# relativistic effects

Relativistic effects are those predicted by Einstein's special theory of relativity, which come into play when objects – such as spacecraft – travel at speeds that are a substantial fraction of the speed of light. These effects include time dilation, mass increase, and length contraction.

Time dilation would, in principle, allow astronauts to travel vast distances
well within their own lifetimes. However, relativistic mass increase would
make it more and more difficult to continue to accelerate a spacecraft.
The factor that determines the amount of mass increase and other relativistic
effects is called γ (gamma). For an object moving with speed *v* relative to an observer
considered to be at rest (for example, on Earth), γ is given by:

γ = 1/√(1 – *v*^{ 2}/*c *^{2})

where *c* is the speed of light.

The relativistic mass, *m*, of a body moving at velocity, *v*,
is then

*m* = γ*m*_{0} = *m*_{0}/√(1 – *v *^{2}/*c *^{2})

where *m*_{0} is the rest mass. Note that when *v* = 0,
this reduces to the non-relativistic result, *m* = *m*_{0}.
The impossibility of accelerating an object up to the speed of light is
shown by the fact that when *v* = *c*, *m* becomes infinite.

Similarly, the relativistic time dilation is given by:

*t* = *t*_{0} = *t*_{0}/γ = *t*_{0}√(1 – *v*^{ 2}/*c *^{2})