fast_kepler

A c implementation for solving kepler's equation in c. Made for astroemperor, put in a different library for public use.

Dependencies

This code makes use of:

• numpy
• cython

Installation

In the console type in your work folder

pip install fast_kepler

Usage

Solution to Kepler's equation. Given mean anomaly, M, and eccentricity, e, solve for E, the eccentric anomaly, which must satisfy:

$$E - e sin(E) - M = 0$$

For a given eccentricity, and an M array, we use:

import fast_kepler
M = np.sort(np.random.uniform(0, 100, size=100))
ecc = 0.11
E = fast_kepler.kepler_array(M, ecc)

More on usage

We can calculate RVs:

# time array of our observations
x = np.sort(np.random.uniform(0, 100, size=100))
# keplerian parameters
period = 4.1  # in days
semi_amplitude = 55  # in m/s
M0 = np.pi/3  # in rad
ecc = 0.23  # from 0 to 1
om = 3*np.pi/5  # in rad

theta = [period, semi_amplitude, M0, ecc, om]

def calc_RV(theta):
  per, K, M0, ecc, om = theta

  freq = 2. * np.pi / per
  M = freq * x + M0
  E = fast_kepler.kepler_array(M, ecc)

  f = np.arctan(((1. + ecc)/(1. - ecc)) ** 0.5 * np.tan(E / 2.)) * 2.
  
  return K * (np.cos(f + om) + ecc * np.cos(om))

# or simply:

def get_RV(theta):
  per, K, M0, ecc, om = theta
  return fast_kepler.calc_rv0(x, per, K, M0, ecc, om)

Additional Options

You can also use a different parameterization to retrieve RVs, with time of periastron passage $T_p$ instead of the mean anomaly $M_0$:

fast_kepler.calc_rv1(x, per, A, tp, ecc, w)