Lorentz_factor

plasmapy.formulary.Lorentz_factor(V: Unit("m / s"))

Return the Lorentz factor.

Parameters:

V (Quantity) – The velocity in units convertible to meters per second.

Returns:

gamma – The Lorentz factor associated with the inputted velocities.

Return type:

float or ndarray

Raises:

• TypeError – The V is not a Quantity and cannot be converted into a ~astropy.units.Quantity.
• UnitConversionError – If the V is not in appropriate units.
• ValueError – If the magnitude of V is faster than the speed of light.

Warns:

~astropy.units.UnitsWarning – If units are not provided, SI units are assumed.

Notes

The Lorentz factor is a dimensionless number given by

\[\gamma = \frac{1}{\sqrt{1-\frac{V^2}{c^2}}}\]

The Lorentz factor is approximately one for sub-relativistic velocities, and goes to infinity as the velocity approaches the speed of light.

Examples

>>> from astropy import units as u
>>> velocity = 1.4e8 * u.m / u.s
>>> Lorentz_factor(velocity)
1.130885603948959
>>> Lorentz_factor(299792458*u.m/u.s)
inf