doppler_relativistic¶

astropy.units.doppler_relativistic(rest)[source]

Return the equivalency pairs for the relativistic convention for velocity.

The full relativistic convention for the relation between velocity and frequency is:

$$V = c \frac{f_0^2 - f^2}{f_0^2 + f^2} ; f(V) = f_0 \frac{\left(1 - (V/c)^2\right)^{1/2}}{(1+V/c)}$$

Parameters: rest : Quantity Any quantity supported by the standard spectral equivalencies (wavelength, energy, frequency, wave number).

References

NRAO site defining the conventions

Examples

>>> import astropy.units as u
>>> CO_restfreq = 115.27120*u.GHz  # rest frequency of 12 CO 1-0 in GHz
>>> relativistic_CO_equiv = u.doppler_relativistic(CO_restfreq)
>>> measured_freq = 115.2832*u.GHz
>>> relativistic_velocity = measured_freq.to(u.km/u.s, equivalencies=relativistic_CO_equiv)
>>> relativistic_velocity  # doctest: +FLOAT_CMP
<Quantity -31.207467619351537 km / s>
>>> measured_velocity = 1250 * u.km/u.s
>>> relativistic_frequency = measured_velocity.to(u.GHz, equivalencies=relativistic_CO_equiv)
>>> relativistic_frequency  # doctest: +FLOAT_CMP
<Quantity 114.79156866993588 GHz>
>>> relativistic_wavelength = measured_velocity.to(u.mm, equivalencies=relativistic_CO_equiv)
>>> relativistic_wavelength  # doctest: +FLOAT_CMP
<Quantity 2.6116243681798923 mm>