The Visible and Illuminated

If you want to calculate light curves and kernel properties, you have to know how your planets are lit up first. This core script handles the details, tracking where the observer and star are over the planet’s surface.

The DirectImaging_Planet class uses degrees for most angles while this backend computing happens in radians. The method SubOS_TimeDeg() takes care of the conversions.

exoplanetsubspots.sub_observerstellar(times, worb, wrot, inc, obl, sol, longzero=0)

Calculates an exoplanet’s sub-observer and -stellar locations over time.

Calculates time-dependent, trigonometric values of an exoplanet’s sub- observer and sub-stellar locations when on a circular orbit. Planet coordinates are colatitude (theta) and longitude (phi). Orbital phase is zero when planet is opposite star from observer (superior conjunction) and increases CCW when system is viewed above star’s North pole. See Appendix A of Schwartz et al. (2016).

Args:
times (1d array, int, or float):
Discrete time values in any unit, with total number n_time. At t=0 planet is at superior conjunction.
worb (int or float):
Orbital angular frequency in radians per unit time. Positive values are prograde orbits (CCW), negative are retrograde (CW).
wrot (int or float):
Rotational angular frequency in radians per unit time. For prograde orbits, positive values are prograde rotation, negative are retrograde (vice versa for retrograde orbits).
inc (int or float):
Inclination of orbital plane to the observer, in radians. Zero is face-on, pi/2 is edge-on.
obl (int or float):
Obliquity relative to the worb vector, in radians. This is the tilt of the planet’s spin axis. Zero is North pole up, pi/2 is maximal tilt, pi is North pole down.
sol (int or float):
The orbital phase of Northern Summer solstice, in radians. If the wrot vector is projected into the orbital plane, then this phase is where that projection points at the star.
longzero (int or float):
Longitude of the sub-observer point when t=0, in radians. Default is zero.
Returns:
trigvals (ndarray):

Array of trigonometric values with shape (8, n_time). First dimension is organized as:

  • sin theta_obs
  • cos theta_obs
  • sin phi_obs
  • cos phi_obs
  • sin theta_st
  • cos theta_st
  • sin phi_st
  • cos phi_st