heyoka.model.vsop2013_elliptic

heyoka.model.vsop2013_elliptic#

heyoka.model.vsop2013_elliptic(pl_idx: int, var_idx: int = 0, time_expr: expression = heyoka.time, thresh: float = 1e-9) → expression#

Get the VSOP2013 formulae (elliptic orbital elements).

Added in version 0.15.0.

Note

A tutorial explaining the use of this function is available.

This function will return an expression representing the time evolution of the heliocentric orbital element of a planet according to the VSOP2013 analytical model.

pl_idx selects the planet and it must be one of:

  • 1: Mercury,

  • 2: Venus,

  • 3: Earth-Moon barycentre,

  • 4: Mars,

  • 5: Jupiter,

  • 6: Saturn,

  • 7: Uranus,

  • 8: Neptune,

  • 9: Pluto.

var_idx selects the heliocentric orbital element and it must be one of:

  • 1: the semi-major axis \(a\),

  • 2: the mean longitude \(\lambda\),

  • 3: \(k=e\cos\varpi\), where where \(e\) is the eccentricity and \(\varpi=\Omega+\omega\) is the longitude of the perihelion,

  • 4: \(h=e\sin\varpi\),

  • 5: \(q=\sin\frac{i}{2}\cos\Omega\), where \(i\) is the inclination and \(\Omega\) is the longitude of the ascending node,

  • 6: \(p=\sin\frac{i}{2}\sin\Omega\).

\(a\) is returned in AU and \(\lambda\) in radians, while the other orbital elements are non-dimensional. The orbital elements are referred to the inertial frame defined by the dynamical equinox and ecliptic J2000. Note that this set of orbital elements is similar (but not exactly equivalent) to the equinoctial orbital elements.

time_expr is the expression to be used as a time coordinate and it must represent the number of Julian millenia elapsed since the Julian date 2451545.0 in the TDB time scale. A Julian millenium consists of exactly 365250 Julian days.

thresh is the theory truncation threshold: larger values produce a shorter but less precise model. A value of zero will return the full untruncated model. thresh must be a finite, non-negative value.

Parameters:

  • pl_idx – the input planet.

  • var_idx – the input orbital element.

  • time_expr – the input time expression.

  • thresh – the theory truncation threshold.

Returns:

an expression for the time evolution of the orbital element of a planet according to the VSOP2013 model.

Raises:

ValueError – in case of invalid input arguments.

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