# Import necessary modules
# ------------------------------------------------------------------------------------------------ #
import numpy as np
# ------------------------------------------------------------------------------------------------ #
# These are helper functions that the user may choose to use for easy calculations.
# They are not called by the remainder of the code.
[docs]
def r(a, e, phi):
"""Compute radius r given semi-major axis a, eccentricity e, and true anomaly phi."""
return a * (1 - e**2) / (1 + e * np.cos(phi))
[docs]
def periapsis(a, e):
"""Compute periapsis distance, r_p."""
return a * (1 - e)
[docs]
def apoapsis(a, e):
"""Compute apoapsis distance, r_a."""
return a * (1 + e)
[docs]
def kappa(r, a):
"""Compute kappa."""
return np.abs(1 - r/a)