pint.derived_quantities.a1sini

pint.derived_quantities.a1sini(mp: ~astropy.units.quantity.Quantity, mc: ~astropy.units.quantity.Quantity, pb: ~astropy.units.quantity.Quantity, i: ~astropy.units.quantity.Quantity = <Quantity 90. deg>) → Quantity[source]

Pulsar’s semi-major axis.

The full semi-major axis is given by Kepler’s third law. This is the projection (\(\\sin i\)) of just the pulsar’s orbit (\(m_c/(m_p+m_c)\) times the full semi-major axis), which is what pulsar timing measures. Can handle scalar or array inputs.

Parameters:

mp (astropy.units.Quantity) – pulsar mass
mc (astropy.units.Quantity) – companion mass
pb (astropy.units.Quantity) – Binary orbital period
i (astropy.coordinates.Angle or astropy.units.Quantity) – orbital inclination

Returns:

a1sini – Projected semi-major axis of pulsar’s orbit in pint.ls

Return type:

astropy.units.Quantity

Raises:

astropy.units.UnitsError – If the input data are not appropriate quantities
TypeError – If the input data are not quantities

Notes

Calculates

\[\begin{split}\\frac{a_p \\sin i}{c} = \\frac{m_c \\sin i}{(m_p+m_c)^{2/3}} G^{1/3}\\left(\frac{P_b}{2\\pi}\\right)^{2/3}\end{split}\]

More details in Timing Models. Also see [8]