supersonic aircraft, by far the fastest means of travel for fare-paying passengers, with the capability to travel at more than twice the speed of sound. The gamma factor, however, played no role in the lives of those on board, since the speed of sound in air («300 ms-1) is about a million times slower than the speed of light, and the term v 2/c 2 = 10-12 .

On the other hand, fundamental particles in cosmic radiation and in accelerators travel at speeds approaching the speed of light (to within a fraction of 1%), and relativis

tic effects such as time dilation become critically important (see table below).

Table 15.1 The relativistic gamma factor.

Orbital velocity

Speed of a

Speed of sound

of earth about the

proton at an

in air = 300 ms-1

sun = 30 kms-1

accelerator

v = 10-6 c

= 10-4 c

0.5 c

0.9 c 0.99 c

= 0.999 c

Y 1.0000000000005

1.000000005

1.15

2.3 7.1

22.3

1

g -

2

v

\

1 - -2

V

c

0 0

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