Vondrak API¶

vondrak.epj(dj)[source]¶

Julian Date to Julian Epoch

vondrak.ltp_PBMAT(jepoch)[source]¶

Long-term precession matrix, including GCRS frame bias.

Given Julian epoch (TT)

Return precession-bias matrix, J2000.0 to date

ltp_PBMAT generates the 3 × 3 rotation matrix P × B, where B is the “frame bias matrix” that expresses the relative orientation of the GCRS and mean J2000.0 reference systems. A simple first-order implementation of the frame bias is used, the departure from rigor being well under 1 μas.

The matrix is in the sense P_date = RPB x P_J2000, where P_J2000 is a vector in the Geocentric Celestial Reference System, and P_date is the vector with respect to the Celestial Intermediate Reference System at that date but with nutation neglected.

A first order bias formulation is used, of sub-microarcsecond accuracy compared with a full 3D rotation.

vondrak.ltp_PECL(jepoch)[source]¶

Long-term precession of the ecliptic

Given Julian epoch (TT).

Return ecliptic pole unit vector.

ltp_PECL generates the unit vector for the pole of the ecliptic, using the series for Pₐ, Qₐ. The vector is with respect to the J2000.0 mean equator and equinox.

vondrak.ltp_PEQU(jepoch)[source]¶

Long-term precession of the equator

Given Julian epoch (TT)

Return equator pole unit vector

ltp_PEQU generates the unit vector for the pole of the equator, using the series for Xₐ, Yₐ. The vector is with respect to the J2000.0 mean equator and equinox.

vondrak.ltp_PMAT(jepoch)[source]¶

Long-term precession matrix

Given Julian epoch (TT)

Return precession matrix, J2000.0 to date

ltp_PMAT generates the 3 × 3 rotation matrix P, constructed using Fabri parameterization (i.e. directly from the unit vectors for the ecliptic and equator poles). The resulting matrix transforms vectors with respect to the mean equator and equinox of epoch 2000.0 into mean place of date.

The matrix is in the sense P_date = RP x P_J2000, where P_J2000 is a vector with respect to the J2000.0 mean equator and equinox and P_date is the same vector with respect to the equator and equinox of epoch EPJ.

vondrak.pdp(a, b)[source]¶

p-vector inner (=scalar=dot) product.

Given two p-vectors (a and b)

Return a * b

vondrak.pn(p)[source]¶

Convert a p-vector into modulus and unit vector.

Given p-vector (p)

Return modulus (r), and unit vector (u)

vondrak.pxp(a, b)[source]¶

p-vector outer (=vector=cross) product.

Given two p-vectors (a and b) Return a x b

vondrak.ra_dec(v)[source]¶

Convert a cartesian position matrix to RA and Dec