dynamics

dynamics#

This is the API for the dynamics module.

class obscurae.dynamics.Dynamics#

Orbital dynamics.

Class to calculate the orbital dynamics of the planet, i.e., the position of the planet on the stellar disk.

static keplersEq(mean_anomaly, ecc, tolerance=1.48e-08, iter_max=300, sci=True)#

Solves Kepler’s equation.

Function that solves Kepler’s equation:

\[M = E - \sin (E),\]

where \(M\) is the mean anomaly and \(E\) the eccentric anomaly.

This is done following the Newton-Raphson method as described in Murray and Correia (2010).

Parameters:

  • mean_anomaly (array) – The mean anomaly.

  • ecc (float) – Eccentricity.

  • tolerance (float, optional) – The tolerance for convergence. Defaults to 1.e-5.

  • iter_max (int, optional) – Maximum number of iterations. Defaults to 300.

  • sci (bool, optional) – Use the scipy implementation of the Newton-Raphson method. Defaults to True.

Returns:

The new eccentric anomaly.

Return type:

array

static trueAnomaly(time, Tw, ecc, per)#

Function that returns the true anomaly.

The approach follows Murray and Correia (2010).

Parameters:

  • time (array) – Times of observations.

  • Tw (float) – Time of periastron.

  • ecc (float) – Eccentricity.

  • per (float) – Orbital period.

  • ww (float) – Argument of periastron in radians.

Returns:

cosine, sine of the true anomaly.

Return type:

(array, array)

static xyPos(cos_f, sin_f, ecc, ww, ar, inc, lam)#

Position of planet on stellar disk.

Function to calculate the position on the stellar disk. Stellar disk goes from 0 to 1 in x and y.

Parameters:

  • cos_f (array) – cosine of the true anomaly

  • sin_f (array) – sine of the true anomaly

  • ecc (float) – Eccentricity.

  • ww (float) – Argument of periastron in radians.

  • ar (float) – Semi-major axis in stellar radii.

  • inc (float) – Inclination in radians.

  • lam (float) – Projected obliquity in radians.

Returns:

x,y position of planet on stellar disk.

Return type:

(array, array)

class obscurae.dynamics.SpotOn#

Spot position.

Class to calculate the position of a spot on the stellar disk.

static spotPos(time, theta, phi, per, t_ref=0.0)#

Position of spot on stellar surface.

Function to calculate the position of a spot at a given (\(\phi\),:math:` heta`) on the stellar surface, where \(\phi\) is the colatitude (\(0^\circ\) at north pole and \(180^\circ\) at the south pole) and :math:` heta` the longitude.

Parameters:

  • time (array) – Times of observations in days.

  • phi (float) – Latitude of spot in radians.

  • theta (float) – Longitude of spot in radians.

  • per (float) – Period of spot crossing/rotation period in days.

  • t_ref (float, optional) – Reference time in days. Defaults to 0.0.

Returns:

x, y position of spot on stellar surface.

Return type:

(array, array)

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