Lorentz_factor

plasmapy.formulary.relativity.Lorentz_factor(V: Quantity)[source]

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 – If V is not a Quantity and cannot be converted into a 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

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

The Lorentz factor is approximately one for sub-relativistic velocities, and \(γ → ∞\) as the velocity approaches the speed of light.

Examples

>>> import astropy.units as u
>>> velocity = 1.4e8 * u.m / u.s
>>> Lorentz_factor(velocity)
 np.float64(1.1308856039...)
>>> Lorentz_factor(299792458 * u.m / u.s)
inf