Kepler#

This module contains a Kepler solver, Keplerian signal calculator, and various other helper functions.

eurydice.kepler.calc_keplerian_signal(times, t_transit, period, ecc, omega, K)#

Compute the radial velocity signal of a transiting exoplanet

Parameters:
  • times (np.array) – time measurements

  • t_transit (float) – time of transit

  • period (float) – period of orbit [days]

  • ecc (float) – eccentricity

  • omega (float) – longitude of periastron (radians)

  • K (float) – Keplarian semi-amplitude

Returns:

array of radial velocity signals

Return type:

(np.array)

eurydice.kepler.calc_mean_anomaly(times, period, t_periastron)#

Compute the mean anomaly at given times during an orbit

Parameters:
  • times (np.array) – times of measurement

  • period (float) – period of orbit [days]

  • t_periastron (float) – time of periastron passage

Returns:

array of mean anomalies

Return type:

(np.array)

eurydice.kepler.calc_true_anomaly(E_anom, ecc)#

Compute the true anomaly at certain points during an orbit

Parameters:
  • E_anom (np.array) – array of eccentric anomalies

  • ecc (float) – eccentricity

Returns:

array of true anomalies

Return type:

(np.array)

eurydice.kepler.kepler_solver(M_anom, ecc, tolerance=1e-07)#

Solves Kepler’s equation using the Newton Raphson method

Parameters:
  • M_anom (np.array) – array of mean anomalies

  • ecc (np.array) – array of eccentricities

  • tolerance (float, optional) – absolute tolerance of iterative computatiom (‘exit condition’). Defaults to 1e-7.

Returns:

array of eccentric anomalies

Return type:

(np.array)

eurydice.kepler.transit_to_periastron(t_transit, period, ecc, omega)#

Convert Time of Transit to Time of Periastron Passage

Parameters:
  • t_transit (float) – time of transit

  • period (float) – period of orbit [days]

  • ecc (float) – eccentricity

  • omega (float) – longitude of periastron (radians)

Returns:

time of periastron passage

Return type:

(float)